Stress-based elastodynamic discrete laminated plate theory

Abstract

A static laminated plate theory based on an assumed piecewise linear through-the-thickness in-plane stress distribution has been extended to include inertia effects. Based on this in-plane stress distribution assumption, outof-plane shear and normal stress component distributions were derived from the three-dimensional equations of motion, resulting in six nonzero stress components. Hamilton's variational principle was used to derive the plate equations of motion, the plate constitutive relationships, and the interface continuity equations. The governing equations were written in a form that is self-adjoint with respect to the convolution bilinear mapping. The resulting system of equations for a single lamina consists of 25 field equations in terms of 9 weighted displacement field variables, 10 stress and moment resultant field variables, and 6 out-of-plane shear and normal stress boundary field variables. For the laminated system, the mixed formulation enforces both traction and displacement continuity at lamina interfaces as it satisfies layer equilibrium. A finite element formulation based on a specialized form of the governing functional was developed. The method is illustrated with results of a free vibration analysis of sandwich and homogeneous plates for which exact solutions are available.