Novel Nonlinear Complementarity Function Approach for Mechanical Analysis of Tensegrity Structures

Cable slacking may be frequently encountered in mechanical analysis of tensegrity structures. Traditional nonlinear finite element analysis in handling this issue may lead to numerical difficulty due to the dramatic changes of the stiffness matrix induced by cables switching between taut and slack states. To deal with the nonsmooth nature induced by cable slacking, we propose in this paper a novel nonlinear complementarity function-based framework for mechanical analysis of tensegrity structures. The core idea is that the constitutive relation of cables is reformulated as a set of equality equations. This is done by first introducing a parametric variable and expressing the constitutive relation with a complementarity condition, and then using the modified Fischer-Burmeister complementarity function. By considering the introduced parametric variables as additional degrees of freedom in the finite element model, it becomes possible to get rid of the nonsmooth nature, as well as to solve a continuous, smooth, differentiable problem by using the classical Newton-Raphson method. The proposed framework is first developed for static analysis and then extended to dynamic analysis, both under large displacement. The closed-form expressions of the Jacobian matrix are analytically derived. Multiple examples are presented to verify the robustness and effectiveness of the proposed framework.

Automated summary

This paper proposes a novel nonlinear complementarity function-based framework to handle cable slacking in tensegrity structures. By reformulating the constitutive relation of cables as a set of equality equations using parametric variables and complementarity conditions, the nonsmooth nature induced by cable slacking can be eliminated, and a continuous, smooth, differentiable problem can be solved using the classical Newton-Raphson method.