Geometric Stiffness and Model Improvement of Rigid Elements for Preloaded Modal Analysis

Abstract

Pretension is utilized by large space structures such as deployable mesh reflector antennas and flexible solar cell wings to maintain forms and stiffness. Geometric nonlinearity must be taken into account in finite element modal analysis of their preloaded vibration modes. For detailed structural components such as hinges and connectors, modeling simplification using rigid elements is commonly adopted at preliminary design stages when global structural modes are concerned. However, the inadequate geometric stiffness of preloaded rigid elements in certain commercial solvers can lead to unacceptable computation errors, particularly in abnormalities where the zero-energy modes of free–free structures are less than six. This study derives the symmetry geometric stiffness matrix for rigid elements in equilibrium by investigating the incremental relationship between nodal loads and displacements, with full consideration of the incremental behavior of nodal moments. Case studies demonstrate that supplementing this matrix can restore all the zero-energy modes, significantly enhancing the validity of the modal analysis results. Moreover, the stiffening effects of the matrix are equivalently established by six elastic spring elements, facilitating the model improvement procedure for the preloaded rigid elements and enabling its integration into existing commercial software to solve complicated engineering problems.