Multi-objective Topology Optimization of Thermo-mechanical Compliant Mechanisms

The material characteristics of a structure will change with temperature variation,and will induce stress within the structure.Currently,the optimal design for the topology of compliant mechanisms is mainly performed in single physical field.However,when compliant mechanisms work in high temperature environments,their displacement outputs are generated not only by mechanical load,but also by the temperature variation which may become the prominent factor.Therefore,the influence of temperature must be considered in the design.In this paper,a novel optimization method for multi-objective topology of thermo-mechanical compliant mechanisms is presented.First,the thermal field is analyzed with finite-element method,where the thermal strain is taken into account in the constitutive relation,and the equivalent nodal thermal load is derived with the principle of virtual work.Then the thermal load is converted into physical loads in elastic field,and the control equation of the thermo-mechanical compliant mechanism is obtained.Second,the mathematical model of the multi-objective topology optimization is built by incorporating both the flexibility and stiffness.Meanwhile,the coupling sensitivity function and the sensitivity analysis equations of thermal steady-state response are derived.Finally,optimality criteria algorithm is employed to obtain numerical solution of the multi-objective topology optimization.Numerical examples show that the compliant mechanisms have better performance and are more applicable if the temperature effect is taken into account in the design process.The presented modeling and analysis methods provide a new idea and an effective approach to topology optimization of compliant mechanisms in electrothermic coupling field and multiphysics fields.