Development Of Software Module For Structural Topology Optimization With Stress Constraints Based On SiPESC

With the rapid development of optimization theory and computer technology,structural topology optimization has been developed rapidly,and its application in the field of industrial design has become more and more extensive.At present,the topology optimization design of maximum structural stiffness has become mature.Stress is also a necessary factor in engineering design,and stress-related problems can be seen everywhere in engineering.Therefore,the topology optimization problem with stress constraints has gradually become a research hotspot.SiPESC.TOPO,based on SiPESC,is a general structural topology optimization software with engineering application ability in China.It integrates a variety of topology optimization algorithms,however,the function of solving topology optimization problems with stress constraints still needs to be developed.This paper develops the Optistruct data file importer based on the SiPESC platform,and realizes the import function of the topology optimization problem.At present,there are two major difficulties in solving the topology optimization problem with stress constraints,such as the singular solution phenomenon caused by the discontinuity of the stress when the material density is zero;the low efficiency even failure of the optimization algorithm caused by the large scale of the local stress constraint in the finite element framework.Based on SiPESC.TOPO,the module for stress constraints that can solve above difficulties is developed in this paper.Aiming at the development of the parallel optimization algorithm module,Open MP technology is used.Focusing on the topology optimization with stress constraints for large-scale structures,multi-level substructure algorithms is combined.The correctness and applicability of the developed algorithm modules are verified by test examples and engineering examples.For model data import,the data importer is designed based on the SiPESC engineering database interface,which realizes the import function of Optistruct finite element model data and optimization problem setting data,therefore the versatility of the SiPESC platform has been expanded.The correctness of the import function is verified by examples of finite element analysis and topology optimization.Aiming at the topological optimization problem of volume minimization with stress constraint,the mathematical model of the optimization problem is established.In this model,the q-p relaxed method is used to relax the stress constraints,and the grouped K-S aggregation method is adopted to aggregate the local stress constraints into global constraints.The sensitivity analysis formula of the stress response is derived in detail.Based on the response calculation module of SiPESC.TOPO,the development of the topology optimization module with stress constraints is realized by adopting the factory design mode.The correctness and engineering applicability of the optimization module are verified by two-dimensional classic examples and three-dimensional engineering examples respectively.Focusing on the low computational efficiency of topology optimization with stress constraints,Open MP parallel technology is used to develop the parallel stress optimization module in this paper.On the basis of the serial program,the efficiency of the serial optimization program is analyzed,and the method in the serial optimization module is modified into a form that can be executed in parallel.For the main time-consuming program segments,the different parallel schemes is proposed to realize parallel acceleration.The test results of the calculation example shows that the optimization results of the parallel program are consistent with the serial results and the parallel module has good acceleration performance.When topology optimization of large-scale structures is performed,the computational efficiency will be further reduced,and there will be a problem of high memory usage.This paper combines the SiPESC platform’s multi-level substructure algorithm on topology optimization with stress constraints,which greatly reduces the computational scale of FEM analysis and sensitivity analysis in the iterative process and improves computational efficiency.Based on the traditional topology optimization process,a new process is constructed,which realizes the function of topology optimization with stress constraints for large-scale structures.A calculation example with tens of millions of degrees of freedom is designed to verify the feasibility of this method.