STRUCTURAL LIGHT DESIGN FOR STEADY HEAT CONDUCTION USING MULTI-MATERIAL

In topology optimization problems of structures containing multiphase materials, it is common practice to set the volume constraint of each constituent phase or total mass of entire constituent phase constraint to control the final material usage. On the practical engineering background for lightweight design, it is of significance that the minimized weight is taken as the objective in optimal model from the engineering point of view. To solve the topology optimization problem of steady heat conductive with the multiple candidate materials, a new modeling method of weight minimization with the given thermal compliance constraint under multiple load cases is proposed. Following the modeling manner of independent continuous mapping method, two sets of independent topological variables are employed to identify elemental thermal conductive matrix and elemental weight, respectively. The sensitivities of thermal compliance and global weight with respect to the design variable are derived, and their approximate expressions are calculated based on the first-order and second-order Taylor expansion. To eliminate checkerboard patterns and mesh-dependence, the first term of the constraint function is filtered as a solution of the partial differential equation, which also ensures the constraint equation is consistent. The approximate optimal model with the objective and constraint in the form of quadratic and linear function is established. The topological optimization model is solved by dual sequential quadratic programming. Various effects such as the constraint value of thermal compliance, the selection of multiple materials, and the multiple constraints in multiple load cases on the optimal result are discussed in four 3D numerical examples. The results demonstrate the feasibility and effectiveness of the proposed optimization approach regarding structural light design using multi-material in steady heat conduction.