Biharmonic analysis of rectilinear plates by the boundary element method

Abstract

An improved boundary element formulation (BEM) for two‐dimensional non‐homogeneous biharmonic analysis of rectilinear plates is presented. A boundary element formulation is developed from a coupled set of Poisson‐type boundary integral equations derived from the governing non‐homogeneous biharmonic equation. Emphasis is given to the development of exact expressions for the piecewise rectilinear boundary integration of the fundamental solution and its derivatives over several types of isoparametric elements. Incorporation of the explicit form of the integrations into the boundary element formulation improves the computational accuracy of the solution by substantially eliminating the error introduced by numerical quadrature, particularly those errors encountered near singularities. In addition, the single iterative nature of the exact calculations reduces the time necessary to compile the boundary system matrices and also provides a more rapid evaluation of internal point values than do formulations using regular numerical quadrature techniques. The evaluation of the domain integrations associated with biharmonic forms of the non‐homogeneous terms of the governing equation are transformed to an equivalent set of boundary integrals. Transformations of this type are introduced to avoid the difficulties of domain integration. The resulting set of boundary integrals describing the domain contribution is generally evaluated numerically; however, some exact expressions for several commonly encountered non‐homogeneous terms are used. Several numerical solutions of the deflection of rectilinear plates using the boundary element method (BEM) are presented and compared to existing numerical or exact solutions. Copyright © 1990 John Wiley & Sons, Ltd

Publication Title

International Journal for Numerical Methods in Engineering

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