Group-theoretic method for efficient buckling analysis of prestressed space structures

Abstract

An efficient group-theoretic method is proposed for the buckling analysis of symmetric prestressed space structures. Tangent stiffness matrices and geometric stiffness matrices of trusses, cables, and frames are given, and thus, the proposed method is applicable not only to pin-jointed structures but also to more general structures with frame and cable elements. Important contribution of initial prestresses is considered in formulating the tangent stiffness matrices for the prestressed structures. By adopting irreducible representations of a symmetry group and projection operator theory, the associated stiffness matrices are converted to symmetry-adapted forms. Subsequently, the original buckling problem is decomposed into a series of independent subproblems with smaller dimensions, which obtain precise solutions but lead to significant reduction in computational cost. To describe the typical process for the group-theoretic method, efficient buckling analyses on four types of symmetric prestressed space structures composed of cables, trusses, and/or frames are carried out. The computational efficiency of the proposed method is dramatically improved in comparison with those of FEM and the conventional numerical method. Comparing the results with the corresponding ones from ABAQUS and published data, we verify that the proposed method is elegant and reliable.