Finite element free flexural vibration analysis of arbitrary plates

Abstract

In the analysis of plates with arbitrary geometry, the isoparametric element is widely used because of its capability to model an arbitrary geometry successfully. But the isoparametric element tends to suffer from the problem of shear locking when applied to very thin plates which are common to many practical structures. Though techniques such as reduced integration or selective integration are used to avoid this effect, they do not necessarily guarantee the solution to the problem and they may lead to the generation of zero energy spurious mechanisms. In this paper a new approach for the analysis of plates of arbitrary shapes is used which successfully models the arbitrary shape of the plate like isoparametric element. But in this new element as the shear deformation is ignored by using Kirchhoff plate element all the above discrepancies inherent in the isoparametric element are completely avoided. Thus is developed for the first time a rectangular element through which a Kirchhoff plate of any arbitrary shape can be analysed.