Iterated Ritz and conjugate gradient methods as solvers in constrained form-finding: A comparison

Abstract

Iterated force density method Conjugate gradient method Iterated Ritz method Cable net GridshellConstrained form-finding results in a nonlinear system of equations unless a linear form-finding method (force density method) is iteratively applied until the given constraints are satisfied. Because the goal of this paper is to contribute to the further development of this method, a brief overview of the method and its existing improvements is provided. Further improvement can be potentially expected by reducing the number of iteration steps in solving systems of linear equations in each application of the force density method. To explore this, a comparison of iterative linear solvers is conducted. The Iterated Ritz method, as a new promising solver (currently under development), was chosen for comparison with typically used conjugate gradients. Form-finding of several truss structures in both tension and compression was performed to compare the number of iteration steps necessary to obtain the solution. The presented form-finding examples indicated a significant reduction in the number of solver iteration steps, showing the potential of the Iterated Ritz method for use as a solver in linear procedures for constrained form-finding.