This contribution presents a theoretical and computational framework for two-scale shape optimisation of nonlinear elastic structures. Particularly, minimum compliance optimisation problems with composite (matrix-inclusion) microstructures subjected to static loads and volume-type design constraints are focused. A homogenisation-based FE\(^2\) scheme is extended by an enhanced formulation of variational (shape) sensitivity analysis based on Noll’s intrinsic, frame-free formulation of continuum mechanics. The obtained overall two-scale sensitivity information couples shape variations across micro- and macroscopic scales. A numerical example demonstrates the capabilities of the proposed variational sensitivity analysis and the (shape) optimisation framework. The investigations involve a mesh morphing scheme for the design parametrisation at both macro- and microscopic scales.

这一贡献为非线性弹性结构的两尺度形状优化提供了理论和计算框架。特别地，着重考虑了复合（基体包含）微结构在静态载荷和体积类型设计约束下的最小柔度优化问题。基于均质化的FE \（^ 2 \）方案通过基于Noll的变分（形状）灵敏度分析的改进公式得到扩展固有的，无框架的连续体力学公式。所获得的总体两尺度灵敏度信息耦合了微观和宏观尺度上的形状变化。一个数值示例说明了所提出的变异敏感性分析和（形状）优化框架的功能。研究涉及用于宏观和微观尺度的设计参数化的网格变形方案。