Hybrid Stress and Analytical Functions for Analysis of Thin Plates Bending

Abstract

In this paper, two efficient elements for analyzing thin plate bending are proposed. They are a triangular element (THS) and a quadrilateral element (QHS), which have 9 and 12 degrees of freedom, respectively. Formulations of these elements are based on hybrid variational principle and analytical homogeneous solution of thin plate equation. Independent fields in hybrid functional are internal stress and boundary displacement field. The internal stress field has been calculated using analytical homogeneous solution and boundary field is related to the nodal degree of freedoms by the boundary interpolation functions. To calculate these functions, the edges of element are assumed to behave like an Euler–Bernoulli beam. The high accuracy and efficiency of the proposed elements are demonstrated in the severe tests.