🤖 AI Summary
To address inaccurate transverse shear stress distribution and poor aspect-ratio sensitivity in static analysis of functionally graded (FG) beams, this paper proposes a force-based beam element formulated within a modified higher-order shear deformation theory (MHSDT). Innovatively embedding MHSDT into a force-based variational framework ensures that shear strains inherently satisfy the zero-stress condition on free surfaces, thereby eliminating the need for empirical shear correction factors. By analytically constructing shape functions and incorporating an FG material constitutive mapping, the model achieves high accuracy across a wide thickness-to-span ratio range (10–100). Compared to classical models, it reduces displacement and stress errors by over 60%, while maintaining free vibration frequency errors below 0.8% across all cases. This significantly enhances modeling fidelity and robustness for multiscale mechanical behavior of FG beams.
