Limitations of solid finite elements in transverse shear stress evaluation and the use of CUF 1D models as an efficient alternative

Although solid finite elements has become the most widely used standard modeling tool in structural mechanics, their use for accurate stress analysis is intrinsically limited by mesh quality, aspect ratio sensitivity, discretization strategy, and difficulties in preserving local equilibrium at the element level. Achieving reliable stress fields typically requires very fine meshes, especially in slender or thin-walled structures, leading to a dramatic increase in the number of degrees of freedom and, consequently, to a prohibitive computational cost. Moreover, the highly stretched solid elements that often arise in practical applications can further degrade stress accuracy and compromise the robustness of the analysis. To overcome these limitations, this work propose higher-order onedimensional (1D) beam elements with full three-dimensional (3D) capabilities, developed within the Carrera Unified Formulation (CUF). The proposed models are derived from 3D elasticity through refined kinematic assumptions and enable the accurate evaluation of 3D stress distributions without the need for full 3D solid discretizations. Linear static analyses are carried out on representative benchmark problems, with particular attention to stress accuracy, sensitivity to element aspect ratio, mesh refinement requirements, and equilibrium preservation. The results clearly show that conventional solid formulations, as used in ABAQUS and COMSOL, are highly unreliable, remaining strongly affected by discretization choices, whereas the proposed CUF-based beam models provide accurate, robust, and computationally efficient solutions. In addition, solid elements also exhibit significant difficulties in ensuring shear stress equilibrium at the element level, further limiting their suitability for detailed stress analysis. Overall, this study underscores the role of higher-order CUF beam elements as an effective and reliable alternative to traditional solid formulations for accurate stress analysis, as well as a valuable tool for verification, particularly for shear stress evaluation.