Thermal-mechanical Coupling Topology Optimization Considering Random-interval Hybrid Uncertainty

Topology optimization method is a kind of structural optimization design method,which uses a given optimization algorithm and iterates repeatedly to obtain the best distribution of materials in the structural design area on the premise of satisfying the constraint conditions.To a certain extent,this method overcomes the problems of long cycle,low utilization efficiency of materials,and difficulty in realizing innovative design of structures due to the limitation of past design experience of engineers,which can effectively reduce the development cost of structures and improve the performance of structures.Traditional topology optimization methods mostly consider the single mechanical load.However,in modern high-end equipment design,the structure is often subjected to extreme conditions of complex loads,which will be coupled by multiple physical fields,especially thermal fields,and the mechanical or heat transfer performance of the structure will be significantly affected.Therefore,in order to avoid the failure of the structure under the coupling of thermal field,it is very important to consider the coupling of thermal field in topology optimization design.However,in recent years,the research on thermal-mechanical coupling topology optimization is based on the deterministic assumption of parameters,without considering the multi-source uncertainties such as material properties,size,boundary conditions and external loads caused by various subjective and objective factors in practical engineering problems.Among these uncertain parameters,some parameters have enough experimental data to accurately describe their probability distribution,while some parameters do not have enough experimental data due to measurement difficulties or cost constraints,and only know their approximate distribution interval,that is,the random-interval mixed uncertainty problem.In order to improve the safety of structures under the influence of these uncertainties,it is of great scientific research and practical significance to study the robust topology optimization design method of thermo-mechanical coupling structures under the influence of random-interval mixed uncertainties.Based on the above ideas,this paper will include the following three aspects:(1)Considering the coupling effect of thermal field,the structure is analyzed by thermalmechanical coupling finite element method,and its finite element equilibrium equation is deduced.Based on the variable density method,the penalty function between structural design variables and thermal and mechanical material parameters is defined,and the topological optimization model of thermal-mechanical coupling structure is constructed.(2)Considering the random-interval mixed uncertainty in practical engineering,in order to solve the uncertain performance response of the structure,the orthogonal polynomial expansion is used to analyze the mixed uncertainty,and the univariate dimension reduction integral method is introduced to solve the polynomial expansion coefficient,so as to solve the problem that the calculation amount in the mixed uncertainty analysis increases rapidly with the increase of the number of variables.(3)Based on the hybrid uncertainty analysis method proposed in this paper,an efficient robust thermo-mechanical coupling topology optimization method is developed.Firstly,a robust objective function considering the worst case is defined and a robust thermo-mechanical coupling topology optimization model is constructed based on it.Then,the interval boundary of low-order moment of structural performance is solved by orthogonal polynomial method based on univariate dimension reduction integral,and then the objective function value of robustness is obtained Finally,based on the uncertainty analysis theory,the sensitivity of topological design variables is deduced and solved by gradient-based optimization algorithm,so as to obtain the robust topological configuration of the thermo-mechanical coupling structure.