A Review of Nonlinear Control Strategies for Shape and Stress in Structural Engineering

Abstract

Structural engineering plays a pivotal role in ensuring the safety, stability, and longevity of civil infrastructure. As the demand for innovative and efficient structural designs grows, the need for advanced control strategies becomes increasingly apparent. This comprehensive review examines the state-of-the-art nonlinear control strategies for shape and stress in structural engineering. Recognizing the limitations of conventional linear approaches, the chapter systematically explores diverse methodologies such as adaptive control, neural networks, fuzzy logic, and model predictive control. It analyzes their individual and integrated applications in shaping structural form and managing stress levels. The review considers the intricate interplay between shape and stress control strategies, addresses challenges, and proposes future research directions. Case studies and a comparative analysis offer practical insights into the performance and adaptability of these strategies. By emphasizing advances in materials, technologies, and sustainability, this chapter provides a holistic perspective on the evolving landscape of nonlinear control in structural engineering. This synthesis aims to guide researchers and practitioners toward innovative solutions that enhance the safety, resilience, and efficiency of structural systems.

1. Introduction

At the nexus of innovation and resilience, structural engineering pursues the continuous development of structures that maximize longevity and performance while also withstanding external stresses. In this pursuit, the increasing understanding of the innate nonlinearities in structural systems is reshaping the traditional paradigm of linear control techniques. This in-depth study, “A Review of Nonlinear Control Strategies for Shape and Stress in Structural Engineering,” looks at the newest developments in using nonlinear control methods to deal with shape and stress, two important parts of structural design.

Traditional linear control schemes [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16], although useful, are not always able to capture the complex behaviors that are inherent in structural systems [17]. In structural engineering, nonlinearities can originate from a number of factors, including geometric configurations, material properties, large deflections or rotations, and dynamic loading scenarios [18, 19, 20, 21]. These nonlinear phenomena frequently make it difficult to precisely control shape and manage tension in structures [22]. However, linear control models depend on assumptions and simplifications, for instance, small deformations and elastic material behavior, that might not be factual for all structural states, potentially resulting in imprecisions in performance optimization. As a result of these drawbacks, scientists are now more frequently using nonlinear control techniques to manage the complexity of structural behavior [23, 24]. Employing the nonlinear controlling strategy improves structural efficiency and tolerates the construction of a more competent and lighter system due to decreasing material consumption while sustaining essential safety boundaries. Besides, nonlinear control techniques offer more flexibility in monitoring and adjusting performance in structures exhibiting nonlinear behavior, leading to more accurate modeling of actual structural responses.

1.1 Most important nonlinear control approaches

The field of nonlinear control strategies comprises a wide range of techniques, each with specific benefits for controlling stress [25, 26, 27], forming structural shapes [16, 28, 29, 30], or both simultaneously [30, 31]. Adaptive control has demonstrated promise for improving adaptability because of its capacity to modify parameters in response to changing structural conditions [32, 33]. Fuzzy logic offers a strong framework for forming structural configurations because of its ability to deal with uncertainty and imprecision [34]. Additionally, stress management in structural systems is greatly aided by model predictive control, which is well known for its capacity to maximize performance based on predictive models [35, 36, 37]. Korkmaz [38] divided the concept of structural control into three subdomains: active control, adaptive control, and intelligent control (see Figure 1). Active structural control utilizes sensors and actuators to alter the deformability and internal stress by modifying the structural response. In adaptive structural control, the alteration process improves the structural response regardless of the previous condition of loadings and actions. In intelligent structural control, on the other hand, the controlling process ensures the preservation and improvement of the structural performance by remembering the changes in behavior and action, adapting to the current target, and using the earlier events for improvement in future responses.

Figure 1.

Structural control and controlling subdomains [38].

1.2 Scope of the review

To clarify these nonlinear control techniques’ separate and combined uses in regulating stress levels and forming structural shapes, this review methodically investigates them. The subsequent sections will explore the subtleties of nonlinearities in structural engineering in Section 2. It is followed by shape control strategies in Section 3 and stress management tactics in Section 4, as well as the complex interactions between shape and stress in Section 5. Section 6 will address the field’s challenges and future directions, while Section 7 will include case studies and applications from the actual world. The review will close with a summary of the most important discoveries and a focus on how nonlinear control strategies may influence structural engineering in the future in Section 8.

2. Nonlinearities in structural engineering

Although structural engineering is based on the concepts of equilibrium and stability, it deals with intrinsic nonlinearities that have a big impact on how structures behave [39, 40]. These nonlinearities originate from different causes, including geometric nonlinearities [41, 42, 43], material nonlinearities [19, 44], large deflection nonlinearities [18, 45, 46], boundary condition nonlinearities [47, 48], and dynamic nonlinearities [49].

2.1 Geometric nonlinearities

Nonlinearities are brought about by geometric complications, particularly when working with thin structures or substantial deformations [41, 42, 43]. The effect of geometric nonlinearities may be ignored by traditional linear analysis, which could result in inaccurate predictions of structural reactions [4, 6, 8, 45, 50, 51, 52]. To accurately represent the behavior of structures under different loads, sophisticated geometrically nonlinear models are essential [53].

2.2 Material nonlinearities

The fundamental components of any structure, materials, frequently behave nonlinearly in a variety of situations [19, 44]. For example, strain-strain correlations in concrete are not linear, especially in the post-yield zone, where strains may not be precisely proportionate to stresses [54, 55]. Furthermore, the nonlinearity of steel materials presents difficulties for linear analysis techniques, particularly in the plastic deformation region [56, 57].

2.3 Large deflection nonlinearities

Large deflection nonlinearity in structures refers to the behavior where deformations become significant enough to cause nonlinear responses, deviating from linear elastic assumptions [18, 45, 46]. Under large deflections, structural elements undergo considerable distortion, altering their stiffness and load-carrying capacity [58]. This phenomenon commonly occurs in slender structures under high loads or flexible materials [46]. Nonlinear structural analysis techniques are employed to accurately predict deformations and stresses in such scenarios, crucial for ensuring structural integrity and safety [45, 59].

2.4 Boundary condition nonlinearities

Nonlinearities also stem from the boundary conditions imposed on structures [47, 48]. The rigidity of connections and supports can influence the overall structural response. In cases where supports are not perfectly rigid or exhibit nonlinear behavior, the overall structural response becomes intricate and necessitates sophisticated analysis methods [48, 60].

2.5 Dynamic nonlinearities

Dynamic nonlinearities are introduced by dynamic loading situations, such as seismic or wind-induced forces, which are difficult for conventional linear approaches to describe [49]. Dynamic force magnitude and frequency might result in nonlinear responses, necessitating specialized tactics for precise forecasting [61, 62].

Developing sophisticated numerical models and simulation methods to better comprehend and measure these nonlinearities has been the main focus of recent research projects [19, 26, 60, 63, 64, 65, 66, 67]. Computational methods and finite element analysis (FEA) have helped shed light on dynamic loading situations, geometric configurations, and nonlinear behavior of materials [21, 68, 69, 70, 71]. Experimental experiments have also helped capture real-world nonlinear reactions and validate numerical models [72, 73].

The nonlinearity of structural engineering in general—which is required to comprehend how stress and shape control are managed in structures—was covered in this part. We will now talk about the latest advances in nonlinear control methods and how they can be used to manage stress and change the shape of structures. This study takes into account the complicated issues that come up because structural engineering is not a straight-line subject.

3. Shape control strategies

Shape control schemes have become essential elements in the field of nonlinear control in structural engineering, as designers strive for exact structural configurations and esthetically pleasing designs. This section delves into many approaches that support the dynamic shaping of structural shapes.

3.1 Adaptive control for shape modification

Among the many methods for dynamically sculpting structural shapes, adaptive control is particularly important. Adaptive control ensures that different external loads and environmental impacts are continuously adapted by changing control parameters based on real-time structural conditions useful [74, 75, 76]. This adaptability is especially useful in situations where structures that are subject to shifting loading circumstances or deployable structures need to have their structural configurations change dynamically over time [38].

3.2 Neural networks for data-driven shape learning

A data-driven paradigm is introduced when shape control algorithms incorporate neural networks [77]. Neural networks may learn and adapt to complicated structural behaviors because they are inspired by complex learning mechanisms [78]. Neural networks, through analyzing large datasets and identifying nonlinear patterns, provide a reliable way to shape structures according to past performance and interactions with the environment [79].

3.3 Fuzzy logic for managing uncertainties in form

Fuzzy logic is used to shape structural configurations because of its reputation for handling uncertainties and imperfect information [80, 81]. Fuzzy logic offers a framework for decision-making that takes uncertainties into account in situations where exact mathematical models may be difficult to develop [82]. When working with materials that have changing characteristics or complex structural geometries, this is especially helpful [35, 83].

3.4 Model predictive control for dynamic form optimization

Model Predictive Control (MPC) is a technique that has gained popularity for optimizing performance using predictive models to shape structural shapes [84, 85]. MPC takes into account restrictions and objectives by using a predictive model of the structure and iteratively adjusting control inputs to attain desired forms [85, 86]. When sustaining ideal structural arrangements requires real-time alterations, this approach works well.

3.5 Various examples of applications of structure-based shape control

The pursuit of geometric perfection is essential in the field of structural engineering for a variety of architectural compositions. Determining nodal points is the first step toward the reality of architectural forms, from the conception of design to the fulfillment of esthetic quality. This requirement is demonstrated by beams [16, 29, 87, 88, 89, 90, 91, 92, 93, 94, 95], trusses [9, 96, 97, 98, 99, 100, 101, 102, 103], and frames [104, 105, 106] by linear or nonlinear methods, where the exact placement of structural components guarantees the effective distribution of loads while maintaining structural integrity. In addition, the sphere [6, 8, 52, 107, 108], antenna structures [100, 109, 110], egg-shaped structure [4], and dome [3, 5, 15, 111] constructions are examples of architectural achievements where geometric precision combines with esthetic appeal and practicality to create memorable areas and famous structures. While cable structures [3, 10, 11, 12, 13, 30, 31, 103, 112, 113, 114, 115, 116, 117, 118, 119] challenge preconceived concepts of stability and balance with their intricate designs, cable structures, with their elegant curves and tensioned forms, epitomize the union of engineering genius with artistic harmony.

4. Stress control strategies

To guarantee the longevity, safety, and structural integrity of designed systems, effective stress control techniques are essential. Various approaches used in nonlinear control to control stress in structural engineering are discussed in this section.

4.1 Adaptive control for stress management

Adaptive control techniques are essential for dynamically regulating stress inside structural parts. Adaptive control makes sure that structures can adapt to shifting loads and environmental variables by continuously modifying control settings depending on real-time stress levels, preventing excessive stress concentrations [120, 121]. When structural elements are subjected to fluctuating and unpredictable stresses, this adaptability is very valuable.

4.2 Neural networks for stress prediction and mitigation

A data-driven approach to stress management is offered by the incorporation of neural networks into stress control techniques. Since neural networks are very good at learning complicated patterns, they can be used to anticipate the distribution of stress inside structures [122, 123, 124]. Neural networks have a role in stress concentration mitigation and structural performance optimization through the utilization of real-time feedback and historical data.

4.3 Fuzzy logic for stress mitigation in uncertain environments

Stress control systems use fuzzy logic, which can handle uncertainties, to govern structural reactions in unpredictable settings [125, 126]. Fuzzy logic helps decision-makers reduce stress concentrations and improve structural resilience when external variables contribute to inaccurate information [127, 128]. This strategy is especially important in places where environmental uncertainty is common.

4.4 Model predictive control for optimal stress regulation

One effective method for controlling stress in structural parts is Model Predictive Control (MPC) [129]. MPC uses predictive models to repeatedly improve control inputs to produce optimal stress distributions while taking goals and constraints into account [130]. When accurate stress modulation is essential for the longevity and safety of structures, this approach works well.

4.5 Various examples of applications of structure-based stress control

Various structural domains can benefit from the practical implementation of stress control systems. These techniques have been used to optimize stress distributions, improve structural safety, and lengthen the lifespan of crucial infrastructure, ranging from buildings to bridge structures. For instance, trusses [2, 7, 26, 103], cables stayed bridges [2] and cable structures [26, 131] by linear [2, 7] or nonlinear [26, 131] methods. The mentioned examples highlight successful implementations and offer insightful information on the efficacy and practicality of stress control techniques.

5. Integration of shape and stress control

One of the most important aspects of managing structural integrity and performance holistically is the relationship between stress distribution and structural shape [2, 7, 14]. The integration of shape and stress control measures is examined in this section, emphasizing the benefits that result from examining these two factors together.

5.1 Simultaneous shape and stress control strategies

A major development in the nonlinear control of structural engineering is the merging of form and stress control techniques [31]. Combining control over stress management with structural form manipulation enables a holistic strategy for maximizing both performance and safety [7, 10, 11, 31, 132]. To accomplish this dual goal, a combination of neural networks, fuzzy logic, model predictive control, and adaptive control can be used [7, 11, 132].

5.2 Dynamic adaptability for form and stress optimization

The integration of form and stress management is largely dependent on adaptive control techniques [35]. Structures are capable of real-time adaptation to changing external loads and environmental factors by dynamically adjusting control settings based on both form and stress conditions [38, 133, 134]. By avoiding both high-stress concentrations and undesired deformations, this dynamic adaptability guarantees both optimal performance and safety [135, 136].

5.3 Learning-based approaches for simultaneous control

Shape and stress are simultaneously controlled by neural networks, which are renowned for their capacity to learn intricate patterns [137, 138]. Neural networks can optimize the distribution of stress and the shape of the structure by using both past data and current feedback [137, 139]. This learning-based strategy works especially well in situations where form and stress have a complex and nonlinear relationship [140].

5.4 Uncertainty management through fuzzy logic

Fuzzy logic is included to help manage the uncertainties in form and stress control [125, 141]. In the face of imperfect information, fuzzy logic offers a framework for decision-making that guarantees the robustness of structural adjustments for shape and stress in unpredictable situations [141]. This method improves a structure’s resistance to changing and erratic circumstances [78, 142].

5.5 Optimal predictive control for form and stress harmony

Through iterative adjustments of control inputs based on predictive models, Model Predictive Control (MPC) excels in maximizing both form and stress [143]. By taking into account both form and stress objectives at the same time, trade-offs between stress management and structural configurations are avoided throughout the optimization process [144, 145].

5.6 Various examples of application of structure-based simultaneous shape and stress control

In structural engineering, combined form and stress control have many real-world uses. These strategies demonstrate the versatility and adaptability of concurrent shape and stress control methodologies, ranging from adaptive building facades that dynamically respond to environmental conditions [7, 10, 11, 31, 132] while managing stress to aerospace structures that optimize both aerodynamics and structural integrity [146, 147]. There are some examples of combined form and stress control, such as beams, trusses [2, 9, 97, 98, 101, 103, 148], spheres [6, 8, 52], antenna structures, cable structures [30, 31, 103, 115, 116], and domes [5, 111] by linear [6, 8, 9, 52, 97, 98, 101, 148] or nonlinear [30, 31] methods. The mentioned examples highlight successful implementations and offer insightful information on the efficacy and practicality of stress control techniques [2, 5, 6, 8, 9, 30, 31, 52, 97, 98, 101, 115, 116, 119, 120, 148, 149, 150].

6. Challenges and future directions

The progression of nonlinear control systems for managing structural shape and stress within structural engineering will give rise to a multitude of opportunities and challenges. The challenges currently encountered by the field’s practitioners and researchers are discussed in this part, along with possible future paths.

6.1 Computational complexity

More computing power is frequently required for the application of complex nonlinear control schemes [151]. Managing computational complexity becomes an increasingly important difficulty as systems become more complicated and real-time responses are required [35]. One persistent issue is manipulating the accuracy of control algorithms with the effectiveness of computing procedures [152].

6.2 Robustness in the face of uncertainties

Nonlinear control systems face difficulties due to the inherent uncertainties in structural engineering, which arise from variations in the environment, material qualities, and load conditions [35, 153, 154, 155]. Although adaptive control and fuzzy logic attempt to manage uncertainties, it is still difficult to guarantee that control algorithms will stay robust in a variety of strange and unpredictable situations [156].

6.3 Advancements in sensing technologies

Sufficient and timely data from sensing technologies are essential for nonlinear control techniques to work well [35, 78]. Continuous sensor advances are essential for improving the accuracy and dependability of control activities [157, 158, 159, 160]. Examples of these sensors include vision-based systems and strain gauges [160]. The development of nonlinear control techniques depends critically on ongoing research in sensor technology.

6.4 Interplay between shape and stress control

Although the integration of stress control mechanisms with shape is a promising option, there are obstacles to comprehending the complex interplay between these factors [2, 7, 14, 17]. A thorough understanding of the complex relationship between stress distribution and structural form is required to maximize synergy without compromising individual objectives [17].

6.5 Future directions

Nonlinear control in structural engineering has a bright future ahead of it. Scholars are presently investigating novel approaches, like the integration of machine learning algorithms, to augment the flexibility of control techniques. Opportunities for autonomous optimization of structural configurations under variable situations are presented by advances in artificial intelligence, specifically in reinforcement learning. More future objectives for studying nonlinear shape and stress control are materials innovation, which includes investigating innovative materials as a means of enhancing nonlinear control techniques. Adaptive smart materials can work in concert with control systems to create new opportunities for materials that dynamically adjust to stress situations, shape memory alloys, and self-healing structures [160].

7. Case studies and applications

Analyzing nonlinear control systems for form and stress in structural engineering in real-world applications offers important insights into the applicability, effectiveness, and flexibility of these approaches. The impact of successful implementations on different structural domains is examined in this section through a variety of case studies.

7.1 Deployable structures for adaptive environments

Deployable structures—whose form dynamically adjusts to changing environmental conditions—have become more and more popular. Examples of case studies demonstrate how adaptive control systems allow structures to adjust to Environments for instance Goliath umbrellas at Nabawi Mosque compound in Medina [161] as shown in Figure 2. With its deployable structures for adaptable situations, Goliath umbrellas at the Nabawi Mosque compound in Medina exhibit the inventiveness of structural engineering. It expands prayer space during busy times, like Ramadan and Hajj, by using modular platforms and temporary umbrellas. Its adaptable layout guarantees a smooth transition with the Prophet’s Mosque, allowing for different audience sizes to be accommodated without compromising the sacredness of the location. It is evidence of creative structural engineering solutions.

Figure 2.

Goliath umbrellas at Nabawi mosque compound in Medina.

7.2 Adaptive morphable structures

Advanced movable structures, which involved altering and controlling the geometric shape of the structures with dynamic motion and altering the behavior of the structures concurrently, were presented at International Expo 2005, Aichi, Japan [162]. He displayed the massive, mobile monument depicted in Figure 3. Three similar movable towers with four moving truss components make up this monument. As a result of the ease with which shape morphing from well-known traditional truss structures can be achieved, as demonstrated in Figure 4, the monument’s shape can be altered to a variety of truss shapes by replacing some of the trusses with linear displacement actuators [163] and adjusting the length of each extendable member (extensible actuator) [164, 165].

Figure 3.

Illustration of the towers displayed during Aichi, Japan’s international Expo 2005 [162].

Figure 4.

Monument shape is altered based on performance trends [162].

7.3 Aerospace structures with dynamic morphing

In the aerospace industry, optimizing aerodynamics through the shaping of aircraft wings and surfaces is largely dependent on nonlinear control systems [166]. For example, Commercial Aircraft Morphing demonstrates how dynamic morphing, increased fuel efficiency [167], and improved overall performance of aeronautical structures may be achieved with the help of adaptive control, neural networks, and model predictive control as shown in Figure 5.

Figure 5.

Diagrams showing the subsystems of the morphing wing gadget [167].

7.4 Bridges with shape and stress optimization

Bridges are an example of vital infrastructure where shape and stress control must be integrated. The case studies were not available; however, the model was demonstrated in the lab to demonstrate how control systems maximize the form and stress distribution of bridge structures [13].

7.5 Tetragonal lattice structure

A shape-morphing control for the space model of a tetragonal lattice system was a case study test validating the nonlinear force method for large deformation control and comparing it to the linear force method [168]. The shape-morphing target was examined in two cases. The first targeting case was approaching the doubly curved surface of the morphing, while the other case was the corner lift of the assembly. In the doubly curved scenario for approaching the target, it required 159 actuators (n_act) by linear control but 606 actuators by nonlinear control out of 1535 members. This great difference from used actuators refers to neglecting the member stress caused by the elongation of other elements. Likewise, for the corner lift scenario, the linear technique overestimated employing almost the whole body of the system as actuators (n_act = 1505), while the nonlinear used 532 actuators for the shape morphing control. The cases demonstrated that compared to the linear technique, the nonlinear controlling approach yields the most fitting results for large deformations of complex assemblies. The findings of both cases are presented in Figure 6 [168].

Figure 6.

Shape morphing control of the tetragonal lattice structure for the (a) linear and (b) nonlinear methods; nodes that are to be moved or pinned are shown by the red circles, and the undeformed structures in the top left corner of each deformation reveal where the actuators are placed; components in gray are fixed, while those in blue are expanding, and those in red are shrinking [168].

8. Conclusions and recommendations

A thorough examination of structural engineering’s nonlinear control techniques for form and stress reveals a vibrant field full of opportunities, difficulties, and advancements. This conclusion summarizes the main conclusions and shows the direction for future research.

8.1 Conclusions

The chapter presents a comprehensive overview of the latest developments in nonlinear control techniques applied to form and stress management in structural engineering. By synthesizing research findings, case studies, challenges, and potential directions, it serves as a roadmap for both scholars and professionals seeking to propel structural engineering into new realms. The findings of this chapter inspire the structural engineering community to deepen their grasp and application of nonlinear control, fostering advancements that will enhance the built environment significantly.

In essence, the chapter offers an in-depth perspective on the evolving landscape of nonlinear control within structural engineering. A pivotal approach highlighted is the fusion of shape and stress control methodologies, which lays the groundwork for resilient, adaptable, and human-centric structural designs. As we navigate through this evolving terrain, collaborative efforts among researchers, practitioners, and experts from diverse fields become indispensable.

The presence of nonlinearities poses significant challenges to traditional control systems, often built upon linear assumptions. Linear control techniques may inadequately capture the true behavior of structures, leading to compromised performance and potential safety hazards. Hence, there is a growing imperative to explore nonlinear control frameworks capable of effectively managing the intricate nonlinear dynamics inherent in structural systems.

8.2 Recommendation

Nonlinear control in structural engineering has a bright future ahead of it. Advances in machine learning, material innovation, and sustainability are areas that researchers are encouraged to investigate. The unification of reinforcement learning, artificial intelligence, and smart materials promises revolutionary discoveries that are in line with the changing needs of the built environment.