Geometric nonlinear analysis of slender layered non-prismatic beams with interlayer slip

This paper presents a novel model that, for the first time, simultaneously captures the effects of variable cross-section and interlayer slip on the geometrically nonlinear response of slender symmetrically layered beams within the framework of a beam theory. While the central layer has a constant cross-section along its length, the height of the two outer layers can vary arbitrarily. A nonlinear axial strain-displacement relationship captures the influence of moderately large deflections for immovably supported beams. The kinematic hypothesis of the Euler-Bernoulli theory is applied layerwise. The relationship between the interlaminar shear tractions and the interlayer slips is assumed to be linear. The Galerkin method is used to solve the derived initial-boundary value problem. Several application examples demonstrate the influence of the interlayer slip, the variable cross-section, and the geometrically nonlinear formulation of the equations of motion on the static and dynamic response. The results of comparative analyses with a numerically much more computational expensive finite element model discretized by plane stress continuum elements are in excellent agreement with the outcomes of the presented theory.