ABSTRACT
Four major sources of nonlinear structural response mechanisms, arising from material behavior, geometric deformation, inter-body contact changes, and external load variability are discussed in Section 12.1. General solution techniques for nonlinear response predictions are also introduced in this Section. Section 12.2 summarizes the basic approaches of how material nonlinear response is handled in finite element formulations. Section 12.3 is devoted to the formulation of geometric nonlinear problems. The basic ideas of contact formulations have been discussed in Section 8.5. Section 12.4 in this chapter provides a brief description of how contact status changes can be included in step-by-step simulation of nonlinear structural responses. Section 12.5 describes the integration of nonlinear response mechanisms in step-by-step implicit and explicit dynamic response analyses of structures. Nonlinear response analysis, with deformation-dependent external loading description, is not explicitly discussed in this book. However, it is understood that such changes can be integrated into general nonlinear analysis steps when required. Section 12.6 is devoted to the discussion of material failure propagation in finite element simulation models. Structural form simulation, a very specialized nonlinear structural engineering problem, is discussed in Section 12.7 followed by Section 12.8 presenting a set of practice problems for nonlinear finite element analysis.
