Boundary element modelling of non-linear buckling for symmetrically laminated plates

摘要

The non-linear buckling of composite laminates, triggered by geometric imperfections, is here analysed adopting a boundary element methodology. The non-linear theory for thin anisotropic plates couples in-plane forces causing buckling with the consequent bending deformation. The adopted formulation for in-plane forces in terms of the stress function is mathematically identical to that for the bending problem, thus boundary integral equations and fundamental solutions of the same form are used. Differential equations governing increments of the stress function and the deflection are obtained; the resulting integral equations include irreducible domain integrals depending on powers or products of the second derivatives of the stress function and the deflection. The latter are calculated through complementary integral equations obtained from the original ones by differentiating the field variables in the domain. The solution process accounts for the domain integrals through an iterative scheme; thus there is no need for modelling any field variables in the plate domain although domain meshing is necessary for performing numerical integrations. The boundary is meshed into quadratic discontinuous elements while the domain is divided into triangular cells with linear discontinuous variation of the relevant field variables for integration purposes. The analysis is implemented through a suit of C codes and applied to a rectangular symmetrically laminated plate. Its predictions are compared with published results obtained by other methods. The accuracy and limitations of the formulation are discussed and alternative approaches for expanding its scope pointed out.