Free Flexural Vibration Analysis of Arbitrary Plates With Arbitrary Stiffeners

Abstract

Isoparametric element tends to lock in shear for very thin plates. Though numerical techniques such as reduced-integration or selective reduced-integration are used to avoid this effect, they do not necessarily guarantee the solution to the problem, even if they increase notably the possibility of convergence with the exact solution. In the present formulation, a new four-noded stiffened-plate bending element, having the elegance of the isoparametric element to model the arbitrary shape of the plate but without any numerical disturbing feature like shear-locking problem, is presented. Another unique feature is the arbitrary placement of the stiffener inside the plate element without any restriction of its orientation. Stiffened plates having various shapes, boundary conditions, and disposition of stiffeners are analyzed and compared with available results in the literature wherever possible.