Analysis of Tapered Thin Plates Using Basic Displacement Functions

Abstract

Presenting new functions, basic displacement functions (BDFs), a novel method is introduced for the analysis of arbitrarily tapered thin plates in preference to primarily mathematically based methodologies. BDFs are obtained through applying unit load theorem and considering two orthogonal strips of unit width in tapered plates based on static deformations. It is shown that new shape functions and consequently structural matrices could be derived in terms of BDFs through a mechanical approach. On the other hand, BDFs could be used to calculate new shape functions, whereas Hermitian functions are used in several elements such as ACM and BFS. It is demonstrated that the accuracy of these new shape functions is significantly improved by considering the geometrical and mechanical properties of the plate element in the evaluation of the structural matrices. So, contrary to usual shape functions used in FE methods, they are susceptible to the thickness variation and then higher accuracy and more rapid convergence could be expected with fewer elements. In order to verify the competency of the proposed method, several numerical examples for classical boundary conditions are carried out and the results are compared with those in the literature.