A consistent finite‐element formulation of non‐linear elastic cables

Abstract

AbstractA finite‐element approach for computing cable structure fully non‐linear response is presented in this work. Both the problems of statics and of dynamics are considered. The formulation encompasses arbitrary large strains and displacements. A very general constitutive equation for non‐linear elastic cables can be posed by an adequate choice for the strain energy function. In this work we consider two model problems, posed by St. Venant's and Ogden's material models. The proposed formulation is set in a fixed reference frame which yields a very efficient finite‐element implementation. The additional advantage of setting the formulation in a fixed reference frame is a bilinear form of the kinetic energy and a simplified solution procedure for dynamic equilibrium equations. Consistent linearization is used at each step of the Newton algorithm to obtain the tangent operators, which provide the quadratic rate of the solution convergence. This is demonstrated in the numerical examples presented herein.