We investigate the systematic design of compliant morphing structures composed of materials reacting to an external stimulus. We add a perimeter penalty term to ensure existence of solutions. We propose a phase-field approximation of this sharp interface problem, prove its convergence as the regularization length approaches 0 and present an efficient numerical implementation. We illustrate the strengths of our approach through a series of numerical examples.

翻译：本研究探讨了由响应外部刺激的材料构成的顺应性变形结构的系统设计方法。我们引入周长惩罚项以确保解的存在性。针对这一尖锐界面问题，我们提出了相场近似方法，证明了当正则化长度趋近于零时该近似的收敛性，并给出了高效的数值实现方案。通过一系列数值算例，我们展示了本方法的优势。