Research On Non-probabilistic Reliability-based Topology Optimization Method For Stress Constraint

Generally,the Deterministic Topology Optimization(DTO)of continuum structure does not consider the parameter uncertainty in the structure and ignores the influence of the parameter uncertainty on the structure.However,in engineering practice,there are inevitably uncertainties related to the parameters of the structure,and these uncertainties will lead to certain failure risk of the structure,making the safety of the structure is poor.In addition,many factors will lead to insufficient sample data,so it is difficult to accurately build a probabilistic reliability model.Therefore,Non-probabilistic Reliability-based Topology Optimization(NRBTO)considering structural uncertainty is of great significance to engineering practice.In this paper,the Optimization Criterion(OC)method and Heaviside projection function are improved,and the uncertainty of material strength is considered.A new Non-probabilistic Reliability-based Topology Optimization(NRBTO)method based on evidence theory is proposed.Based on this idea,this paper has carried out and completed the following research work:(1)The gray element filtering technology based on improved OC method and improved Heaviside projection function is proposed.Firstly,aiming at the problem of low iteration efficiency of the bi-section method nested in the OC method,the iterative formula of the advance and retreat method is modified,and the bi-section method nested in the OC method is replaced.The results of several examples show that the proposed method can significantly improve the convergence speed,and the change of compliance after convergence can be ignored,and even the structures with lower compliance can be obtained.Secondly,aiming at the problem that traditional Heaviside projection function calls element density matrix too many times,a new Heaviside projection function is proposed.The Heaviside projection function and its derivative contain only a first order term of density,and do not contain a second order term of density.The results of several examples show that the Heaviside projection function can reduce the number of calls of element density matrix and obtain structures with lower flexibility and fewer gray elements.(2)A stress-constrained topology optimization method based on the improved Adaptive Volume Constraint(AVC)method is proposed.In this chapter,the iterative formula of the AVC method is modified,and the constraint condition is satisfied by adjusting the volume fraction,so that the topology optimization structures can meet the design requirements,and the complex sensitivity derivation in the traditional stress-constrained topology optimization method is avoided.The computational results of several numerical examples demonstrate the effectiveness of the proposed method.(3)A new NRBTO method considering the uncertainty of material strength is proposed.For the problem that the sample data of element stress is limited,it is difficult to construct probability reliability analysis model.In this chapter,the evidence theory is adopted to analyze non-probabilistic reliability of the structure and the complex sensitivity derivation is avoided by the AVC method.The results of several numerical examples show that the proposed method can significantly reduce the plausibility measure of structural and improve the reliability of structures.