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This study introduces a force-based higher-order shear deformable beam finiteelement model that incorporates a rational shear stress distribution, designedfor the precise analysis of functionally graded sandwich beams. Unlikeconventional higher-order shear beam finite elements that regard generalizeddisplacements as unknown fields, this model considers the distributions ofstress resultants along the beam axis as the unknown fields. The specific formsof these stress resultants and the generalized displacements are analyticallydetermined, based on the differential equilibrium equations of the higher-ordershear beam. This approach effectively circumvents numerical errors that canarise from finite element discretization. Furthermore, the model introduces astress equilibrium equation to accurately depict the distribution of transverseshear stress across the beam thickness. A corrected shear stiffness, whichtakes into account rational shear stress, is derived and incorporated into theproposed beam element. Numerical examples underscore the accuracy and efficacyof the proposed higher-order beam element model in the static analysis offunctionally graded sandwich beams, particularly in terms of true transverseshear stress distribution.

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