Inelastic Analysis of Transverse Deflection of Plates by the Boundary Element Method

Abstract

A numerical scheme for time-dependent inelastic analysis of transverse deflection of plates of arbitrary shape by the boundary element method is presented in this paper. The governing differential equation is the inhomogeneous biharmonic equation for the rate of small transverse deflection. This complicated boundary-value problem for an arbitrarily shaped plate is solved by using a novel combination of the boundary element method and finite-element methodology. The number of unknowns, however, depends upon the boundary discretization and is therefore less than in a finite-element model. A combined creep-plasticity constitutive theory with state variables is used to model material behavior. The computer code developed can solve problems for an arbitrarily shaped plate with clamped or simply supported boundary conditions and an arbitrary loading history. Some illustrative numerical results for clamped and simply supported rectangular and triangular plates, under various loading histories, are presented and discussed.

BEM formulation for von Kármán plates

“…Although the integrals along the cell sides in Eq. (12) are not singular, one can use the same proposed sub-element scheme to compute the quasi-singular boundary elements to improve the computed vales.…”

“…(5)- (7) can be transformed to cell side integrals using a transformation similar to the one employed to obtain Eqs. (12) and (15). The integrals containing the kernels w*, i and w*, ij , in Eqs.…”

“…One of the first works treating this subject was proposed by Morjaria [12]. Kamiya and Sawaki [13] have proposed a BEM formulation for elastic plates governed by the Berger equation.…”