Robust Topology Optimization Of Thermoelastic Structures With Hybrid Uncertainties

Topology optimization had been applied in actual engineering due to its advantages of more design freedom,high resource utilization efficiency and great application potential.However,with the incre asing complexity of the structural service environment and the high cost of quantifying the accurate parameters,the traditional topological design may have an unpredictable impact on the structural components.On the one hand,structural components in maj or fields such as aerospace,which are more sensitive to performance index,are generally in the situation of high speed,high pressure and high temperature.When mechanical and thermal loads occur simultaneously,the shape and topology of the structural components become complex or even unintuitive.On the other hand,most studies in the field of topology optimization are carried out based on the deterministic assumptions.Nevertheless,the uncertainties due to manufacturing tolerance,load,geometric size,material properties and boundary conditions are widespread in practical engineering.Therefore,it is of great significance to study the robust topology optimization subject to the mechan ical and thermal loads.The main research contents of this paper are organized as follows.(1)A two-scale finite element modeling and analysis method in consideration of the thermal effect is explored.Firstly,a kind of material model with linear elasticity and isotropy is studied.The constitutive theory is established by introducing the equilibrium equation of thermal elasticity problem.Then,the macroscopic finite element model of constant thermo-mechanical coupling is constructed by solving the equation of thermal elasticity problem.The stress-strain information of thermoelastic structure is obtained when the boundary conditions are given.Finally,considering the periodic material structures will be helpful to achieve the performance breakthrough in the complex environment,the effective property of the microscopic periodic structure is obtained by using the homogenization method of progressive expansion.Therefore,the computational method can effectively deal with the two-scale model of thermoelastic structures.(2)A concurrent topology optimization method for th ermoelastic structures is proposed.Based on the bi-directional evolutionary structural optimization(BESO)method,the topology optimization formulations of thermo-mechanical coupling are established by integrating the thermal elasticity problem into topo logical design.At the same time,the mathematical formulation and constraint equation for thermoelastic concurrent topology optimization are constructed to obtain the optimized results in both two scales.The objective is to minimize the macrostructural compliance subject to the mechanical and thermal loads.Finally,several numerical examples are given to show the effectiveness of the proposed method.(3)A robust topology optimization(RTO)method considering uncertainties of material property is developed.Firstly,a set of interval random variables that follow the normal distribution is defined due to the unstable and insufficient samples.The interval random hybrid uncertainty model is established to deal with both aleatory and epistemic uncertainties.In order to effectively solve the problem of uncertainty propagation,a hybrid uncertainty perturbation analysis method(HUPAM)is proposed to calculate the worst case with uncertain parameters.Then,the HUPAM is integrated into the topology optimization formulation.The objective function is represented as a linear combination of the mean and standard variance.By minimizing the maximum value of the objective function,the RTO problem is formulated.In the end,a series of numerical examples are given to demonstrate the effectiveness of the proposed algorithm.(4)Based on the theory of thermoelastic concurrent topology optimization and RTO method,the concurrent RTO model for thermoelastic structures is established.Aim to the influence caused by the uncertainties of structural material parameter and thermal expansion coefficient,the effects of temperature change and uncertain parameters on the final structural topologies are studied.The differences between the deterministic design and the robust design of the thermoelastic structures are compared.The Monte Carlo simulation(MCS)is employed to verify the accuracy of the robust optimization algorithm.Finally,several numerical examples are given to illustrate the necessity of considering thermal effect and the capability of the proposed method in dealing with uncertainty.