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A boundary element solution of the plate buckling problem
Abstract Boundary integral equations are obtained from the variational equation governing the buckling mode of a thin elastic plate through the well established procedure of introducing the two fundamental solutions of the classical plate bending problem to the variational functionals. The existence in these equations of domain integrals containing the unknown lateral post-buckling deflection of the plate requires the introduction of domain in addition to boundary unknowns in the formulation. Through the boundary and domain discretisation, two linear algebraic systems of equations are obtained from which the boundary unknowns are eliminated and the eigenvalue problem for the buckling load and the buckling mode is thus formulated. Two alternative approximations of the post-buckling deflection have been tried for the evaluation of the domain integrals. The first involves finite element type triangular cells, the second trigonometric series. The various examples solved include simply supported or clamped square plates under a variety of edge loadings as well as an equilateral triangular plate under uniform edge compression. The numerical results obtained demonstrate the validity of the formulation through the convergence of the approximate model indicating at the same time the degree of accuracy which can be achieved.
A boundary element solution of the plate buckling problem
Abstract Boundary integral equations are obtained from the variational equation governing the buckling mode of a thin elastic plate through the well established procedure of introducing the two fundamental solutions of the classical plate bending problem to the variational functionals. The existence in these equations of domain integrals containing the unknown lateral post-buckling deflection of the plate requires the introduction of domain in addition to boundary unknowns in the formulation. Through the boundary and domain discretisation, two linear algebraic systems of equations are obtained from which the boundary unknowns are eliminated and the eigenvalue problem for the buckling load and the buckling mode is thus formulated. Two alternative approximations of the post-buckling deflection have been tried for the evaluation of the domain integrals. The first involves finite element type triangular cells, the second trigonometric series. The various examples solved include simply supported or clamped square plates under a variety of edge loadings as well as an equilateral triangular plate under uniform edge compression. The numerical results obtained demonstrate the validity of the formulation through the convergence of the approximate model indicating at the same time the degree of accuracy which can be achieved.
A boundary element solution of the plate buckling problem
Syngellakis, Stavros (author) / Kang, Man (author)
Engineering Analysis ; 4 ; 75-81
1987-01-01
7 pages
Article (Journal)
Electronic Resource
English
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