Reduction 3D equations of composite plate to 2D equations on base of mapping contraction principle

The spatial equations of the theory of elasticity for the plate are taken into consideration. The elasticity modulus and Poisson's ratio are considered as the functions of the cross-section height. The integration of the system is produced by the method of the simple iteration that allows establishing the form of the asymptotic expansions and determining the weight coefficients for each unknown. If the load is slowly varying along the coordinates, the solution also reduces to the determination of the slowly varying unknown functions of the stresses and displacements. In this case, the problem is significantly simplified and reduced to solving a sequence of classical problems so that the output data from one of the elementary problem are input ones for the next problem.