Zhiping Qiu

By Wang Lei, Qiu Zhiping and Zheng Yuning

The finite element analysis of a mechanical system is conventionally performed in the context of deterministic inputs. However, uncertainties associated with material properties, geometric dimensions, subjective experiences, boundary conditions, and external loads are ubiquitous in engineering applications. The most popular techniques to handle these uncertain parameters are the probabilistic methods, in which uncertainties are modeled as random variables or stochastic processes based on a large amount of statistical information on each uncertain parameter. Nevertheless, subjective results could be obtained if insufficient information unavailable and nonprobabilistic methods can be alternatively employed, which has led to elegant procedures for the nonprobabilistic finite element analysis. In this chapter, each nonprobabilistic finite element analysis method can be decomposed as two individual parts, i.e., the core algorithm and preprocessing procedure. In this context, four types of algorithms and two typical preprocessing procedures as well as their effectiveness were described in detail, based on which novel hybrid algorithms can be conceived for the specific problems and the future work in this research field can be fostered.

Part of the book: Uncertainty Quantification and Model Calibration

By Qiu Zhiping, Zhang Zesheng and Wang Lei

Fatigue and fracture problems, which lead to 95% of structural failure, have attracted much attention of engineers and researchers all over the world. Compared with experimental method, numerical simulation method based on empirical models shows its remarkable advantages in structure design because of less cost and higher efficiency. However, the application of numerical simulation method in fatigue lifetime prediction is restricted by low accuracy and poor applicability in some circumstances. Most numerical method is based on empirical models. This chapter first reviews various kinds of empirical models of fatigue and fracture problems, including some modifying methods of basic empirical models, which have been widely applied to fatigue lifetime prediction and indicated their advantages and disadvantages. Then, FEM is introduced as an important method to obtain stress intensity factor or crack growth route. At last, this chapter is finished with existing problems and current trends in fatigue lifetime prediction via numerical method.

Part of the book: Contact and Fracture Mechanics