Deformation of rectangular orthotropic laminate resting on thin elastic foundation with nonlinear change of displacements over thickness under edge loading

Abstract

Deformation of rectangular orthotropic laminate resting on a thin elastic orthotropic foundation with fully fixed bottom plane is studied in this paper. The laminate is subjected to an in-plane uniaxial load uniformly distributed over one of its edges. Models of joint deformation of the laminate and foundation are created based on the equations of plane elasticity for an orthotropic body. The applicability of such equations is justified by the uniformity of edge loading. A laminate model allows for the transverse shear strain, whereas a model created for the foundation considers a nonlinear character of variation of the transverse and axial displacements. A governing system of differential equationsmodelling the joined deformation of the laminate and foundation is derived using static and kinematic contact conditions. The corresponding boundary value problem is solved using the sweep method. Based on this solution, effects of laminate and foundation thicknesses, and elasticity characteristics on the stress–strain state of the jointed structure are investigated. The model created and the method of its analysis enable the strong oscillating behaviour of stresses and strains to be studied. The results obtained can be utilized for verification of solutions of similar problems found by other numerical methods, including finite-element analyses.