Nonlinear analysis of structures made of no-tension/compression materials using an efficient projection-contraction algorithm

Abstract

Nowadays, it is still difficult to analyze no-tension/compression materials by using commercial software packages, although the option of no-tension/compression constitutive law has been provided. The paper presents a variational principle for bi-modulus elasticity that can be used to model no-tension/compression materials and structures. Equivalence between the derived complementarity finite element formulation and a variational inequality is proved, such that an efficient projection-contraction (PC) algorithm can be employed to solve the problem. Three numerical examples, including a tensegrity structure, wrinkled membranes and masonry-like structures are presented to show its applications in analysis of no-tension/compression structures. Some results of simulations are verified by the existing experimental data. The proposed method is of good numerical stability and an improved computational efficiency. It is expected to be extended to the finite strain case and other non-smooth problems of mechanics, with an alternative constitutive law embedded into the variational inequality computational framework.