Approximate Analytical Solution of a Physically Nonlinear Spatial Problem on the Elastic Equilibrium of a Multilayer Rectangular Plate

A three-dimensional boundary-value problem for a multilayer rectangular plate is solved under the physically nonlinear theory of elasticity. Various types of interlayer contact conditions are considered. The nonlinear relation between stresses and small strains is assumed to be of the Kauderer form. The solution is represented by a series in powers of a dimensionless small parameter. The problem posed is reduced to a recurrent sequence of linear boundary-value problems. The stress distribution and the effect of physical nonlinearity on the elastic equilibrium of the plate are studied