Effective insights into the geometric stability of symmetric skeletal structures under symmetric variations

Geometric stability is a necessary criterion to guarantee stable equilibrium in engineering structures. However, we generally encounter enormous calculations to examine the geometric stability when we make variations on the geometry or the connectivity of a given kinematically and statically indeterminate structure. This study describes how symmetry is utilized to enhance the mobility and geometric stability analysis of symmetric skeletal structures. Symmetry-extended mobility distinguishes representations of the internal mechanisms and self-stress states from relative mobility based on their inherent symmetries using group-theoretic method. Thus, it acts as an efficient tool to evaluate the order of internal mechanisms that may be indistinguishable by traditional structural approaches. Further, it is used to gain effective insights into the mobility and geometric stability of a symmetric skeletal structure with symmetrically perturbed connectivity or geometry. The first-order changes of symmetry-extended mobility are deduced to describe the changes induced by the variations of nodal coordinates, members, and kinematic constraints, respectively. Examples are given to verify the correctness and effectiveness of the proposed method. We show that the geometry or connectivity of kinematically indeterminate symmetric skeletal structures can be altered while at the same time retaining geometric stability and some or all of the original symmetry. The results have potential application in the design of novel deployable structures. (C) 2015 Elsevier Ltd. All rights reserved.