State-of-the-Art Nonprobabilistic Finite Element Analyses

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.