Elasticity alternatives to generalized Vlasov and Timoshenko models for composite beams

The static response of homogeneous and composite beams is studied using approximations of the pointwise displacement components of linear three-dimensional elasticity theory. This method differs from many one-dimensional theories in that the displacements over the beam cross-section are allowed to vary rather than limiting the kinematic model at the start of the analysis. Polynomial approximations are used over the beam cross-section with the resulting integrals computed over the subdomains of differing materials. Several example problems are considered and results are compared with highly accurate one-dimensional beam theories, with very good agreement being found.