Vibration of thick and thin plates using a new triangular element

Abstract

A triangular element based on Reissner–Mindlin plate theory is developed and it is applied to free vibration analysis of plates in different situations. The element has three corner nodes, three mid-side nodes and an internal node at the element centroid where each node contains three usual degrees of freedom (transverse displacement and bending rotations). To make the element free from the shear locking problem, the formulation is done in an efficient manner taking transverse displacement and transverse shear rotations as the field variables. The degrees of freedom of the internal node are condensed out to improve the computational elegance. As the condensation cannot be done with a consistent mass matrix, a lumped mass matrix having no mass contribution at the internal node is used. In this context two mass lumping schemes are proposed where the effect of rotary inertia is considered in one of these schemes. All these features have made the element quite elegant, which is tested with numerical examples to show its performance.