A pseudo-complementary finite element approach for the vibration analysis of thin plates in bending

Abstract

The present paper is concerned with the numerical analysis of the steady-state and transient response of thin elastic plates. Based on a modification of the variational principle due to Hamilton wherein in contrast to the classical formulation not only displacements but also stress resultants represent independent (primal) variables, a new mixed hybrid finite element model is proposed. Introducing separate approximations for the displacement and stress field, stiffness and consistent mass matrix of a triangular plate element with three kinematic degrees of freedom per nodal point are obtained. The performance of the new element scheme is evaluated on the basis of several test examples representing a broad range of circumstances encountered in linear elastokinetic thin plate analysis. The obtained numerical results demonstrate that in terms of efficiency, reliability and accuracy the new element scheme competes most favorably with a series of well-established plate elements.