\r\n\t \r\n\tComputer graphics are not entirely an original topic, because it defines and solves problems using some already established techniques such as geometry, algebra, optics, and psychology. The geometry provides a framework for describing 2D and 3D space, while the algebraic methods are used for defining and evaluating equality related to the specific space. The science of optics enables the application of the model for the description of the behavior of light, while psychology provides models for visualization and color perception. \r\n\t \r\n\t3D computer graphics (or 3D graphics, three-dimensional computer graphics, three-dimensional graphics) is a term describing the different methods of creating and displaying three-dimensional objects by using computer graphics. \r\n\tThe first types of graphic interpretations were put in the plane (two-dimensional 2D). Requirements for a universal interpretation led to a three-dimensional (3D) interpretation content. From these creations have arisen applied mathematics and information disciplines of graphic interpretation of content - computer graphics. It relies on the principles of Mathematics, Descriptive Geometry, Computer Science and Applied Electronics. \r\n\t \r\n\t3D computer graphics or three-dimensional computer graphics use a three-dimensional representation of geometric data (often in terms of the Cartesian coordinate system) that is stored on a computer for the purpose of doing the calculation and creating 2D images. The images that are made can be stored for later use (probably as animation) or can be displayed in real-time. \r\n\t \r\n\tObjects within the 3D computer graphics are often called 3D models. Unlike rendered (generated) images, data that are ""tied"" to the model are inside graphic files. The 3D model is a mathematical representation of a random three-dimensional object. The model can be displayed visually as a two-dimensional image through a process called 3D rendering or can be used in non-graphical computer simulations and calculations. With 3D printing, models can be presented in real physical form. \r\n\t \r\n\tComputer graphics have remained one of the most interesting areas of modern technology, and it is the area that progresses the fastest. It has become an integral part of both application software, and computer systems in general. Computer graphics is routinely applied in the design of many products, simulators for training, production of music videos and television commercials, in movies, in data analysis, in scientific studies, in medical procedures, and in many other fields.
",isbn:null,printIsbn:"979-953-307-X-X",pdfIsbn:null,doi:null,price:0,priceEur:0,priceUsd:0,slug:null,numberOfPages:0,isOpenForSubmission:!1,hash:"de29c8802680e89528bdbecf055dffd1",bookSignature:"Dr. Dragan Mladen Cvetković",publishedDate:null,coverURL:"https://cdn.intechopen.com/books/images_new/8770.jpg",keywords:"Vector Graphics, Graphic design, 3D model, Computer-Aided Design (CAD), Computer-Aided Architectural Design (CAAD), 3D Rendering, Virtual engineering, 3D Mapping, 3D projection on 2D planes, Video games, 3D Printing, 3D Computer Graphics in Science",numberOfDownloads:null,numberOfWosCitations:0,numberOfCrossrefCitations:0,numberOfDimensionsCitations:0,numberOfTotalCitations:0,isAvailableForWebshopOrdering:!0,dateEndFirstStepPublish:"October 28th 2019",dateEndSecondStepPublish:"March 6th 2020",dateEndThirdStepPublish:"May 5th 2020",dateEndFourthStepPublish:"July 24th 2020",dateEndFifthStepPublish:"September 22nd 2020",remainingDaysToSecondStep:"a year",secondStepPassed:!0,currentStepOfPublishingProcess:5,editedByType:null,kuFlag:!1,biosketch:null,coeditorOneBiosketch:null,coeditorTwoBiosketch:null,coeditorThreeBiosketch:null,coeditorFourBiosketch:null,coeditorFiveBiosketch:null,editors:[{id:"101330",title:"Dr.",name:"Dragan",middleName:"Mladen",surname:"Cvetković",slug:"dragan-cvetkovic",fullName:"Dragan Cvetković",profilePictureURL:"https://mts.intechopen.com/storage/users/101330/images/system/101330.jpg",biography:"Dragan Cvetković graduated in Aeronautics from the Faculty of Mechanical Engineering, University of Belgrade, in 1988. He defended his doctoral dissertation in December 1997.\n\nHe has published 64 books, scripts and practicums about computers and computer programs, aviation weapons and flight mechanics. He has also published a large number of scientific papers, both nationally and internationally.\n\nIn 2014, he became a full professor in the field of Informatics and Computing at Singidunum University, Belgrade. Previously he had served as an assistant professor. 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1. Introduction
The incidence varies from 0.8 to 4.4% for inguinal hernia in children less than 18 years [1]. A unilateral hernia is approximately 85% of children with an inguinal hernia. The incidence of incarceration ranges from 6 to 18% for the untreated hernias in infants and young children, but it is about 30% in infancy [2]. A surgical intervention for inguinal hernia is one of the most common operations performed in children [3]. The individualized treatment program was established for pediatric inguinal hernia in the authors’ department and provided a relatively reasonable surgical treatment. This chapter was mainly to describe the individualized treatment program applied to pediatric inguinal hernia.
2. Etiology
Indirect inguinal hernias in children are basically caused by embryologic development, which is mainly composed of patency of processus vaginalis (Figure 1). At the early stage of gestation, the testes begin to descend from retroperitoneum and remain at the level of the internal inguinal rings as the kidney ascends into its usual position. The final descent of testes into the scrotum through canalis inguinalis occurs between gestation weeks 28 and 36 [4], combining peritoneum, transversalis fascia, and abdominal wall muscles. The testes descent is “guided” by the gubernaculums. Descending peritoneum ultimately forms the processes vaginalis, and the distal portion of the processus vaginalis wrapped around the testes becomes the tunica vaginalis. In the normal development, the processus vaginalis closes between 36 and 40 weeks of gestation or even shortly after birth [5]. The rate of patency is inversely proportional to the age of children, approximately 80% close to 2 years of age [4]. The left testis descends before the right one and the closure of the patent processus vaginalis on the left also precedes closure on the right, therefore, indirect inguinal hernia occurs more on the right side.
Though the embryology has been widely described, the cell‐molecular mechanism is still unclear. Inguinal hernias most probably are inherited [6]. Zhang et al.\'s [7] team have found that the functional sequence variants of some genes may be a risk factor for indirect inguinal hernia, such as gene TBX1, gene TBX3, gene SIRT1, and gene GATA6. These variants may affect the differentiation and proliferation of human skeletal muscles and fibroblasts [7–10].
3. Clinical manifestation
A reducible bulge or mass in the inguinal region or unilateral or bilateral enlargement of the scrotum (Figure 2a and b) is the main diagnostic finding in most groin hernias. These symptoms can occur when abdominal pressure increases, such as while standing, coughing, crying, constipation, and playing, and disappears when patients lie down or fall asleep. Children less than two years of age will express themselves only by crying and screaming, so if children continue crying without obvious reasons, groin hernia should be considered.
Figure 2.
Pediatric hernias. (a) Right inguinal hernia, (b) bilateral inguinal hernia, (c) incarcerated left inguinal hernia.
There may be associated pain or vague discomfort in the region. Groin hernias are usually not extremely painful unless incarceration (Figure 2c) or strangulation has occurred [11]. The bowels inside the hernia sac being incarcerated or strangulated may cause intestinal obstruction, and the testis may turn red gradually. At this time, the spermatic cord is oppressed and the testicle may be diagnosed with ischemic necrosis. As the age increases, the size of hernia sac will gradually increase. The falling bowels pull down the mesentery and cause not only abdominal pain, nausea, and other gastrointestinal symptoms but also walking inconvenience. In addition, the spermatic cord being pressed continuously by the hernia sac will cause spermatic vessel reflux disorder and blood supply reduction as well as spermophlebectasia and testicular atrophy.
4. Physical and accessory examination
The inguinal region is examined with the child in the standing position or with the infant held in the vertical position by parents. The examiner visually inspects and palpates the inguinal region, looking for asymmetry, bulge, or a mass [11]. Having the patient cough or cry can facilitate in the identification of a hernia. The examiner puts a fingertip into the external inguinal ring by invaginating the scrotum to detect a small inguinal hernia. If a bulge moves from lateral to medial in the inguinal canal, an indirect hernia is suspected. A bulge progressing from the deep to superficial through the inguinal floor suggests a direct hernia [11].
Ultrasound is very useful in the diagnosis, which can avoid the adverse effects of radiation in CT on children’s development. There is a high degree of sensitivity and specificity for ultrasound in the detection of occult hernias [11]. An ultrasound can determine the hernia sac, the defect, the hernia contents (the bowel, the omentum, or the bladder), and complications such as hydrocele, guiding the surgical treatment.
5. Diagnosis and differential diagnosis
The diagnosis of inguinal hernia in children is mainly suggested by the history of the bulges or masses in groin area, usually found in children crying or regular physical examination. For slightly older children, blowing bubbles, tickling them to make them laugh, or having them blow up balloons (e.g., examination gloves) will increase intra‐abdominal pressure and the hernias may appear. When they are in supine position, the bulges or mass may reduce by itself or by hands, which is called reduction.
For typical cases, it is generally not difficult to make the diagnosis, while for the unclear inguinal abnormalities, doctors can combine with the results of ultrasonic testing or further examination just like CT or MRI if it is necessary. Mainly depending on the different degree and level of processus vaginalis obliteration failure, these methods may help to find the abnormality of inguinal canal, including various types of hydrocele (communicating, non‐communicating, funicular), spermatic cord cyst in males, hydrocele of the canal of Nuck in females, cyst of the round ligament of uterus, and indirect inguinal hernias [12]. Communicating hydrocele results from the patent processus vaginalis throughout its length. The fluid collection communicates with the peritoneal cavity and the scrotum. Non‐communicating hydrocele happens at the time processus vaginalis obliterates and some fluid accumulates between the cavities of the tunica vaginalis enclosing the testis. Spermatic cord hydrocele results from an abnormal closure of the processus vaginalis, leading to fluid accumulation alongside the spermatic cord, which is separated from and located above the testis. A transillumination test, an ordinary means to distinguish the hydrocele and hernia, is widely used in clinical works. The scrotum is exposed in a dark room with a flashlight under it. If it contains fluid, light is allowed to go through. When it is opaque, a hernia will be detected. Hydrocele and cyst of the canal of Nuck are caused by the incomplete obliteration of the processus vaginalis in girls, which is unusual. The hernia of the canal of Nuck is also an uncommon condition in females, which is homogenous to the indirect inguinal hernia in males. The distinction of these abnormalities, facilitating diagnosis for early surgical intervention, needs to be paid much attention in specific conditions.
6. Treatment
6.1. Indications for surgery
The processus vaginalis is a finger‐like projection of peritoneum that typically closes between the 36th and 40th week of gestation. It is thought that 40% closes in the first few months after birth and an additional 20% by the age of 2 [4]. Congenital inguinal hernia is a common malformation in children that requires operative treatment [13]. Surgery is indicated for all pediatric patients in whom the diagnosis of inguinal hernia has been made. The hernia in infants younger than 6 months should be operated as soon as possible due to high incidence of incarceration. Surgical treatment can be booked selectively for older children with few symptoms [14, 15]. Surgical procedure is provided for inguinal hernia to avoid the complications such as incarceration and obstruction, potentially resulting in ischemia/necrosis of the hernia contents and surrounding cord structures. In females, it is also possible that torsion/ischemia of the ovary can happen [16, 17].
Repair of inguinal hernias is one of the most common pediatric surgical procedures. Indirect inguinal hernias are congenital in origin due to a patent processus vaginalis. In recent years, with the development of materials technology and minimally invasive surgical techniques, surgical treatments of inguinal hernia in children were transitioned from the traditional open surgery to the laparoscopic high ligation of hernia sac and the use of biological patch in open surgery. The different techniques have their own indications and advantages. The authors carried out the individualized treatment of inguinal hernia in children, receiving significant clinical results.
The high hernia sac ligation is the primary treatment for younger patients from 1 to 13 years old. These patients had shorter medical history, smaller diameter of the hernia ring, and less serious defects of the transverse fascia or the inguinal canal posterior wall, therefore, the traditional high ligation of hernia sac can correct the condition. In the last 10 years, the authors have performed laparoscopic hernia sac ligation for the patients younger than 13 years old and have obtained satisfactory results.
According to the results of our clinical study [18], the authors found that the simple high hernia sac ligation is inadequate for adolescents (13 to 18 years old) with a longer medical history, larger diameter of internal inguinal ring, and more serious transverse fascia defects. The inguinal hernia treated with simple high hernia sac ligation in adolescents is prone to postoperative recurrence; therefore, the procedure, similar to the treatment of adult inguinal hernia, should be taken, for example, repairing the transverse fascia and strengthening of the posterior wall of the inguinal canal.
The therapy for pediatric inguinal hernia was carried out by the individualized treatment program in authors’ department, which can provide a relatively reasonable surgical treatment. Individualized treatment programs consisted of three kinds of surgical procedures as described below.
6.2. Modified open pediatric inguinal hernia repair
The etiology of pediatric inguinal hernia is a patent processus vaginalis; therefore, inguinal hernias were generally repaired with open simple high ligation of the hernia sac for the patient younger than 13 years. The traditional open technique with high ligation of hernia is the classic surgical treatment method for pediatric inguinal hernia. An inguinal approach is taken for the traditional open technique of inguinal hernia repair. A 3–4‐cm‐long inguinal incision is made on the same side as the inguinal hernia that is to be corrected. The procedure includes the slit of external oblique aponeurosis, the isolation of the hernia sac from the surrounding cord structures which consist of the cremasteric muscle, vas deferens, and the testicular vessel surrounding the ligament. A high ligature is located on the proximal separated sac. The distal sac is divided and resected. The external inguinal ring is reconstructed. Although the traditional open inguinal approach is effective for hernia repair in the pediatric population [19–21], it carries numerous risks, including immediate and long‐term postoperative complications [22–24]. Postoperative pain, surgical trauma, local swelling usually last 3–5 days for children. In addition, visualization of possible contralateral defects is limited and there remains a risk of hernia recurrence [25].
For the patients with a small hernia sac, the modified open operation of inguinal hernia repair with a small incision in the external inguinal ring could be performed to correct this pathological condition without slitting of the external oblique aponeurosis and ligating highly the hernia sac. This modified approach can maintain the normal anatomy of the inguinal canal to reduce complications. The modified open operation is widely used in Chinese primary hospitals at present, where it is relatively easy to do operations with low recurrence rate but has not been done for a long time in the authors’ department.
6.2.1. Operative steps for the modified open pediatric inguinal hernia repair
A small skin incision of about 1–1.5 cm is made along the skin crease, which is located on the surface projection of external inguinal ring supra pubic tubercle. Incision is carried down through the dermis to expose the subcutaneous fat, Camper’s fascia. Using sharp and blunt dissection, Scarpa’s fascia is identified, grasped, and incised in the direction of the external inguinal ring. A gentle retraction is needed to maintain excellent exposure. Cremaster muscle is dissected to expose spermatic cord and the hernia sac within the external inguinal ring. The external inguinal ring is not opened. The hernia sac is elevated off the inguinal floor and isolated from the surrounding tissue with a blunt dissection in the internal inguinal ring. The hernia sac is opened (Figure 3a). If the hernia sac is small, it is directly ligated at its neck where extraperitoneal fat can be seen. If it is large, it is cut to about 2 cm, away from its neck, and then sutured and ligated at its neck (Figure 3b). The internal inguinal ring is sutured for 1–2 stitches for repair, if it is large. Subcutaneous tissue and skin are subsequently closed after hemostasis is done carefully.
Figure 3.
(a) The hernia sac was opened and (b) the hernia sac was sutured and ligated at its neck.
6.3. Laparoscopy high hernia sac ligation assisted with a needle‐type grasper
In the last 2 decades, the advent of minimally invasive surgery has completely changed the management of pediatric inguinal hernias [26, 27]. Laparoscopic surgery, since its advent in the early 1990s, is increasingly being preferred by the surgeons and patients worldwide due to its overall benefits, evident by operative results and patient satisfaction [28]. Montupet is credited with performing the first intracorporeal laparoscopic pediatric hernia repair in 1993 [26]. The authors treated pediatric inguinal hernia with laparoscopy high ligation of the hernia sac with the aid of a needle‐type grasper (Figure 4) [29]. With almost similar results to open mesh repair, laparoscopy provides an alternative to inguinal hernia repair especially in bilateral or recurrent cases [30].
Figure 4.
Needle‐type grasper.
6.3.1. Preoperative preparation
Preoperative preparation includes fasting for 6 h. To be intraoperatively better exposed and minimize the risk of bladder injury, the bladder should be emptied before surgery.
6.3.2. Patient and team position
All patients underwent general anesthesia. The patient is positioned supine with both arms tucked (Figure 6a). To remove the intestine away from the operative area and to improve exposure of the working area, the patients are changed in 15–20° of the Trendelenburg position during the procedure (Figure 6b). The surgeon is on the opposite side of the defect to be repaired. The assistant with the camera is on the same side as the hernia to be treated, and surgical nurse should be located on the right side of the patient near the patient\'s knee. The monitor is placed at the foot of the operating bed.
6.3.3. Surgical procedures
An incision at the infra or supra umbilicus is then made for placement of a 5‐mm trocar (we use a 5‐mm 30° laparoscope). Access of the peritoneal cavity is achieved using standard techniques with a Veress needle to create the pneumoperitoneum. The pneumoperitoneal pressure was maintained at 8–10 mmHg. Once access to the peritoneal cavity has been established, an inspection of bilateral internal inguinal ring is made in search of hernia defects. A 1.5‐mm incision at or above the linea alba midpoint between the umbilicus and pubic symphysis is made for entering the needle‐type grasper. Another 1.5‐mm small incision is made at the 12 o clock surface projection of internal inguinal ring. Through it, the endo‐closure device (Figure 5) with No. 4 polyester thread was rotated back and forth and entered into the pre‐peritoneal space at 11 (right side) or 1(left side) o clock of the internal inguinal ring under laparoscopic monitoring. The endo‐closure device was then advanced along the lateral side of inferior epigastric vessels within the extraperitoneal space and around the internal inguinal ring and bypassed the vas deferens and spermatic vessels with the aid of needle‐type grasper (Figure 6d–f). The tip of endo‐closure device was pierced the peritoneum into the abdominal cavity at 6 o clock of internal inguinal ring. No. 4 polyester thread was pulled out from the endo‐closure device with a needle‐type grasper and cleaved into the abdominal cavity (Figure 6g), and the endo‐closure device was pulled out of the body. The endo‐closure device was inserted into the same skin incision again. From 12 o clock of internal inguinal ring to the beginning, the endo‐closure device was rotated back and forth and advanced along the lateral side of internal inguinal ring beneath the peritoneum. The endo‐closure device entered into the abdominal cavity at the same peritoneal hole as the No. 4 polyester thread had gone through (Figure 6h). The endo‐closure device was then taken and the No. 4 polyester thread was taken out of the body. After squeezing the air out of the scrotal and groin area, No. 4 polyester thread was then tightened and tied, and the knot was subcutaneously buried. The high ligation of hernia sac was finished (Figure 6i). Bilateral indirect hernia was treated the same way. An inspection of the abdominal cavity is made before ending operation. The needle‐type grasper is removed under laparoscopic monitoring. A 5‐mm trocar was removed after the abdominal cavity air was emptied. Umbilical incision was sutured, and skin incision was intradermally sutured and stuck together with glue.
Figure 5.
Endo‐closure device (COVIDIEN).
Figure 6.
(a) The child with inguinal hernia has been disinfected and draped, (b) intraoperative location of the laparoscopic, needle‐type grasper, and endo‐closure device with the thread, (c) indirect inguinal hernia, (d) and (e) endo‐closure device with No. 4 polyester thread entering into the pre‐peritoneal space and then advanced along the lateral side of inferior epigastric vessels and around internal inguinal ring, (f) with the aid of needle‐type grasper, the tip of endo‐closure device bypassed the vas deferens which was under the tip of endo‐closure device in this picture, (g) and (h) the endo‐closure device advanced along the lateral side of internal inguinal ring beneath the peritoneum and entered into the abdominal cavity at the same peritoneal hole as the No. 4 polyester thread had gone through, and (i) high hernia sac ligation was finished.
The manipulation of laparoscopy high hernia sac ligation with the aid of the needle‐like grasper is easy to bypass the structure of the vas deferens and spermatic vessels under direct vision and does not injure it. Laparoscopic approaches offer the superior visualization to potentially avoid trauma to the vas deferens and spermatic vessels and the opportunity to accomplish a safe high ligation of the hernia sac at the internal ring [23, 31–33].
Laparoscopic approaches offer the opportunity to visually inspect the contralateral canal for the presence of an occult hernia without incision, and the contralateral hernia, hiding hernia (Figure 7), or other affections can be intraoperatively diagnosed and repaired at the same time while diagnosing unilateral cases, preoperatively. The sensitivity and specificity of laparoscopic examination for detecting hidden PV patency have been reported to be 99.4 and 99.5%, respectively [1]. Compared to the traditional open approach, the advantages of laparoscopic hernia repair include minimal dissection, excellent visual exposure, less complications, comparable recurrence rates, as well as improved cosmetic results. In addition, laparoscopic hernia repair also makes it possible for contralateral inguinal hernias to be defined and repaired in the same operation [34–36]. Up to now, no scrotal hematoma or effusion has been found in the authors’ department. At present, laparoscopy high hernia sac ligation assisted with the needle‐type grasper is more favorable than open pediatric inguinal hernia repair, which is one of the most common surgical procedures in the authors’ department. The operation could be implemented as long as there were no anesthetic or pneumoperitoneum contraindications.
Figure 7.
Hidden hernia was found with the aid of a needle‐type clamp.
The laparoscopic high inguinal hernia sac ligation must establish pneumoperitoneum, which can only be used in general anesthesia, which needs the endotracheal intubation and ventilator‐assisted breathing and increases surgical costs and anesthesia‐related problems. In addition, the families of children have some psychological concerns with the side effects of general anesthesia, which had a bad effect on surgical treatment.
6.4. Lichtenstein hernioplasty using a biological patch
As for the children from 13 to 18 years old, because simple hernia sac ligation surgery is not enough, the recurrence rate is high. The posterior wall of inguinal canal should also be repaired and strengthened in order to prevent recurrence. At present, it wasn\'t advocated for the children with hernia, from 13 to 18 years old, to be treated with non‐biological synthetic patch (e.g., polypropylene) because they are still in the growth and development stage. Not stretching or contracting, the non‐degradable patch can result in local postoperative obvious traction; local foreign body sensation and chronic pain may also cause spermatic cord adhesion and even affect fertility. For children and adolescents, their muscle and fascia tissue will gradually become strong in the growth and development stage. The absorbable biological materials can rely on their own characteristics to repair defects in the early stage and generate the new tissue plates through tissue replacement to prevent recurrence of hernia in the long term. After the biological materials are absorbed or degraded gradually, the biological patch will be replaced by autologous tissue without affecting the growth and development.
The authors found that the simple high hernia sac ligation is inadequate for adolescents who had a longer medical history, larger diameter of internal inguinal ring, and more serious transverse fascia defects and that the procedure similar to the treatment of adult inguinal hernias should be taken in order to repair the transverse fascia and strengthen of the posterior wall of the inguinal canal. The authors proposed the application of the biological patch to the treatment of the inguinal hernia of the patients who are 13–18 years old, and results show that compared with the traditional high ligation of hernia sac, the biological patch tension‐free hernia repair surgery did not significantly increase the wound infection, male scrotal effusion, chronic pain or local foreign body sensation, and other complications.
Open “tension free” mesh repair technique, pioneered by Lichtenstein in 1984, is still considered the method of choice for primary inguinal hernia [37, 38]. For children from 13 to 18 years of age, inguinal hernia was treated with Lichtenstein hernioplasty with the biological patch, in which biological patch is placed in front of the transversalis fascia to reinforce the posterior wall of the inguinal canal.
6.4.1. Surgical procedures
The operative steps include dissection of the spermatic cord, dissection and resection of the hernia sac with high ligation (Figure 8b–d), and reconstruction of the floor of the inguinal canal. The inguinal canal is dissected to expose the shelving edge of the inguinal ligament, the pubic tubercle, and the sufficient area for biological patch. The biological patch must be large enough to overlap 1.5–2 cm medial to the pubic tubercle. The lateral portion of the patch is split into two tails such that the superior tail constitutes two‐thirds of its width, and the inferior tail is the remaining one‐third of its width (Figure 8e). The lateral tail of the biological patch passed through beneath the spermatic cord from medial to lateral and then sutured together with the medial tail using two vicryl 2/0 interrupted stitches, leaving a hole as large as the diameter of the spermatic cord, which was placed around the spermatic cord at the internal ring, but not too tight to strangulate it (Figure 8f). Two interrupted sutures with vicryl 2/0 thread were used to fix the inferior edge of the patch to the shelving edge of the inguinal ligament. The upper edge of the patch was then fixed to the inferior surface of external oblique aponeurosis with two vicryl 2/0 interrupted stitches. The tails were then placed on the surface of internal oblique muscle and fixed with glue. The medial edge of the patch was overlapped the pubic tubercle by 1.5–2 cm and fixed with medical glue in order to prevent medial recurrence. The reinforcement of the floor of the inguinal canal was finished (Figure 8g). External oblique aponeurosis was sutured with vicryl 2/0. Subcutaneous tissue is closed with vicryl 4/0. The skin incision was intradermally sutured with vicryl 4/0 and stuck together with medical glue.
Figure 8.
(a) The child with big indirect inguinal hernia, (b) and (c) the hernia sac was dissected and sheared, (d) the hernia sac was sutured and ligated at its neck, (e) a cellular tissue matrix patch (Grandhope Biotech Co., Ltd.) was prepared, (f) the two tails of the biologic patch were sutured together with 2/0 vicryl to surround the spermatic cord, (g) the fixation for the biological patch was finished.
Generally, it is not difficult to diagnose inguinal hernia in children; however, before surgery, there is no effective auxiliary examination to diagnose how much the hernia ring defect ranges, which is based on the options of individualized treatment of pediatric inguinal hernia. For some patients who are 13–18 years old, if the extent of hernia ring defect belonged to Gilbert type I or II, laparoscopic high hernia sac ligation could still be used. Preoperative non‐invasive examinations, such as ultrasound, which can define the size of the hernia ring defect in most cases, are helpful to choose the surgery and carry out the individualized treatment program of inguinal hernia in children.
The individualized treatment of inguinal hernia in children is currently an effective and relatively reasonable treatment program to improve treatment of morbidity. However, it does not take a long time to use laparoscopic high hernia sac ligation and the biological patch repair. It must be further observed for the long‐term effects and needs to be studied on the basis of the present in order to improve the clinical effects and reduce the postoperative complications.
\n',keywords:"hernia, inguinal, children, herniorrhaphy, laparoscopic, biological patch, individualized",chapterPDFUrl:"https://cdn.intechopen.com/pdfs/55382.pdf",chapterXML:"https://mts.intechopen.com/source/xml/55382.xml",downloadPdfUrl:"/chapter/pdf-download/55382",previewPdfUrl:"/chapter/pdf-preview/55382",totalDownloads:888,totalViews:994,totalCrossrefCites:0,totalDimensionsCites:1,hasAltmetrics:0,dateSubmitted:"November 9th 2016",dateReviewed:"March 29th 2017",datePrePublished:null,datePublished:"August 30th 2017",dateFinished:null,readingETA:"0",abstract:"The incidence of inguinal hernias in various age groups of children ranges from 0.8 to 4.4%. Pediatric indirect inguinal hernia is congenital, originating in the patent processus vaginalis. The inguinal hernia repair is one of the most common pediatric operations. The traditional high hernia sac ligation is the primary treatment for younger patients from 1 to 13 years of age and can correct the condition. The authors performed the high ligation of the hernia sac by the laparoscopic approach for the patients under 13 years old and achieved good therapeutic results in the last 10 years. However, through our clinical study, the authors found that the simple high ligation of hernia sac is inadequate for patients from 13 to 18 years of age, who had a longer medical history, larger diameter of the internal inguinal ring, and more serious defects of the transverse fascia. Pediatric inguinal hernias are prone to postoperative recurrence if the patients were only treated with the high ligation of hernia sac. To repair the transverse fascia and strengthen the posterior wall of the inguinal canal, Lichtenstein hernioplasty with a biological patch was performed for the patients from 13 to 18 years in the authors’ department. The aims of this chapter are to narrate the individualized treatment of inguinal hernia in children and try to provide relatively reasonable operative methods.",reviewType:"peer-reviewed",bibtexUrl:"/chapter/bibtex/55382",risUrl:"/chapter/ris/55382",book:{slug:"hernia"},signatures:"Jie Chen, ChengBing Chu, YingMo Shen, ZhenYu Zou and Xin Yuan",authors:[{id:"200981",title:"Prof.",name:"Jie",middleName:null,surname:"Chen",fullName:"Jie Chen",slug:"jie-chen",email:"chenjiejoe@sina.com",position:null,institution:{name:"Peking Union Medical College Hospital",institutionURL:null,country:{name:"China"}}},{id:"206011",title:"Dr.",name:"ChengBing",middleName:null,surname:"Chu",fullName:"ChengBing Chu",slug:"chengbing-chu",email:"cbchu72@163.com",position:null,institution:null},{id:"206012",title:"Prof.",name:"YingMo",middleName:null,surname:"Shen",fullName:"YingMo Shen",slug:"yingmo-shen",email:"shenyingmo@126.com",position:null,institution:null},{id:"206013",title:"Dr.",name:"ZhenYu",middleName:null,surname:"Zou",fullName:"ZhenYu Zou",slug:"zhenyu-zou",email:"zouzhenyu301@sina.cn",position:null,institution:null},{id:"206014",title:"MSc.",name:"Xin",middleName:null,surname:"Yuan",fullName:"Xin Yuan",slug:"xin-yuan",email:"yuanxin610@126.com",position:null,institution:null}],sections:[{id:"sec_1",title:"1. Introduction",level:"1"},{id:"sec_2",title:"2. Etiology",level:"1"},{id:"sec_3",title:"3. Clinical manifestation",level:"1"},{id:"sec_4",title:"4. Physical and accessory examination",level:"1"},{id:"sec_5",title:"5. Diagnosis and differential diagnosis",level:"1"},{id:"sec_6",title:"6. Treatment",level:"1"},{id:"sec_6_2",title:"6.1. Indications for surgery",level:"2"},{id:"sec_7_2",title:"6.2. Modified open pediatric inguinal hernia repair",level:"2"},{id:"sec_7_3",title:"6.2.1. Operative steps for the modified open pediatric inguinal hernia repair",level:"3"},{id:"sec_9_2",title:"6.3. Laparoscopy high hernia sac ligation assisted with a needle‐type grasper",level:"2"},{id:"sec_9_3",title:"6.3.1. Preoperative preparation",level:"3"},{id:"sec_10_3",title:"6.3.2. Patient and team position",level:"3"},{id:"sec_11_3",title:"6.3.3. Surgical procedures",level:"3"},{id:"sec_13_2",title:"6.4. Lichtenstein hernioplasty using a biological patch",level:"2"},{id:"sec_13_3",title:"6.4.1. Surgical procedures",level:"3"}],chapterReferences:[{id:"B1",body:'Miltenburg DM, Nuchtern JG, Jaksic T, et al. Laparoscopic evaluation of the pediatric inguinal hernia: A meta‐analysis. Journal of Pediatric Surgery. 1998;33(6):874–879'},{id:"B2",body:'Parelkar SV, Oak S, Gupta R, et al. Laparoscopic inguinal hernia repair in the pediatric age group—experience with 437 children. Journal of Pediatric Surgery. 2010;45(4):789–792'},{id:"B3",body:'Lau S, Lee Y, Caty M. Current management of hernias and hydroceles. Seminars in Pediatric Surgery. 2007;16(1):50–57'},{id:"B4",body:'Brandt ML. Pediatric hernias. Surgical Clinics of North America. 2008;88:27–43'},{id:"B5",body:'Toki A, Watanabe Y, Sasaki K. Adopt a wait‐and‐see attitude for patent processus vaginalis in neonates. Journal of Pediatric Surgery. 2003;38(9):1371–1373'},{id:"B6",body:'Burcharth J, Pommergaard HC, Rosenberg J. The inheritance of groin hernia: A systematic review. 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Department of Hernia and Abdominal Wall Surgery, Beijing Chao‐Yang Hospital, Capital Medical University, Beijing, China
Department of Hernia and Abdominal Wall Surgery, Beijing Chao‐Yang Hospital, Capital Medical University, Beijing, China
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1. Introduction
The fractional calculus has recently been widely used to study the theory and applications of derivatives and integrals of arbitrary non-integer order. This branch of mathematical analysis has emerged in recent years as an effective and powerful tool for the mathematical modeling of various engineering, industrial, and materials science applications [1, 2, 3]. The fractional-order operators are useful in describing the memory and hereditary properties of various materials and processes, due to their nonlocal nature. It clearly reflects from the related literature produced by leading fractional calculus journals that the primary focus of the investigation had shifted from classical integer-order models to fractional order models [4, 5]. Fractional calculus has important applications in hereditary solid mechanics, fluid dynamics, viscoelasticity, heat conduction modeling and identification, biology, food engineering, econophysics, biophysics, biochemistry, robotics and control theory, signal and image processing, electronics, electric circuits, wave propagation, nanotechnology, etc. [6, 7, 8].
Numerous mathematicians have contributed to the history of fractional calculus, where Euler mentioned interpolating between integral orders of a derivative in 1730. Then, Laplace defined a fractional derivative by means of an integral in 1812.
Lacroix introduced the first fractional order derivative which appeared in a calculus in 1819, where he expressed the nth derivative of the function y=xm as follows:
dndxn=Γm+1Γm‐n+1xm‐nE1
Liouville assumed that dvdxveax=aveaxforv>0 to obtain the following fractional order derivative:
dvx‐adxv=‐1vΓa+vΓax‐a‐vE2
Laurent has been using the Cauchy’s integral formula for complex valued analytical functions to define the integration of arbitrary order v>0 as follows:
cDxvfx=cDxm‐ρfx=dmdxm1Γρ∫cxx−tρ−1ftdt,0<ρ≤1E3
where cDxv denotes differentiation of order v of the function f along the x‐axis.
Cauchy introduced the following fractional order derivative:
f+α=∫fτt‐τα‐1Γ‐αdτE4
Caputo introduced his fractional derivative of order α<0 to be defined as follows:
D∗αft=1Γm‐α∫0tfmτt‐τα+1‐mdτ,m−1<α<m,α>0E5
Recently, research on nonlinear generalized magneto-thermoelastic problems has received wide attention due to its practical applications in various fields such as geomechanics, geophysics, petroleum and mineral prospecting, earthquake engineering, astronautics, oceanology, aeronautics, materials science, fiber-optic communication, fluid mechanics, automobile industries, aircraft, space vehicles, plasma physics, nuclear reactors, and other industrial applications. Due to computational difficulties in solving nonlinear generalized magneto-thermoelastic problems in general analytically, many numerical techniques have been developed and implemented for solving such problems [9, 10, 11, 12, 13, 14, 15, 16, 17]. The boundary element method (BEM) [18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31] has been recognized as an attractive alternative numerical method to domain methods [32, 33, 34, 35, 36] like finite difference method (FDM), finite element method (FEM), and finite volume method (FVM) in engineering applications. The superior feature of BEM over domain methods is that only the boundary of the domain needs to be discretized, which often leads to fewer elements and easier to use. This advantage of BEM over other domain methods has significant importance for modeling and optimization of thermoelastic problems which can be implemented using BEM with little cost and less input data. Nowadays, the BEM has emerged as an accurate and efficient computational technique for solving complicated inhomogeneous and non-linear problems in physical and engineering applications [37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69].
In the present chapter, we introduce a practical engineering application of fractal analysis in the field of thermoelasticity, where the thermal field is described by time fractional three-temperature radiative heat conduction equations. Fractional order derivative considered in the current chapter has high ability to remove the difficulty of our numerical modeling. A new boundary element method for modeling and optimization of 3T fractional order nonlinear generalized thermoelastic multi-material initially stressed multilayered functionally graded anisotropic (ISMFGA) structures subjected to moving heat source is investigated. Numerical results show that the fractional order parameter has a significant effect on the sensitivities of displacements, total three-temperature, and thermal stresses. Numerical examples show that the fractional order parameter has a significant effect on the final topology of ISMFGA structures. Numerical results of the proposed model confirm the validity and accuracy of the proposed technique, and numerical examples results demonstrate the validity of the BESO multi-material topology optimization method.
A brief summary of the chapter is as follows: Section 1 introduces the background and provides the readers with the necessary information to books and articles for a better understanding of fractional order problems and their applications. Section 2 describes the physical modeling of fractional order problems in three-temperature nonlinear generalized magneto-thermoelastic ISMFGA structures. Section 3 outlines the BEM implementation for modeling of 3T fractional nonlinear generalized magneto-thermoelastic problems of multi-material ISMFGA structures subjected to moving heat source. Section 4 introduces an illustration of the mechanisms of solving design sensitivities and optimization problem of the current chapter. Section 5 presents the new numerical results that describe the effects of fractional order parameter on the problem’s field variations and on the final topology of multi-material ISMFGA structures.
2. Formulation of the problem
Consider a multilayered structure with n functionally graded layers in the xy‐plane of a Cartesian coordinate. The x‐axis is the common normal to all layers as shown in Figure 1. The thickness of the layer is denoted by h. The considered multilayered structure has been placed in a primary magnetic field H0 acting in the direction of the y‐axis.
Figure 1.
Geometry of the considered problem.
According to the three-temperature theory, the governing equations of nonlinear generalized magneto-thermoelasticity in an initially stressed multilayered functionally graded anisotropic (ISMFGA) structure for the ith layer can be written in the following form:
σab,b+τab,b−Γab=ρix+1mu¨aiE6
σab=x+1mCabfgiuf,gi−βabiTαi−Tα0i+τ1Ṫα1E7
τab=μix+1mh˜aHb+h˜bHa−δbah˜fHfE8
Γab=Pix+1m∂uai∂xb−∂ubi∂xaE9
According to Fahmy [10], the time fractional order two-dimensional three-temperature (2D-3 T) radiative heat conduction equations in nondimensionless form can be expressed as follows:
where σab, τab, and uki are mechanical stress tensor, Maxwell’s electromagnetic stress tensor, and displacement vector in the ith layer, respectively, cα(α = c, I, p) are constant Tα0i, Tαi, Cabfgi, and βabi are, respectively, reference temperature, temperature, constant elastic moduli, and stress-temperature coefficients in the ith layer: μi, h˜, Pi, ρi, and csαi are, respectively, magnetic permeability, perturbed magnetic field, initial stress, density, isochore specific heat coefficients in the ith layer; τ is the time; τ0 and τ1 are the relaxation times; i=1,2,…,n represents the parameters in multilayered structure; and m is a functionally graded parameter. Also, we considered in the current study that the medium is subjected to a moving heat source of constant strength moving along x‐axis with a constant velocity v. This moving heat source is assumed to have the following form:
Qxτ=Q0δx−vτE15
where, Q0 is the heat source strength and δ is the delta function.
where inertia term, temperature gradient, and initial stress terms are treated as the body forces.
In this section, we are interested in using a boundary element method for modeling the two-dimensional three-temperature radiation heat conduction equations coupled with electron, ion, and phonon temperatures.
According to finite difference scheme of Caputo at times f+1Δt and fΔτ, we obtain [1].
DτaTαif+1+DτaTαif≈∑j=0kWa,jTαif+1−jr−Tαif−jrE17
where
Wa,0=Δτ−aΓ2−a,Wa,j=Wa,0j+11−a−j−11−aE18
Based on Eq. (17), the fractional order heat Eq. (10) can be replaced by the following system:
Now, according to Fahmy [10], and applying the fundamental solution which satisfies (19), the boundary integral equations corresponding to (10) without heat sources can be expressed as
Tαiξ=∫STαiqi∗−Tαi∗qidC−∫RfabTαi∗dRE20
Thus, the governing equations can be written in operator form as follows:
Lgbufi=fgb,E21
LabTαi=fabE22
where the operators Lgb, fgb, Lab, and fab are as follows:
The differential Eq. (21) can be solved using the weighted residual method (WRM) to obtain the following integral equation:
∫RLgbufi−fgbudai∗dR=0E26
Now, the fundamental solution udfi∗ and traction vectors tdai∗ and tai can be written as follows:
Lgbudfi∗=−δadδxξE27
tdai∗=Cabfgudf,gi∗nbE28
tai=t¯aix+1m=Cabfguf,gi−βabiTαi+τ1TαinbE29
Using integration by parts and sifting property of the Dirac distribution for (26), then using Eqs. (27) and (29), we can write the following elastic integral representation formula:
In order to convert the domain integral in (42) into the boundary, we approximate the source vector SA by a series of known functions fAEq and unknown coefficients αEq as
SA≈∑q=1EfAEqαEqE51
Thus, the representation formula (42) can be written as follows:
By applying the point collocation procedure of Gaul et al. [43] to Eqs. (51) and (61), we obtain
Sˇ=Jα¯,Ui=J′γ,E65
Similarly, applying the same point collocation procedure to Eqs. (64), (46), (47), (48), and (49) yields
SˇTαi=BTγE66
SAu=ψUiE67
SˇTαι̇=Γ¯AFU̇iE68
SˇTαι¨=δ¯AFU¨iE69
Sˇu¨=Ⅎ¯U¨iE70
where ψ¯, Γ¯AF, δ¯AF, and Ⅎ¯ are assembled using the submatrices ψ, ΓAF, δAF, and Ⅎ, respectively.
Solving the system (65) for α¯ and γ yields
α¯=J−1Sˇ,γ=J′−1UiE71
Now, the coefficient α¯ can be written in terms of the unknown displacements Ui, velocities U̇i, and accelerations U¨i as
α¯=J−1Sˇ0+BTJ′−1+ψ¯Ui+Γ¯AFU̇i+Ⅎ¯+δ¯AFU¨iE72
An implicit-implicit staggered algorithm has been implemented for use with the BEM to solve the governing equations which can now be written in a suitable form after substitution of Eq. (72) into Eq. (60) as
M⏞U¨i+Γ⏞U̇i+K⏞Ui=Q⏞iE73
X⏞T¨αi+A⏞Ṫαi+B⏞Tαi=Z⏞U¨i+R⏞E74
where V=η℘ˇ−ζUˇJ−1,M⏞=VℲ¯+δ¯AF,Γ⏞=VΓ¯AF,K⏞=−ζˇ+VBTJ′−1+ψ¯, Q⏞i=−ηTˇ+VSˇ0,X⏞=−ρicsαiτ0,A⏞=−Kαi,B⏞=ξ∇Kαi∇,Z⏞=βabiTα0iτ0,R⏞=−Q0δx−vτ.
where U¨i,U̇i,Ui,Ti and Q⏞i are, respectively, acceleration, velocity, displacement, temperature, and external force vectors, and V,M⏞, Γ⏞, K⏞, A⏞, and B⏞ are, respectively, volume, mass, damping, stiffness, capacity, and conductivity matrices.
In many applications, the coupling term Z⏞U¨n+1i that appear in the heat conduction equation is negligible. Therefore, it is easier to predict the temperature than the displacement.
Hence Eqs. (73) and (74) lead to the following coupled system of differential-algebraic equations (DAEs):
M⏞U¨n+1i+Γ⏞U̇n+1i+K⏞Un+1i=Q⏞n+1ipE75
X⏞T¨αn+1i+A⏞Ṫαn+1i+B⏞Tαn+1i=Z⏞U¨n+1i+R⏞E76
where Q⏞n+1ip=ηTαn+1ip+VSˇ0 and Tαn+1ip is the predicted temperature.
Now, a displacement predicted staggered procedure for the solution of (80) and (85) is as follows:
The first step is to predict the propagation of the displacement wave field: Un+1ip=Uni. The second step is to substitute for U̇n+1i and U¨n+1i from Eqs. (77) and (75), respectively, in Eq. (85) and solve the resulted equation for the three-temperature fields. The third step is to correct the displacement using the computed three-temperature fields for the Eq. (80). The fourth step is to compute U̇n+1i, U¨n+1i, Ṫαn+1i, and T¨αn+1i from Eqs. (79), (81), (82), and (86), respectively.
The continuity conditions for temperature, heat flux, displacement, and traction that have been considered in the current chapter can be expressed as
Tαixzτx=hi=Tαi+1xzτx=hiE87
qixzτx=hi=qi+1xzτx=hiE88
ufixzτx=hi=ufi+1xzτx=hiE89
t¯aixzτx=hi=t¯ai+1xzτx=hiE90
where n is the total number of layers, t¯a are the tractions which is defined by t¯a=σabnb, and i=1,2,…,n−1.
The initial and boundary conditions of the present study are
ufixz0=u̇fixz0=0forxz∈R∪CE91
ufixzτ=Ψfxzτforxz∈C3E92
t¯aixzτ=Φfxzτforxz∈C4,τ>0E93
Tαixz0=Tαixz0=0forxz∈R∪CE94
Tαixzτ=f¯xzτforxz∈C1,τ>0E95
qixzτ=h¯xzτforxz∈C2,τ>0E96
where Ψf, Φf, f, and h¯ are prescribed functions, C=C1∪C2=C3∪C4, and C1∩C2=C3∩C4=0.
4. Design sensitivity and optimization
According to Fahmy [58, 60], the design sensitivities of displacements components and total 3T can be performed by implicit differentiation of (75) and (76), respectively, which describe the structural response with respect to the design variables, and then we can compute thermal stresses sensitivities.
The bi-directional evolutionary structural optimization (BESO) is the evolutionary topology optimization method that allows modification of the structure by either adding or removing material to or from the structure design. This addition or removal depends on the sensitivity analysis. Sensitivity analysis is the estimation of the response of the structure to the modification of design variables and is dependent on the calculation of derivatives [70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80].
The homogenized vector of thermal expansion coefficients αH can be written in terms of the homogenized elasticity matrix DH and the homogenized vector of stress-temperature coefficients βH as follows:
αH=DH−1βHE97
For the material design, the derivative of the homogenized vector of thermal expansion coefficients can be written as
∂αH∂Xklm=DH−1∂βH∂Xklm−∂DH∂XklmαHE98
where ∂DH∂Xklm and ∂βH∂Xklm for any lth material phase can be calculated using the adjoint variable method [73] as
In order to show the numerical results of this study, we consider a monoclinic graphite-epoxy as an anisotropic thermoelastic material which has the following physical constants [57].
Mass density ρ=7820kg/m3 and heat capacity c = 461 J/kg K.
The proposed technique that has been utilized in the present chapter can be applicable to a wide range of three-temperature nonlinear generalized thermoelastic problems of ISMFGA structures. The main aim of this chapter was to assess the impact of fractional order parameter on the sensitivities of total three-temperature, displacement components, and thermal stress components.
Figure 2 shows the variation of the total temperature sensitivity along the x‐axis. It was shown from this figure that the fraction order parameter has great effects on the total three-temperature sensitivity.
Figure 2.
Variation of the total 3T sensitivity along x-axis.
Figures 3 and 4 show the variation of the displacement components u1 and u2 along the x‐axis for different values of fractional order parameter. It was noticed from these figures that the fractional order parameter has great effects on the displacement sensitivities.
Figure 3.
Variation of the displacement u1 sensitivity along x-axis.
Figure 4.
Variation of the displacement u2 sensitivity along x-axis.
Figures 5–7 show the variation of the thermal stress components σ11, σ12, and σ22, respectively, along the x‐axis for different values of fractional order parameter. It was noted from these figures that the fractional order parameter has great influences on the thermal stress sensitivities.
Figure 5.
Variation of the thermal stress σ11 sensitivity along x-axis.
Figure 6.
Variation of the thermal stress σ12 sensitivity along x-axis.
Figure 7.
Variation of the thermal stress σ22 sensitivity along x-axis.
Since there are no available results for the three-temperature thermoelastic problems, except for Fahmy’s research [10, 11, 12, 13, 14]. For comparison purposes with the special cases of other methods treated by other authors, we only considered one-dimensional numerical results of the considered problem. In the special case under consideration, the displacement u1 and thermal stress σ11 results are plotted in Figures 8 and 9. The validity and accuracy of our proposed BEM technique were demonstrated by comparing our BEM results with the FEM results of Xiong and Tian [81], it can be noticed that the BEM results are found to agree very well with the FEM results.
Figure 8.
Variation of the displacement u1 sensitivity along x-axis.
Figure 9.
Variation of the thermal stress σ11 waves along x-axis.
Example 1. Short cantilever beam.
The mean compliance has been minimized, to obtain the maximum stiffness, when the structure is subjected to moving heat source. In this example, we consider a short cantilever beam shown in Figure 10, where the BESO final topology of considered short cantilever beam shown in Figure 11a for α=0.5 and shown in Figure 11b for α=1.0. It is noticed from this figure that the fractional order parameter has a significant effect on the final topology of the multi-material ISMFGA structure.
Figure 10.
Design domain of a short cantilever beam.
Figure 11.
The final topology of a short cantilever beam: (a) α = 0.5 and (b) α = 1.0.
Example 2. MBB beam.
It is known that extraordinary thermo-mechanical properties can be accomplished by combining more than two materials phases with conventional materials [75]. For this reason, it is essential that the topology optimization strategy permits more than two materials phases within the design domain. In this example, we consider a MBB beam shown in Figure 12, where the BESO final topology of MBB beam has been shown in Figure 13a for α=0.5 and shown in Figure 13b for α=1.0 to show the effect of fractional order parameter on the final topology of the multi-material ISMFGA structure.
Figure 12.
Design domain of a MBB beam.
Figure 13.
The final topology of MBB beam: (a) α = 0.5 and (b) α = 1.0.
Example 3. Roller-supported beam.
In this example, we consider a roller-supported beam shown in Figure 14, where the BESO final topology of a roller-supported beam shown in Figure 15a for α=0.5 and shown in Figure 15b for α=1.0.
Figure 14.
Design domain of a roller-supported beam.
Figure 15.
The final topology of a multi-material roller-supported beam: (a) α = 0.5 and (b) α = 1.0.
Example 4. Cantilever beam (validation example).
In order to demonstrate the validity of our implemented BESO topology optimization technique, we consider isotropic case of a cantilever beam shown in Figure 16 as a special case of our anisotropic study to interpolate the elasticity matrix and the stress-temperature coefficients using the design variables XM, then we compare our BESO final topology shown in Figure 17a with the material interpolation scheme of the solid isotropic material with penalization (SIMP) shown in Figure 17b.
Figure 16.
Design domain of a cantilever beam.
Figure 17.
The final topology of a cantilever beam: (a) MMA and (b) BESO.
The BESO topology optimization problem implemented in Examples 1 and 4, to find the distribution of the M material phases, with the volume constraint can be stated as
Find XM
That minimize CM=12PMTuM=12fM,ter+fM,mecTuM
Subject to VM,∗−∑i=1NViMXiM=0
KMuM=PM
XiM=xminV1
where XM is the design variable; CM is the mean compliance; P is the total load on the structure, which is the sum of mechanical and thermal loads; uM is the displacement vector; VM,∗ is the volume of the solid material; N is the total number of elements; KM is the global stiffness matrix; xmin is a small value (e.g., 0.0001), which it guarantee that none of the elements will be removed completely from design domain; fM,mec is the mechanical load vector; and fM,ter is the thermal load vector. Also, the BESO parameters considered in Examples 1–4 can be seen in Tables 1–4, respectively.
Variable name
Variable description
Variable value
VfM
Final volume fraction
0.5
ERM
Evolutionary ratio
1%
ARmaxM
Volume addition ratio
5%
rminM
Filter ratio
3 mm
τ
Convergence tolerance
0.1%
N
Convergence parameter
5
Table 1.
BESO parameters for minimization of a short cantilever beam.
Variable name
Variable description
Variable value
Vf1M
Final volume fraction of the material 1 for both interpolations
0.10
Vf2M
Final volume fraction of the material 2 for both interpolations
0.20
ERM
Evolutionary ratio for interpolation 1
2%
ERM
Evolutionary ratio for interpolation 2
3%
ARmaxM
Volume addition ratio for interpolation 1
3%
ARmaxM
Volume addition ratio for interpolation 2
2%
rminM
Filter ratio for interpolation 1
4 mm
rminM
Filter ratio for interpolation 2
3 mm
τ
Convergence tolerance for both interpolations
0.01%
N
Convergence parameter for both interpolations
5
Table 2.
Multi-material BESO parameters for minimization of a MBB beam.
Variable name
Variable description
Variable value
Vf1M
Final volume fraction of the material 1 for both interpolations
0.25
Vf1M
Final volume fraction of the material 2 for both interpolations
0.25
ERM
Evolutionary ratio for interpolation 1
3%
ERM
Evolutionary ratio for interpolation 2
3%
ARmaxM
Volume addition ratio for interpolation 1
1%
ARmaxM
Volume addition ratio for interpolation 2
1%
rminM
Filter ratio for interpolation 1
4 mm
rminM
Filter ratio for interpolation 2
4 mm
τ
Convergence tolerance for both interpolations
0.5 %
N
Convergence parameter for both interpolations
5
Table 3.
Multi-material BESO parameters for minimization of a roller-supported beam.
Variable name
Variable description
Variable value
VfM
Final volume fraction
0.4
ERM
Evolutionary ratio
1.2%
ARmaxM
Volume addition ratio
3%
rminM
Filter ratio
0.19 mm
τ
Convergence tolerance
0.1%
N
Convergence parameter
5
Table 4.
BESO parameters for minimization of a cantilever beam.
The BESO topology optimization problem implemented in Examples 2 and 3, to find the distribution of the two materials in the design domain, which minimize the compliance of the structure, subject to a volume constraint in both phases can be stated as.
Find XM
That minimize CM=12PMTuM=12fM,ter+fM,mecTuM
Subject to VjM,∗−∑i=1NViMXijM−∑i=1j−1ViM,∗=0;j=1,2
KMuM=PM
XiM=xminV1;j=1,2
where VjM,∗ is the volume of jth material phase and i and j denote the element ith which is made of jth material.
6. Conclusion
The main purpose of this chapter is to describe a new boundary element formulation for modeling and optimization of 3T time fractional order nonlinear generalized thermoelastic multi-material ISMFGA structures subjected to moving heat source, where we used the three-temperature nonlinear radiative heat conduction equations combined with electron, ion, and phonon temperatures.
Numerical results show the influence of fractional order parameter on the sensitivities of the study’s fields. The validity of the present method is examined and demonstrated by comparing the obtained outcomes with those known in the literature. Because there are no available data to confirm the validity and accuracy of our proposed technique, we replace the three-temperature radiative heat conduction with one-temperature heat conduction as a special case from our current general study of three-temperature nonlinear generalized thermoelasticity. In the considered special case of 3T time fractional order nonlinear generalized thermoelastic multi-material ISMFGA structures, the BEM results have been compared graphically with the FEM results; it can be noticed that the BEM results are in excellent agreement with the FEM results. These results thus demonstrate the validity and accuracy of our proposed technique. Numerical examples are solved using the multi-material topology optimization algorithm based on the bi-evolutionary structural optimization method (BESO). Numerical results of these examples show that the fractional order parameter affects the final result of optimization. The implemented optimization algorithm has proven to be an appropriate computational tool for material design.
Nowadays, the knowledge of 3T fractional order optimization of multi-material ISMFGA structures, can be utilized by mechanical engineers for designing heat exchangers, semiconductor nano materials, thermoelastic actuators, shape memory actuators, bimetallic valves and boiler tubes. As well as for chemists to observe the chemical processes such as bond breaking and bond forming.
\n',keywords:"boundary element method, modeling and optimization, time fractional order, three-temperature, nonlinear generalized thermoelasticity, initially stressed multilayered functionally graded anisotropic structures, moving heat source",chapterPDFUrl:"https://cdn.intechopen.com/pdfs/72883.pdf",chapterXML:"https://mts.intechopen.com/source/xml/72883.xml",downloadPdfUrl:"/chapter/pdf-download/72883",previewPdfUrl:"/chapter/pdf-preview/72883",totalDownloads:133,totalViews:0,totalCrossrefCites:0,dateSubmitted:"April 11th 2020",dateReviewed:"May 18th 2020",datePrePublished:"July 23rd 2020",datePublished:null,dateFinished:null,readingETA:"0",abstract:"The main purpose of this chapter, which represents one of the chapters of a fractal analysis book, is to propose a new boundary element method (BEM) formulation based on time fractional order theory of thermoelasticity for modeling and optimization of three temperature (3T) multi-material initially stressed multilayered functionally graded anisotropic (ISMFGA) structures subjected to moving heat source. Fractional order derivative considered in the current chapter has been found to be an accurate mathematical tool for solving the difficulty of our physical and numerical modeling. Furthermore, this chapter shed light on the practical application aspects of boundary element method analysis and topology optimization of fractional order thermoelastic ISMFGA structures. Numerical examples based on the multi-material topology optimization algorithm and bi-evolutionary structural optimization method (BESO) are presented to study the effects of fractional order parameter on the optimal design of thermoelastic ISMFGA structures. The numerical results are depicted graphically to show the effects of fractional order parameter on the sensitivities of total temperature, displacement components and thermal stress components. The numerical results also show the effects of fractional order parameter on the final topology of the ISMFGA structures and demonstrate the validity and accuracy of our proposed technique.",reviewType:"peer-reviewed",bibtexUrl:"/chapter/bibtex/72883",risUrl:"/chapter/ris/72883",signatures:"Mohamed Abdelsabour Fahmy",book:{id:"9886",title:"Fractal Analysis",subtitle:"Selected Examples",fullTitle:"Fractal Analysis - Selected Examples",slug:"fractal-analysis-selected-examples",publishedDate:"September 9th 2020",bookSignature:"Robert Koprowski",coverURL:"https://cdn.intechopen.com/books/images_new/9886.jpg",licenceType:"CC BY 3.0",editedByType:"Edited by",editors:[{id:"50150",title:"Dr.",name:"Robert",middleName:null,surname:"Koprowski",slug:"robert-koprowski",fullName:"Robert Koprowski"}],productType:{id:"1",title:"Edited Volume",chapterContentType:"chapter",authoredCaption:"Edited by"}},authors:[{id:"233766",title:"Prof.",name:"Mohamed Abdelsabour",middleName:"Abdelsabour",surname:"Fahmy",fullName:"Mohamed Abdelsabour Fahmy",slug:"mohamed-abdelsabour-fahmy",email:"mohamed_fahmy@ci.suez.edu.eg",position:null,institution:{name:"Suez Canal University",institutionURL:null,country:{name:"Egypt"}}}],sections:[{id:"sec_1",title:"1. Introduction",level:"1"},{id:"sec_2",title:"2. Formulation of the problem",level:"1"},{id:"sec_3",title:"3. BEM numerical implementation",level:"1"},{id:"sec_4",title:"4. Design sensitivity and optimization",level:"1"},{id:"sec_5",title:"5. Numerical examples, results, and discussion",level:"1"},{id:"sec_6",title:"6. Conclusion",level:"1"}],chapterReferences:[{id:"B1",body:'Cattaneo C. Sur une forme de i’equation de la chaleur elinant le paradox d’une propagation instantanc. Comptes Rendus de l’Académie des Sciences. 1958;247:431-433'},{id:"B2",body:'Oldham KB, Spanier J. The Fractional Calculus: Theory and Applications of Differentiation and Integration to Arbitrary Order. Mineola: Dover Publication; 2006'},{id:"B3",body:'Podlubny I. Fractional Differential Equations. San Diego, California, USA: Academic Press; 1999'},{id:"B4",body:'Ezzat MA, El Karamany AS, Fayik MA. Fractional order theory in thermoelastic solid with three-phase lag heat transfer. Archive of Applied Mechanics. 2012;82:557-572'},{id:"B5",body:'Kilbas AA, Srivastava HM, Trujillo JJ. Theory and Applications of Fractional Differential Equations, vol. 204 of North-Holland Mathematics Studies. Amsterdam, The Netherlands: Elsevier Science; 2006'},{id:"B6",body:'Sabatier J, Agrawal OP, Machado JAT. Advances in Fractional Calculus: Theoretical Developments and Applications in Physics and Engineering. Dordrecht, The Netherlands: Springer; 2007'},{id:"B7",body:'Ezzat MA, El-Bary AA. Application of fractional order theory of magneto-thermoelasticity to an infinite perfect conducting body with a cylindrical cavity. Microsystem Technologies. 2017;23:2447-2458'},{id:"B8",body:'Soukkou A, Belhour MC, Leulmi S. Review, design, optimization and stability analysis of fractional-order PID controller. International Journal of Intelligent Systems Technologies and Applications. 2016;8:73-96'},{id:"B9",body:'El-Naggar AM, Abd-Alla AM, Fahmy MA. 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Computerized Boundary Element Solutions for Thermoelastic Problems: Applications to Functionally Graded Anisotropic Structures. Saarbrücken: LAP Lambert Academic Publishing; 2017'},{id:"B26",body:'Fahmy MA. Boundary Element Computation of Shape Sensitivity and Optimization: Applications to Functionally Graded Anisotropic Structures. Saarbrücken: LAP Lambert Academic Publishing; 2017'},{id:"B27",body:'Fahmy MA. A time-stepping DRBEM for 3D anisotropic functionally graded piezoelectric structures under the influence of gravitational waves. In: Proceedings of the 1st GeoMEast International Congress and Exhibition (GeoMEast 2017); 15–19 July 2017; Sharm El Sheikh, Egypt. Facing the Challenges in Structural Engineering, Sustainable Civil Infrastructures. 2017. pp. 350-365'},{id:"B28",body:'Fahmy MA. 3D DRBEM modeling for rotating initially stressed anisotropic functionally graded piezoelectric plates. 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A computerized boundary element model for simulation and optimization of fractional-order three temperatures nonlinear generalized piezothermoelastic problems based on genetic algorithm. In: AIP Conference Proceedings 2138 of Innovation and Analytics Conference and Exihibiton (IACE 2019); 25-28 March 2019; Sintok, Malaysia. 2019. p. 030015'},{id:"B32",body:'Soliman AH, Fahmy MA. Range of applying the boundary condition at fluid/porous Interface and evaluation of beavers and Joseph’s slip coefficient using finite element method. Computation. 2020;8:14'},{id:"B33",body:'Eskandari AH, Baghani M, Sohrabpour S. A time-dependent finite element formulation for thick shape memory polymer beams considering shear effects. International Journal of Applied Mechanics. 2019;10:1850043'},{id:"B34",body:'Huang R, Zheng SJ, Liu ZS, Ng TY. Recent advances of the constitutive models of smart materials—Hydrogels and shape memory polymers. 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Computer implementation of the DRBEM for studying the generalized thermo elastic responses of functionally graded anisotropic rotating plates with two relaxation times. British Journal of Mathematics & Computer Science. 2014;4:1010-1026'},{id:"B53",body:'Fahmy MA. A 2D time domain DRBEM computer model for magneto-thermoelastic coupled wave propagation problems. International Journal of Engineering and Technology Innovation. 2014;4:138-151'},{id:"B54",body:'Fahmy MA, Al-Harbi SM, Al-Harbi BH. Implicit time-stepping DRBEM for design sensitivity analysis of magneto-thermo-elastic FGA structure under initial stress. American Journal of Mathematical and Computational Sciences. 2017;2:55-62'},{id:"B55",body:'Fahmy MA. The effect of anisotropy on the structure optimization using golden-section search algorithm based on BEM. Journal of Advances in Mathematics and Computer Science. 2017;25:1-18'},{id:"B56",body:'Fahmy MA. DRBEM sensitivity analysis and shape optimization of rotating magneto-thermo-viscoelastic FGA structures using golden-section search algorithm based on uniform bicubic B-splines. Journal of Advances in Mathematics and Computer Science. 2017;25:1-20'},{id:"B57",body:'Fahmy MA. A predictor-corrector time-stepping DRBEM for shape design sensitivity and optimization of multilayer FGA structures. Transylvanian Review. 2017;XXV:5369-5382'},{id:"B58",body:'Fahmy MA. Shape design sensitivity and optimization for two-temperature generalized magneto-thermoelastic problems using time-domain DRBEM. Journal of Thermal Stresses. 2018;41:119-138'},{id:"B59",body:'Fahmy MA. Boundary element algorithm for modeling and simulation of dual-phase lag bioheat transfer and biomechanics of anisotropic soft tissues. International Journal of Applied Mechanics. 2018;10:1850108'},{id:"B60",body:'Fahmy MA. Shape design sensitivity and optimization of anisotropic functionally graded smart structures using bicubic B-splines DRBEM. Engineering Analysis with Boundary Elements. 2018;87:27-35'},{id:"B61",body:'Fahmy MA. Modeling and optimization of anisotropic viscoelastic porous structures using CQBEM and moving asymptotes algorithm. Arabian Journal for Science and Engineering. 2019;44:1671-1684'},{id:"B62",body:'Fahmy MA. Boundary element modeling and simulation of biothermomechanical behavior in anisotropic laser-induced tissue hyperthermia. Engineering Analysis with Boundary Elements. 2019;101:156-164'},{id:"B63",body:'Fahmy MA, Al-Harbi SM, Al-Harbi BH, Sibih AM. A computerized boundary element algorithm for modeling and optimization of complex magneto-thermoelastic problems in MFGA structures. Journal of Engineering Research and Reports. 2019;3:1-13'},{id:"B64",body:'Fahmy MA. A new LRBFCM-GBEM modeling algorithm for general solution of time fractional order dual phase lag bioheat transfer problems in functionally graded tissues. Numerical Heat Transfer, Part A: Applications. 2019;75:616-626'},{id:"B65",body:'Fahmy MA. Design optimization for a simulation of rotating anisotropic viscoelastic porous structures using time-domain OQBEM. Mathematics and Computers in Simulation. 2019;66:193-205'},{id:"B66",body:'Fahmy MA. A new convolution variational boundary element technique for design sensitivity analysis and topology optimization of anisotropic thermo-poroelastic structures. Arab Journal of Basic and Applied Sciences. 2020;27:1-12'},{id:"B67",body:'Fahmy MA. Thermoelastic stresses in a rotating non- homogeneous anisotropic body. Numerical Heat Transfer, Part A: Applications. 2008;53:1001-1011'},{id:"B68",body:'Abd-Alla AM, Fahmy MA, El-Shahat TM. Magneto-thermo-elastic problem of a rotating non-homogeneous anisotropic solid cylinder. 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Design of multiphysics actuators using topology optimization—Part i: One-material structures. Computer Methods in Applied Mechanics and Engineering. 2001;190(49):6577-6604'},{id:"B75",body:'Sigmund O, Torquato S. Composites with extremal thermal expansion coefficients. Applied Physics Letters. 1996;69(21):3203-3205'},{id:"B76",body:'Sigmund O, Torquato S. Design of materials with extreme thermal expansion using a three-phase topology optimization method. Journal of the Mechanics and Physics of Solids. 1997;45(6):1037-1067'},{id:"B77",body:'Sigmund O, Torquato S. Design of smart composite materials using topology optimization. Smart Materials and Structures. 1999;8:365-379'},{id:"B78",body:'Yang XY, Xei YM, Steven GP, Querin OM. Bidirectional evolutionary method for stiffness optimization. AIAA Journal. 1999;37(11):1483-1488'},{id:"B79",body:'Wang Y, Luo Z, Zhang N, Wu T. Topological design for mechanical metamaterials using a multiphase level set method. Structural and Multidisciplinary Optimization. 2016b;54:937-954'},{id:"B80",body:'Xu B, Huang X, Zhou S, XIE Y. Concurrent topological design of composite thermoelastic macrostructure and microstructure with multi-phase material for maximum stiffness. Composite Structures. 2016;150:84-102'},{id:"B81",body:'Xiong QL, Tian XG. Generalized magneto-thermo-microstretch response during thermal shock. Latin American Journal of Solids and Structures. 2015;12:2562-2580'}],footnotes:[],contributors:[{corresp:"yes",contributorFullName:"Mohamed Abdelsabour Fahmy",address:"mohamed_fahmy@ci.suez.edu.eg",affiliation:'
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UK Research and Innovation (former Research Councils UK (RCUK) - including AHRC, BBSRC, ESRC, EPSRC, MRC, NERC, STFC.) Processing charges for books/book chapters can be covered through RCUK block grants which are allocated to most universities in the UK, which then handle the OA publication funding requests. It is at the discretion of the university whether it will approve the request.)
UK Research and Innovation (former Research Councils UK (RCUK) - including AHRC, BBSRC, ESRC, EPSRC, MRC, NERC, STFC.) Processing charges for books/book chapters can be covered through RCUK block grants which are allocated to most universities in the UK, which then handle the OA publication funding requests. It is at the discretion of the university whether it will approve the request.)
Wellcome Trust (Funding available only to Wellcome-funded researchers/grantees)
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