Extended Bi-directional Evolutionary Structural Optimization Method For Stress Constrained Structural Topology Optimization Design

Topology optimization is an effective design method with high degree of design freedom and has attracted many researchers from all kinds of area with successful applications in industry during several decades.At present,most of research work on topology optimization concentrates on compliance minimization design rather than the stress-based optimization design.There are three additional challenges in stress-based optimization design compared to compliance minimization design,they are the so-called “singularity” phenomenon,the local nature of stress constraint and the highly nonlinear stress behavior.This paper proposes an extended bi-directional evolutionary structural optimization(BESO)method for stress-based optimization design for the first time and has been proved to be very effective.This paper consists of three parts.The first part proposes an evolutionary topology optimization method for stress minimization design based on BESO method.The p-norm stress aggregation scheme is adopted for the measure of global stress level.A computationally efficient sensitivity number formulation is derived from the adjoint method.The proposed method has been shown efficient and practical in reducing the stress level of optimization structure through a series of benchmark designs including the L bracket design.The second part combines the traditional compliance objective function with the p-norm stress aggregation scheme by introducing one or multiple Lagrangian multipliers based on above method to realize double restraint of material dosage and strength;the real maximum stress of optimization structure is adopted as the judgement criteria of updating Lagrangian multipliers to constrain stress level strictly;a series of comparison studies on benchmark designs have validated that this method can effectively decrease the compliance of optimization structure while limit the stress level below the allowable stress level.The third part applys the two methods introduced in chapter 2 and 3 to thermal elastic structures optimization design considering the coupling impact of mechanical load and temperature load.The analytical sensitivity number formulation of stress indicators under the thermo-mechanical coupled load is derived by adjoint method;the optimization design results validated that this method can effectively deal with the thermal elastic structures optimization design while strictly limits the maximum stress below the permissible stress.