Bi-directional Evolutionary, Reliability-based, Geometrically Nonlinear, Elasto-Plastic Topology Optimization, of 3D Structures

An extension of bi-directional evolutionary structural optimization, by considering three-dimensional geometrically nonlinear reliability-based elasto-plastic topology optimization, is presented in this study. Due to the important role of the existence of uncertainties to make structural design more practical, this study considers the reliability -based design. Thus, for probabilistic purposes, volume fraction is considered random. The reason of considering the volume fraction as random variable that the application of reliability-based topology optimization shows different topological results comparing to those which are obtained through deterministic designs. By adopting Monte-Carlo technique, the reliability indices are calculated based on the failure probabilities. Different values of volume fractions are considered to explore the effect of changing it on the resultant topologies in case of deterministic design. Furthermore, study the influence of considering different values of reliability indices on the results of probabilistic designs. The plastic-limit analysis is considered in this study in case of elasto-plastic models. A 3D elasto-plastic L-shape beam is considered as a benchmark problem to demonstrate the proficiency of the proposed method. In addition, 3D cantilever beam is considered for deterministic and probabilistic topology optimization designs in cases of elastic and elasto-plastic materials.