Approximate analytical solution of a physically nonlinear space problem of elastic equilibrium of a layered rectilinear plate

A three-dimensional boundary problem of physically nonlinear theory of elasticity is considered for a layered rectilinear plate with different types of mechanical contact between layers. The nonlinear dependence between stresses and small strains is assumed to be of Kauderer's form. The solution is looking for the form of series on powers of dimensionless small parameter. The stated physically nonlinear problem is reduced to a recurrent sequence of appropriate linear boundary problems. An influence of physical nonlinearity of the material on an elastic equilibrium of layered plate is determined. Two plate variants are considered. In the first case the upper and lower layers are made of steel out the middle one from copper. In the second case the upper and lower layers are fabricated from copper and the middle one from steel.