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

许多关于连续弹性和弹塑性物体的理论对许多实际问题都能给出可接受的结果。在继续寻找更好的非线性和非弹性行为理论的同时，也在继续寻找离散近似的方法，这些方法提供了准确、可靠和经济的手段来利用现有的理论和计算设施。研究的重点将集中在简单三角形和四边形单元的行为和固有困难，特别是与横向剪切变形相关的过度刚度。胡和津定理将被用来作为一种工具来获得洞察力，追踪刚性的起源，并为有效的“平面”单元提供合理的基础。这项研究还将探索实施离散(基尔霍夫)约束抗横向剪切的合理方法。

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.