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

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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.