The development of materials with specific structural properties is of huge practical interest, for example, for medical applications or for the development of light weight structures in aeronautics. In this article, we combine shape optimization and homogenization for the optimal design of the microstructure in scaffolds. Given the current microstructure, we apply the isogeometric boundary element method to compute the effective tensor and to update the microstructure by using the shape gradient in order to match the desired effective tensor. Extensive numerical studies are presented to demonstrate the applicability and feasibility of the approach.

翻译：具有特定结构特性的材料的开发具有巨大的实际意义,例如医疗应用或航空轻重结构的开发。在本条中,我们将形状优化和同质化结合起来,以优化脚手架微结构的设计。鉴于目前的微结构,我们采用异构分界要素法来计算有效的电压,并使用形状梯度来更新微结构,以便与理想的有效电压相匹配。我们提出了广泛的数字研究,以证明该方法的适用性和可行性。