Elastic Bending and Transverse Compression of a Thin Plate with Density-Dependent Young’s Modulus

The equilibrium equation governing the plane strain static problem for a thin elastic layer is studied using asymptotic analysis for a material with generalized Young’s modulus weakly dependent on the mass density. Within the context of the adopted scaling, the effect of a physical nonlinearity arises at the second order along with shear deformation and other linear phenomena. Refined equations for plate bending and transverse compression are derived. Numerical examples illustrating the role of the corrections due to the considered constitutive behavior are presented.