Vibration of plates in different situations using a high-precision shear deformable element

Abstract

A high-precision thick plate element proposed by the last author of this paper has been applied to free vibration analysis of plates to study its performance. The element has a triangular shape and it has three nodes at its corners, three mid-side nodes on each side and four nodes within the element. The transverse displacement and rotations of the normal have been taken as independent field variables and they have been approximated with polynomials of different orders. This has not only helped to include the effect of shear deformation but also made the element free from locking in shear. Initially, the number of degrees of freedom of the element is 35, which is reduced to 30 by eliminating the degrees of freedom of the internal nodes. This has been done through static condensation. To facilitate the condensation process, efficient mass lumping schemes have been recommended to form the mass matrix having zero mass for the internal nodes. Recommendation has also been made for the inclusion of mass for rotary inertia in a lumped mass matrix. Numerical examples of plates having different shapes and boundary conditions have been solved by this element. Examples of plates having internal cutout and concentrated mass have also been studied. The results obtained in all the cases have been compared with the published results to show the accuracy and range of applicability of the present element.