Finite-Layer Method: Bending and Twisting of Laminated Plates with Delaminations

Abstract

Based on the finite-layer method, considering the multilayered package as a set of jointly deforming layers, a method to analyze laminated plates with delaminations, which enables one to determine all the functions describing the stress-strain state of the plate, including interlayer stresses, is proposed. A refined deformation model of an anisotropic plate-layer taking into account the transverse linear and shear deformations and ensuring the exact fulfillment of boundary conditions on surfaces of the plate with consideration of all derivatives of existing surface loads is presented. Calculation of the multilayer plate is reduced to the solution of a boundaryvalue problem for a system of ordinary differential equations including the interlaminar shear stress. The order of the system depends on the number of layers in the package. The system is stiff, and the boundary value problem is solved by the stable Godunov–Grigorenko numerical method. As examples, the calculations of bending and twisting of two-layered plates with a partial delamination are presented.