A New Rectangular Finite Element for Static and Dynamic Analysis of Arbitrarily Tapered Plates

Abstract

This paper presents the formulation of a new efficient and conforming rectangular finite element for analysis of thin plates with any arbitrary variation of thickness along both edges. Shape functions of this new element are derived from multiplying shape functions of non-prismatic Euler–Bernoulli beam extracted from basic displacement functions. To provide [Formula: see text] consistency along the edges of elements, twist is added to conventional degrees of freedom, namely deflection and slopes resulting in an element with 16 degrees of freedom. The proposed element is used to solve various static and dynamic problems, and it is seen that the convergence of a new formulation occurs with much fewer elements compared to existing finite elements as a direct result of considering the variation of geometry in the derivation of shape functions, which renders the formulation competitive in both exactness and economy.