ACCURACY EVALUATION OF BOUNDARY CHARACTERISTIC ORTHOGONAL POLYNOMIALS (BCOPs) IN DETERMINING STATIC AND DYNAMIC RESPONSES OF THIN RECTANGULAR PLATES WITH OPENINGS

Abstract

In this article, the efficiency of Boundary Characteristic Orthogonal Polynomials (BCOPs) in analyzing the static and dynamic behavior of thin rectangular plates with openings versus the Finite Element Method (FEM) and the analytical solutions (if they exist), is investigated. Despite this simple procedure, according to the obtained results, the accuracy of BCOPs in most of the studied cases compared to the analytical solutions or those obtained via FEM is acceptable. Besides, different sizes for the openings are assumed and in one case a steel strip is used to stiffen the plate around the opening. Maximum deflection of the plate is the core parameter to be compared seeking the convergence rate of the employed method. Furthermore, natural frequencies of the plate are obtained and compared to assess the capability of BCOPs in dynamic analysis of thin plates. In all of the studied cases, the efficiency of the BCOPs is evident based on its simplicity in comparison with conventional FEM or other competitive methods. Furthermore, one of the main advantages of using these functions in comparison with eigenfunction expansion method in analytical and semi-analytical approaches in the analysis of thin rectangular plates is the existence of all plates’ shape functions for any arbitrary boundary conditions, while this is limited to some special cases in the exact eigen problem solution of the plate.

Keywords

• boundary characteristic orthogonal polynomials
• finite element method
• thin plates with opening
• static analysis
• dynamic analysis