Optimal topologies considering fatigue with reliability constraint

The process of design optimization is generally accompanied by a decrease of the level of reliability. It can be even more problematic when one can elaborate topology optimization tasks, where the optimization process is based on material removal in least stressed areas. In order to control the safety level of the structure, it is necessary to include estimation of the probability of failure in the optimization procedure by adding constraint(s) for the reliability index. This approach is called Reliability Based Topology Optimization (RBDO). The lighter/thinner design is more likely to fail due to random factors. Among them, wind or accidental loads are most often mentioned as uncertain effects for structures. In the case of mass production of some parts, there may also be a material parameters or geometrical dimensions, which are characterized by a certain scatter caused by a production accuracy. The aim of this paper is to formulate an iterative algorithm for topology optimization taking into account fatigue based reliability constraints. As the performance function number of cycles has been taken for low cycle fatigue problem. Combination of recently proposed topology optimization method and reliability analysis of the Authors of this presentation may lead to very complex and time consuming procedure. To tackle with this problem a First Order Reliability Method (FORM) is applied. There are several kinds of procedures within the first order approach such as: Reliability Index Approach (RIA) or the family of Performance Measure Approach (PMA) algorithms.