Finite Element Buckling Analysis of Thin Plates with Complicated Geometry

Abstract

The plates used as structural elements in the field of aerospace, offshore, ocean, mechanical, nuclear, and civil engineering take different shapes due to their functional and structural requirements as well as for aesthetic considerations. Their application with complex configuration is of practical importance and requires accurate and efficient analysis of their stability. In this paper, finite element buckling analysis of different complicated shaped thin plates is presented. In the formulation, the arbitrary plan-form of the whole plate is mapped into a square domain where a cubic serendipity shape function is used to represent the complicated geometry and an ACM plate bending element is considered for the displacement function. Many researchers have used different elements to analyze plates but these elements are limited to solve a particular type of geometry only. This element is capable to model different geometries just like isoparametric element without the shear locking problem and generation of spurious mechanisms which is inherent in the isoparametric formulation. The versatility of the element is proved by undertaking different plate geometries. New results are presented as no such geometries are analyzed in any previous published literatures.