Form-finding of tensegrity structures based on the Levenberg–Marquardt method

• DOI: 10.1016/j.compstruc.2017.07.005
• Publication Date: 2017-08-09T03:30:58Z
• Authors: Xing-Fei Yuan; Shuo Ma; Shu-Hui Jiang
• Keywords: Tensegrity; Levenberg–Marquardt algorithm

Nonlinear equilibrium equations with node coordinates as variables are proposed.Nonlinear equilibrium equations are converted to nonlinear least-squares problems.Levenberg-Marquardt method is used to deal with singularity of Jacobian matrix.Tensegrities, mechanisms, structures with proper constraints can be analyzed. This paper presents a novel and versatile form-finding method for tensegrity structures that is based on solving nonlinear equilibrium equations. Linear equilibrium equations in terms of force densities are transformed into nonlinear equilibrium equations in which the nodal coordinates vector is variable. The input parameters for the form-finding method are the topology, initial configuration of the structure, rest lengths, and axial stiffness of elements. The form-finding process is performed by solving nonlinear least-squares problems converted from nonlinear equilibrium equations, and the LevenbergMarquardt method is used to deal with the singularity of the stiffness matrix. Several numerical examples are given to demonstrate the accuracy and efficacy of the proposed method.