An efficient algorithm for mechanical analysis of bimodular truss and tensegrity structures

Abstract

A new stable algorithm is developed for the geometric nonlinear analysis of bimodular truss and tensegrity structures based on the parametric variational principle (PVP) and the co-rotational approach. The bilinear constitutive model is proposed for modeling tensegrity structures which consist of prestressed struts and cables. The PVP for bimodular truss is first introduced for small deformation analysis, and then the geometric nonlinear formulation is derived by combining the PVP linear formulation with the co-rotational approach. The Newton–Raphson (NR) scheme combined with Lemke’s algorithm is employed to solve the resulting nonlinear complementarity equations. Numerical examples are given to demonstrate the validity and efficiency of the proposed PVP method for mechanical analysis of bimodular truss and tensegrity structures. Convergence behaviors of different computational schemes for geometric linear and nonlinear analyses are also discussed in detail, which shows the good numerical stability and efficiency of the proposed method.