A boundary element approach to buckling of laminated plates subjected to arbitrary in-plane loading

Abstract

Laminated plate buckling is analyzed by the boundary element method (BEM). Ignoring bending stretching coupling, a solution is first sought for the membrane stresses due to arbitrary in plane loading. Using the stress function concept, it is shown that this problem is mathematically equivalent to the plate-bending problem.
Based on this similarity, a new boundary element formulation is developed for the prediction of the pre-buckling membrane state of stress in an anisotropic plate. The integral equations for the buckling mode are then derived from a variational principle using the fundamental solution of the plate-bending problem. An irreducible domain integral depending on plate deflection rather than curvatures is numerically accounted for by adopting deflection modeling over the plate in addition to boundarymodeling. Linear discontinuous boundary elements as well as domain cells are used along with special schemes for the approximation of jump term at corners.
Analytical integration of singular integrals is performed over elements containing the source point. Thus a set of integral equations is transformed into an eigenvalue problem from which the critical load is evaluated. The reliability of the proposed analysis is established by comparing BEM predictions with solutions available from the literature or obtainable through a general purpose finite element program.

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