We present a novel approach to topology optimization based on thermodynamic extremal principles. This approach comprises three advantages: (1) it is valid for arbitrary hyperelastic material formulations while avoiding artificial procedures that were necessary in our previous approaches for topology optimization based on thermodynamic principles; (2) the important constraints of bounded relative density and total structure volume are fulfilled analytically which simplifies the numerical implementation significantly; (3) it possesses a mathematical structure that allows for a variety of numerical procedures to solve the problem of topology optimization without distinct optimization routines. We present a detailed model derivation including the chosen numerical discretization and show the validity of the approach by simulating two boundary value problems with large deformations.

我们提出了一种基于热力学极值原理的拓扑优化新方法。这种方法具有三个优点：（1）它适用于任意超弹性材料配方，同时避免了我们先前基于热力学原理进行拓扑优化的方法所必需的人工程序；（2）解析地满足了有限的相对密度和总结构体积的重要约束，大大简化了数值实现；（3）它具有一个数学结构，可以使用多种数值程序来解决拓扑优化问题，而无需使用不同的优化例程。