A shape-finding approach of tree-like structure based on grouping strategy and generalized inverse matrix theory

Abstract Unstable link models in equilibrium transfer their loads only through axial forces and the generalized inverse matrix theory can be used in the shape-finding analysis of unstable link structures. According to this principle and the generalized inverse matrix theory, a shape-finding approach for tree-like structure is proposed, which forms a progressive process to update the shape of branching model until the potential energy of the model reaches minimum. In the proposed approach, members of the branching model are grouped and the total length of the members in the same group are constrained. The total length can be redistributed among the members in the same group in the shape-finding process. The redistribution of length is particularly useful for the shape-finding of tree-like structure as it can avoid the generation of inefficient members in the shape-found structure. Changing the grouping mode of members is a way to generate multiple schemes of structural shapes. Numerical examples illustrate the features of the approach and validate its effectiveness.