论文标题
关于非线性弹性板和壳的材料优化
On Material Optimisation for Nonlinearly Elastic Plates and Shells
论文作者
论文摘要
本文研究了弹性板上硬质和软材料的最佳分布。在等距变形的类别中，研究了带有合并材料硬度功能的基尔chhoff板功能的固定点，并考虑了合规性成本功能。在对称材料分布和负载的对称性假设下，表明圆柱溶液是固定点。此外，证明了圆柱形变形，夹紧矩形板的最佳设计是无琐的，即具有材料分布不仅取决于板上的一个轴向方向。使用合适的有限元离散化和材料阶段的相位场描述，将分析结果与数值优化结果相辅相成。最后，使用数值方法对非异对象变形板和壳的最佳设计进行前景。
This paper investigates the optimal distribution of hard and soft material on elastic plates. In the class of isometric deformations stationary points of a Kirchhoff plate functional with incorporated material hardness function are investigated and a compliance cost functional is taken into account. Under symmetry assumptions on the material distribution and the load it is shown that cylindrical solutions are stationary points. Furthermore, it is demonstrated that the optimal design of cylindrically deforming, clamped rectangular plates is non trivial, i.e. with a material distribution which is not just depending on one axial direction on the plate. Analytical results are complemented with numerical optimization results using a suitable finite element discretization and a phase field description of the material phases. Finally, using numerical methods an outlook on the optimal design of non isometrically deforming plates and shells is given.
