Modeling sliding cables and geodesic lines through dynamic relaxation

Abstract

The Dynamic Relaxation Method (DRM) is an interesting alternative to solve complicated nonlinear equilibrium problems, solved via a pseudo-dynamic analysis, with explicit time integration, carried out exclusively by fast vector manipulations. In the current paper, we present the theoretical formulation and the implementation of the load vectors of a class of finite elements capable of representing the slippage between border cables and membrane sheaths, without friction. The paper also details some improvements in a procedure to search geodesic lines onto triangle-faceted surfaces, relating the expression of the internal load vector of the geodesic string element to the internal vector of a sliding-cable superelement, and proposing a new average nodal normal vector, insensitive to the arbitrary division of a given geometry into different triangular meshes.