An efficient stiffness-based finite element thermo-mechanical modeling of elastically linked double curved non-prismatic beams

This study presents an efficient stiffness-based finite element formulation for the mechanical and thermo-mechanical analysis of double-curved beam systems coupled via a continuous elastic interlayer. Utilizing an explicit stiffness matrix developed by the authors, the formulation accurately incorporates axial, shear, and bending deformations and allowing both prismatic and non-prismatic geometries to be handled with high fidelity, while a systematic static condensation reduces the 12-DOF element into an equivalent 6-DOF model without loss of accuracy. A distributed system of translational and rotational springs models the interlayer, and the unit load approach extends the method to capture uniform and gradient temperature fields in both prismatic and non-prismatic configurations. Principal results from extensive numerical benchmarks demonstrate that the formulation achieves rapid convergence and high accuracy, exactly matching analytical limits at zero ( \(\:k=0\) ) and infinite ( \(\:k\to\:\infty\:\) ) interlayer stiffness. Major findings confirm that interlayer stiffness smoothly governs the coupled structural response, transitioning behavior between independent and fully composite action, and that the proposed approach predicts thermo-mechanical interactions with superior computational efficiency.