A high precision shear deformable element for free vibration analysis of isotropic trapezoidal plate

Abstract

A high precision triangular element developed by the second author of this paper has been used for free vibration analysis of isotropic trapezoidal plates. The element has twelve nodes at the three sides and four nodes inside the element. Initially, the element has 35 degrees-of-freedom, which has been reduced to 30 by eliminating the degrees-of-freedom of the internal nodes through static condensation. Plate having different side ratios (b/a), boundary conditions and thickness ratios (h/a = 0.01, 0.1 and 0.2) have been analyzed by this shear locking free element. An efficient mass lumping scheme has been recommended, where the effect of rotary inertia has been included. The results obtained by the present element have been compared with the analytical solutions for h/a = 0.01 and have got excellent agreement. The numerical results for h/a = 0.1 and 0.2 have been given as new results.