An Investigation of Simple Finite Elements Via the Hu- Washizu Theorem

连续弹性体和弹塑性体的许多理论， 已知对许多实际问题给出可接受的结果。 而 寻求更好的非线性和非弹性行为理论 继续，搜索也继续为离散的方法， 提供准确、可靠和经济的方法， 利用现有的理论和计算设备。 研究 将重点放在简单的行为和固有的困难 三角形和四边形元素，特别是，过度 与横向剪切变形有关的刚度。 的 Hu-Washizu定理将被用作获得见解的工具， 追溯刚度的来源，并提供合理的依据 一个有效的“扁平”元件。 本研究还将探讨合理的 实现横向离散（基尔霍夫）约束的方法 切变

Numerous theories for continuous elastic and elastic-plastic bodies are known to give acceptable results for many practical problems. While the search for better theories of nonlinear and inelastic behavior continues, the search also continues for methods of discrete approximations which provide accurate, reliable and economical means to utilize existing theories and computational facilities. The research will focus on the behavior and inherent difficulties in the simple triangular and quadrilateral elements, in particular, excessive stiffnesses associated with transverse shear deformations. The Hu-Washizu theorem will be employed as a tool to gain insights, to trace the origins of the stiffnesses and to provide rational bases for an effective "flat" element. The study will also explore rational means to implement discrete (Kirchhoff) constraints against transverse shear.