Researches On A Topology Optimization Method And Its Application Of Structures Under Multiple Load Cases Including Ill Loaded Case

In a structural topology optimization process of the conventional optimization methods considering multiple load cases,if there is a load case with some weak loads and strong loads or a load case with only weak loads except for a strong load case,and the weak loads are not located in the transmission path of the strong load,there will be no material to support the weak loads in the final optimal structure.It is called as an ill-loaded problem of topology optimization.Some parts of important load-bearing mechanical structures in engineering should be reserved to be used for the installation of sensors or some working platforms,and it means that these structures are subject to a load case with some weak loads and strong loads or a load case with only weak loads.Therefore,researches on methods of solving the ill-loaded problem possess important engineering application value and theoretical significance?First of all,based on the conventional SIMP method,another SIMP method,based on a feasible domain adjustment,namely a FDA-SIMP method,is proposed.The effects of different moving limits and initial topologies on the optimal structural topology obtained by FDA-SIMP are investigated.Then,a duplicate compliance aggregation function of a structure under multiple load cases is built,and a new continnum topology optimization model is formed in order to solve the ill-loaded problem.Based on the rational approximation for material properties(RAMP)and the Method of Moving Asymptotes(MMA),explicit convex and separable quadratic approximate functions of objective and constraint functions are derived.A compliance topology optimization approach for multiple load cases,possessing convergence,is proposed by adopting a smooth dual algorithm.Finally,a large number of numerical simulation examples are given,and simulation designs of several engineering structures under ill-loaded cases are completed.Comparing to the existing methods,it is concluded from given examples that the proposed method can solve the ill-load problem of structural compliance topology optimization under multiple load cases,and may obtain a more optimal topology with clear 0/1 distribution than the existed methods.The research work possesses important engineering application value and theoretical significance.