Two-scale shape optimisation based on numerical homogenisation techniques and variational sensitivity analysis
Two-scale shape optimisation based on numerical homogenisation techniques and variational sensitivity analysis
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DOI：
10.1007/s00466-020-01955-6
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发表时间：
2021-03
影响因子：
4.1
通讯作者：
Wojciech Kijanski;F. Barthold
中科院分区：
文献类型：
--
作者：
Wojciech Kijanski;F. Barthold
这一贡献提出了非线性弹性结构的两尺度形状优化的理论和计算框架。特别是，复合材料（基体-夹杂物）微结构在静载荷和体积型设计约束下的最小顺应性优化问题。基于连续介质力学的noll固有的无框架公式，通过增强变分（形状）灵敏度分析的公式，扩展了基于均质化的fesme格式。得到的总体双尺度灵敏度信息耦合了微观和宏观尺度上的形状变化。一个数值例子证明了所提出的变分灵敏度分析和（形状）优化框架的能力。研究涉及一个网格变形方案的设计参数化在宏观和微观尺度。
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 FEscheme is extended by an enhanced formulation of variational (shape) sensitivity analysis based onNoll’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.