Reliability-Based Structural Optimization of an Elastic-Plastic Beam

The application of reliability-based optimization to an elastic-plastic beam is studied. The objective is to demonstrate the benefits of reliability-based optimization over the deterministic optimization in such applications where the design requirements of the member tolerate some plastic behavior. Also, some of the difficulties that one might encounter while performing reliability-based optimization of elastic-plastic beams are addressed. A graphical method was used here to avoid the problems of high nonlinearity and derivative discontinuity of the reliability function. The method starts by obtaining a deterministic optimum design that has the lowest possible weight for a prescribed safety factor, and, based on that design, the method obtains an improved optimum design that has either a higher reliability or a lower weight or cost. In this application three failure modes are considered for an elastic-plastic beam of T cross section under combined axial, bending, and shear loads. The failure modes are based on the beam total plastic failure in a section, buckling, and maximum allowable deflection. The results show that it is possible to get improved optimum designs (more reliable or lighter) using reliability-based optimization as compared to the design given by deterministic optimization. Also, the results show that the reliability function can be highly nonlinear with respect to the design variables with discontinuous derivatives.