Three - Dimensional Dynamic Stress Analysis of Sandwich Panels

摘要

A layerwise geometrically nonlinear theory for a thick sandwich plate was developed by introducing assumptions on a variation of transverse strains in the thickness direction of the faces and the core of the plate. An effect of transverse extensibility or compressibility of the core and the face sheets is taken into account, and the terms associated with transverse shear strain of the face sheets and the core are included into the expression for the strain energy. Displacements, obtained by integration of the strain-displacement relations, depend nonlinearly on a coordinate in the thickness direction, and are continuous at the boundaries between the face sheets and the core. The non- linear von-Karman strain-displacement relations are used in order to provide a representation of the moderately large rotations. The in-plane stresses are computed from the constitutive relations in each ply of the face sheets, using each ply's material properties, and the transverse stresses are computed by substituting the in-plane stresses into equations of motion and by integrating the equations of motion. Such a method of computation of the transverse stress components allows one to obtain accurate results, because this method leads to satisfaction of conditions of continuity of the transverse stresses at the boundaries between the face sheets and the core, at the boundaries between the plies of the face sheets, and allows to satisfy stress boundary conditions at both the upper and lower external surfaces. A finite element formulation was developed for a sandwich cargo platform under its impact against the ground, modeled as an elastic Winkler foundation. This formulation was done for a plate in cylindrical bending, and a finite element program was written on the basis of this formulation, with the capability of taking account of damage progression in time.