A discrete material optimization method with a patch strategy based on stiffness matrix interpolation

A discrete material optimization method with a patch strategy based on the stiffness matrix interpolation is proposed, and a comprehensive technical process of patch discrete material optimization using existing finite element software was developed. This method employs the stiffness matrix instead of the constitutive matrix for material interpolation, which facilitates the optimization process integrated with the existing finite element software. The element stiffness matrix can be derived directly from the finite element analysis, which can not only ensure the correctness of the data, but also reduce the programming work of solving the numerical integration of the composite constitutive matrix. The mathematical model of the patch discrete material optimization is established, which takes the artificial density as the design variable, the minimum compliance as the objective function, and the sequential quadratic programming (SQP) algorithm as the optimization solver. Numerical examples show that by seeking a balance between the number of regions and practical production, the performance of the composite could be further improved using the discrete material optimization method with a patch strategy. Besides, the convergence rate of the optimization is increased by introducing the sum constraints of the design variables and the value functions. The effectiveness and the feasibility of the method were verified.

Automated summary

A discrete material optimization method based on the stiffness matrix interpolation is proposed, with a comprehensive technical process developed using existing finite element software. By using the stiffness matrix instead of the constitutive matrix, the optimization process can be easily integrated with the software. The method has been verified to effectively improve the performance of composite materials.