An effective and straightforward method to implement topology optimization using high-level programming is presented. The method uses the LiveLink for MATLAB, which couples the commercial COMSOL Multiphysics software with MATLAB programming environment via COMSOL Application Programming Interface (API). The integrated environment allows one to implement advanced and customized functions and methods from scratch easily. Topology optimization of an acoustic-structure interaction problem with a mixed displacement–pressure (u/p) formulation is employed to demonstrate the effectiveness of the presented implementation method to design multiphysics problems systematically. The governing equations of the system are derived in a weak form, which is inserted directly in equation-based modeling in COMSOL Multiphysics via MATLAB programming environment. The tight integration of MATLAB and COMSOL Multiphysics allows one to easily pass the matrices and derivatives to perform design sensitivity analysis. A comprehensive code to perform the optimization of the acoustic-structure interaction problem is provided in Appendix. The well-structured code can be used as a platform for educational and research purposes, and it can be extended to other topology optimization applications involving various types of physical problems that use the equation-based modeling functionality of COMSOL.

提出了一种使用高级编程实现拓扑优化的有效且直接的方法。该方法使用 LiveLink for MATLAB，它通过 COMSOL 应用程序编程接口 (API) 将商业 COMSOL Multiphysics 软件与 MATLAB 编程环境耦合。集成环境使人们可以轻松地从头开始实施高级和定制的功能和方法。具有混合位移-压力 ( u)的声-结构相互作用问题的拓扑优化/p) 公式用于证明所提出的实现方法对系统地设计多物理场问题的有效性。系统的控制方程以弱形式导出，通过 MATLAB 编程环境直接插入到 COMSOL Multiphysics 中基于方程的建模中。MATLAB 和 COMSOL Multiphysics 的紧密集成使人们可以轻松地传递矩阵和导数来执行设计灵敏度分析。附录中提供了执行声学-结构相互作用问题优化的综合代码。结构良好的代码可以用作教育和研究目的的平台，