Planar Bending of Sandwich Beams with Transverse Loads off the Centroidal Axis

Abstract

Conventional analysis methods for beams do not distinguish between transverse loads that are applied at the beam centroidal axis and those acting either above or below the centroidal axis. In contrast, this paper formulates a sandwich beam finite element solution which models the effect of load height relative to the centroidal axis. Towards this goal, the governing equilibrium equations and associated boundary conditions are derived based on a Timoshenko beam formulation for the core material. Special shape functions satisfying the homogeneous form of the equilibrium equations are derived and subsequently used to formulate exact stiffness matrices. By omitting the stiffness terms related to the faces, the formulation for a homogeneous Timoshenko beam can be recovered. Also, the Euler–Bernouilli counterpart of the formulation is recovered as a limiting case of the current Timoshenko beam formulation. Effects of load height relative to the centroid are observed to have similarities with those induced by axial forces in beam-columns. For a simply supported beam, downward acting loads located below the centroidal axis are found to induce a stiffening effect while those acting above the centroidal axis are found to induce a softening effect, resulting in higher transverse displacements.