A Boundary Element Method Based Meshless Method for Buckling Analysis of Elastic Plates

摘要

In this paper a BEM-based meshless method is developed for buckling analysis of elastic plates. The presented method is achieved using the concept of the Analog Equation Method (AEM). According to this method the original eigenvalue problem for a governing differential equation of buckling is replaced by an equivalent problem for plate bending problem subjected to an "appropriate" fictitious load under the same boundary conditions. The fictitious load is established using a technique based on BEM and approximated by using the radial basis functions. The eigenmodes of the actual problem are obtained from the known integral representation of the solution for the classical plate bending problem, which is derived using the fundamental solution of the biharmonic equation. Thus, the kernels of the boundary integral equations are conveniently established and evaluated. The presented method has all the advantages of the pure BEM. To validate its effectiveness, accuracy as well as applicability of the proposed method, numerical results of various problems are presented.