An integral-equation formulation of nonlinear deformation in a stack of buffered plates

An integral-equation formulation has been derived for nonlinear deformation in a stack of buffered Kirchhoff plates. The plates are assumed to follow a nonlinear bending moment-curvature law and the buffer material to follow the generalized Hooke’s law. By employing the recently derived special Green’s function for multilayers with interfacial membrane and flexural rigidities as the kernel, the integral-equation formulation only involves the surface loading area (for application to an indentation problem) and the portion of plates undergoing nonlinear deformation. Based on the integral equation, an efficient and accurate boundary element method has been derived to numerically solve the cylindrical indentation problem of the material with a bilinear flexural bending law for the plates. Numerical examples are presented to show a progressive damage process of yielding across a stack of plates as well as to demonstrate the validity and accuracy of the present integral-equation formulation.