In this paper, the numerical approximation of isometric deformations of thin elastic shells is discussed. To this end, for a thin shell represented by a parametrized surface, it is shown how to transform the stored elastic energy for an isometric deformation such that the highest order term is quadratic. For this reformulated model, existence of optimal isometric deformations is shown. A finite element approximation is obtained using the Discrete Kirchhoff Triangle (DKT) approach and the convergence of discrete minimizers to a continuous minimizer is demonstrated. In that respect, this paper generalizes the results by Bartels for the approximation of bending isometries of plates. A Newton scheme is derived to numerically simulate large bending isometries of shells. The proven convergence properties are experimentally verified and characteristics of isometric deformations are discussed.
翻译:本文讨论了薄弹性弹壳等离子变形的数值近似值。 为此,对于以对称表面为代表的薄壳,演示了如何为对称变形变形转化储存的弹性能量,这样最高顺序的变形术语是四级的。对于这个重制模型,则显示存在最佳的等离子变形。使用分立基尔肖夫三角形(DKT)方法获得的有限元素近近近似值,并演示离散最小化器与连续最小化器的融合。在这方面,本文概括了Bartels在板块弯曲异形近似方面的结果。 牛顿法是用数字模拟大弯曲式贝壳的产物。 已经证实的趋同特性是实验性的,并且讨论了非对称变形特性。