Dynamic relaxation method with finite rotations and automatic mass-tuning for the static analysis of lightweight structures

This paper presents a Dynamic Relaxation Method framework for the nonlinear static analysis of lightweight structures predominantly composed of tensile cables and membranes. To accommodate a broader class of lightweight structures and include flexible beams, this study proposes an extension of the Dynamic Relaxation Method to address finite rotations, which are integral to the behavior of geometrically exact beams. The framework utilizes the Rodrigues pseudovector to parameterize the rotation tensor with only three degrees of freedom, thereby eliminating the need for trigonometric functions and allowing direct updates of rotations in pseudovector form. This approach also integrates the kinetic damping technique with the allocation of fictitious masses, here denoted as mass-tuning , applied to each element in the finite element mesh to achieve a consistent critical time step across all elements, thus circumventing the need for assembling the global stiffness matrix. A special mass-tuning technique is developed for beam elements to evaluate a common parameter for both mass and inertia. The robustness of the proposed algorithm is evaluated using classical benchmark tests. Subsequently, a more complex structure, integrating beam, membrane, and cable elements, is tested to evaluate the feasibility and robustness of the proposed method, with the results being compared to those obtained using independent structural analysis software. • Our framework extends the dynamic relaxation method to finite rotations using the Rodrigues pseudovector. • Element-level mass tuning in DRM avoids defining the global stiffness matrix and unifies cable, membrane, and beam elements. • Membrane wrinkling and slackening are treated with a polar decomposition technique. • Vector-based implementation avoids large matrix operations, thereby improving efficiency.