LINEARIZATION AND ENERGY METHOD ABOUT CONTACT PROBLEM OF COMPOSITE BEAM

The nonlinear contact problem of composite beams is linearized by an inverse method, that is to say, the loading distribution on the contact zone with the adjustable parameter and the contact width are assumed to be given and the curvature of the cylinder is to be solved. By means of the principle of superposition, the loading state is decomposed into symmetric and antisymmetric ones. The trigonometric series and Legendre series are applied to describe the displacement field of the above two 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 composite beam 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 indentor curvature is determined. Then many families of straight lines passing through the origin of the indentor curvature varying as the loading with different contact zones can be figured out. Based on the above straight lines, the contact zone can be determined from the known indentor curvature and loading. From the computational results, it can be shown that the displacements and stresses converge very well and the distribution of shearing stress obtained from the constitutive equation and from the equilibrium equation agree with each other very well. The distribution of stress of the composite beam has the local effects, and at the place far from local loading the distribution of stress is the same as the results of classical beam theory.