Convergence of the TRUNC plate element
The paper presents a mathematical analysis of the TRUNC element proposed by \textit{P. G. Bergan} [e.g. Comput. Struct. 12, 497-509 (1980; Zbl 0443.73069)] and developed by \textit{J. Argyris, M. Haase, H.-P. Mlejnek} and \textit{P. K. Schmolz} [Int. J. Numer. Methods Eng. 22, 93-115 (1986; Zbl 0593.73077)]. It is shown that the TRUNC element uses the same finite element space as Zienkiewicz's cubic element. The convergence of the TRUNC element for an arbitrary mesh geometry is proved. The original Zienkiewicz element can only converge to the true solution, if the meshes are parallel to three given directions. The new element imposes no restrictions on the meshes and needs less computational cost, while it gives better results in comparison with many other plate elements.
numerical integrations of part of stiffness matrix
scientific article; zbMATH DE number 3999430