Stiffness optimization of multi-material composite structure under dependent load

Aiming at the characteristics that gravity load changes with the disappearance of unit in the topology optimization iteration, the optimization model of multi-material stiffness is established considering the dependent load. The structural stiffness optimization is applied to the multi-material composite structure. The sensitivity of the mathematical formula is derived, and the complete optimization iteration process is given. Base on multi-material theory, the relationship between the multi-material model and the single material model is discussed. Two kinds of models are used to analyze the topology optimization of the structure which contain two kinds of materials and three kinds of materials, respectively. Then, the optimization results of the two models are compared, which are consistent with the laws of mechanical properties of materials. The obtained structure is similar to the actual engineering structure. It demonstrates the method is feasible to solve the topology optimization of a single material or a variety of materials.