A force-based higher-order shear beam element model with rational shear stress distribution for accurate analyses of FG sandwich beams

This study introduces a force-based higher-order shear deformable beam finite element model that incorporates a rational shear stress distribution, designed for the precise analysis of functionally graded sandwich beams. Unlike conventional higher-order shear beam finite elements that regard generalized displacements as unknown fields, this model considers the distributions of stress resultants along the beam axis as the unknown fields. The specific forms of these stress resultants and the generalized displacements are analytically determined, based on the differential equilibrium equations of the higher-order shear beam. This approach effectively circumvents numerical errors that can arise from finite element discretization. Furthermore, the model introduces a stress equilibrium equation to accurately depict the distribution of transverse shear stress across the beam thickness. A corrected shear stiffness, which takes into account rational shear stress, is derived and incorporated into the proposed beam element. Numerical examples underscore the accuracy and efficacy of the proposed higher-order beam element model in the static analysis of functionally graded sandwich beams, particularly in terms of true transverse shear stress distribution.