Penalty-Based Coupling of Non-Matching Beam Cross-Section Meshes for Large-Scale Design Optimization

This paper presents a new method for computing the cross-sectional stiffness matrix of prismatic beam structures from non-matching, overlapping finite element meshes. The approach introduces a variational coupling formulation that enforces interfacial traction compatibility and rigid body motion constraints between independently meshed subdomains using a mortar- style background mesh. A Nitsche-like term is employed to weakly enforce stress equilibrium across interfaces. This formulation enables robust handling of overlapping or non-conforming meshes without the need for remeshing or geometry pre-processing, a current challenge in multi-disciplinary design analysis and optimization. The method is compatible with natural, component-level parameterizations of structural features, such as spar cap thickness, and is designed to integrate directly into state of the art gradient-based optimization workflows critical for tasks like rotor blade shape optimization. Validation against a conformal reference solution demonstrates that the penalty-coupled approach achieves a relative error of less than 1% in the stiffness matrix while producing smooth, physically consistent warping functions for all six fundamental loading modes. The proposed method offers a flexible and optimization-ready framework for high-fidelity beam modeling in the design of advanced aerospace structures.