A boundary method using equilibrated basis functions for bending analysis of in-plane heterogeneous thick plates

N. Noormohammadi, B. Boroomand

Archive of Applied Mechanics. 91:487-507

Abstract

A simple boundary method is developed for the solution of isotropic thick plates with in-plane arbitrarily variable material properties or thickness. Equilibrated Basis Functions (EqBFs) which have proved to be effective in a variety of problems, are adopted for the bending problem of thick plates. The bases are created through a weighted residual approach over a fictitious rectangular domain so as to approximately satisfy the Partial Differential Equation (PDE) of the problem. This omits the necessity of the bases to analytically satisfy the equilibrium, thus simplifying the application of the method. Boundary conditions are applied to the approximate solution through a collocation technique, which considerably reduces its computational expenses. Mindlin’s first order and Levinson’s third order shear deformation theories are adopted for the formulation. To accommodate more complicated geometries, a simple domain decomposition approach is also developed.

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