Finite Rotations and Finite Elements of Thin Elastic Shells

建议的调查包括理论和计算 问题研究作者早些时候提出了基本概念。 这个想法源于变形的几何性质， 通常出现在薄壳、板、拱和梁中;这些 变形通常以小应变为特征， 伴随着有限的旋转。 这些特征具有深远的意义 在当代的程序中， 结构的有限元方法。 由于菌株是 小的，相对旋转在元素内是小的。 因此，委员会认为， 可以用线性方程来描述单个单元的变形 方程，如果材料是胡克的，整个描述 该单元由线性方程给出。 然后， 可以引入有限旋转和相关的非线性 全球矩阵的形成。 上述观察结果表明， 用于描述的模型的应用和制定 并预测它们的反应。 但不少 问题仍然没有答案，关于这种准确性的问题， 收敛标准的制定、适用性和实际 这些程序的利弊。 的目的 建议是通过仔细研究理论上的问题来寻求答案。 基，替代泛函，平稳和/或极值 的搜索. 最近 互补泛函的公式化提供了 结束。 数字和符号的计算程序 调查是探索和检验 结果的实用性。

The proposed investigation includes theoretical and computational studies. The underlying concept was presented earlier by the author. The idea stems from the geometrical nature of the deformations which often occur in thin shells, plates, arches and beams; these deformations are usually characterized by small strains but often accompanied by finite rotations. These features have far-reaching consequences in the contemporary procedures for approximating such structures by the method of finite elements. Since the strains are small, relative rotations are small within elements. Consequently, one can describe the deformations of the individual element by linear equations and, if the material is hookean, the entire description of the element is given by linear equations. Then the occurrence of finite rotations and the associated nonlinearities can be introduced in the formation of the global matrix. The foregoing observations suggest practical advantages in the application and formulation of the models which are used to describe the thin structures and to predict their response. However, many questions remain unanswered, questions about the accuracy of such formulation, applicability of convergence criteria, and practical advantages and disadvantages of such procedures. The purpose of the proposal is to seek the answers by scrutinizing the theoretical bases, the alternative functionals, stationary and/or extremal criteria. Recent formulations of the complementary functionals provide means to that end. Computational programs for numerical and symbolic investigations are other means for exploring and for testing the practicality of the results.