Topology Optimization Designs Of Structures Under Stochastic Loads Based On Feasible Domain Adjustment

Currently,deterministic parameters are adopted in most of mechanical structural optimization designs,such as deterministic material parameters,geometric size and external load parameters.In the engineering structural designs,there are some deviations between values of these parameters and their true values,and these parameter deviations or parameter randomness will lead to structural damages or even failures.Therefore,it is of great significance to investigate the structural optimization problems with stochastic parameters,especially load uncertainty.Considering stochastic cases of load values and directions,a robust method of structural compliance topology optimization with multiple constraints,is proposed in this paper.Firstly,explicit approximate expressions of the compliance expected value,its variance and their derivatives are derived;Secondly,an improved feasible domain adjustment scheme and a set of algorithms for robust topology optimization designs are given;The effects of the weighted coefficients of the objective function and the variance of the perturbations on the optimized solutions,are investigated by use of a large number of simulation examples.In order to extend the robust topology optimization method to the displacement constrained optimization problem,a robust approximate compliance topology optimization model with multiple constraints,is constructed,based on the above work.The robust topology compliance optimization method with a volume and multiple displacement constraints is proposed,and its simulation examples are given.Given simulation examples show that the proposed method is feasible and effective,and the optimal topology can be obtained in a binary way.Conclusions can be obtained as follows:stochastic cases of loads have a significant impact on the results of topology optimization;topology optimization designs of structures under stochastic loads are of important theoretical significance and engineering application values.