Novel nodal relaxation algorithm with its application on nonlinear analysis of tensegrity-based structures

Abstract

This study proposes a robust technique for static and dynamic nonlinear analysis of tensegrity-based structures using a novel method, entitled the Node Relaxation algorithm (NR). Regular numerical algorithms are usually invalid in dealing with flexible tensegrities due to singularities arising from large displacements and/or rotations following any alteration of the internal actuated components or externally applied loads. Especially in tackling dynamic problems, it becomes even more challenging to predict structural deformation when its member forces are varied constantly. In this paper, a novel iterative algorithm, consisting of consecutive releasing and restraining of each node, is raised to oblige the structural form to gradually evolve to its final equilibrium configuration. The tangential unbalance force on each node, selected as the sensitivity index, is employed to accelerate the structure searching for its stable state. The Newmark-β method is also adopted to update the position of free nodes in each iterative step, which assists the NR algorithm in finding updated equilibrium structural configuration during the nonlinear dynamic analysis. Two kinds of tensegrity-based structures, namely the spring-rod tensegrity and the cable-rod tensegrity, are given as the illustrative examples to confirm the effectiveness and robustness of the presented method.