Energy approach to a linearization contact problem of simply supported cross-ply laminated composite plate

The nonlinear contact problem of laminated composite plate is linearized by inverse method, i.e. the contact zone and the loading distribution with adjustable parameter on contact zone are assumed to be given to solve the curvature of indenter––a rigid sphere. By means of the principle of superposition, the loading state is decomposed into symmetric state and antisymmetric state. The antisymmetric state is decomposed further to obtain simpler loading state for analysis. The Fourier series and Legendre series are applied to describing the displacement field of contact loading states, and the principle of minimum potential energy is used to determine the unknown coefficients of the above series. Then the displacement and stress fields of the laminated composite plate are known. The adjustable parameter of loading distribution is used to satisfy the compatibility conditions of displacements along the contact surface. By the way the indenter curvature is determined. Then, a series of curves can be figured out after the operation with definite steps. Be based on these curves, the contact zones can be determined from known indenter curvature and the loading. In addition, the glue layers are considered completely the same as other composite plies in this analysis. From the computational results, it can be shown that the displacements and stresses converge very well, and the distributions of shearing and normal stresses obtained from constitutive equation and from equilibrium equation agree with each other very well