Application and comparison of numerical methods in the solution of systems of linear equations in space trusses problems

Abstract

One of the interesting civil engineering applications is space truss, a three dimensional element, particularly used as roof for industrial and commercial structure, covering large open areas with few or no internal supports. This paper aims to compare different numerical methods implemented computationally for the solution of the linear equations systems generated from the Newton-Raphson iterations in the incremental process. The numerical solution of such linear systems are computationally costly, thus it is of our interest to determine which numerical methods best suit the problem. To compare the computational cost of the algorithms, a study of complexity is performed. Numerical simulations with the Matlab software are made of space truss problems with geometric nonlinear behavior. The system of nonlinear equations is solved using the Standard Newton-Raphson method associated with the Linear Arc-Length path-following technique. The structures are discretized by the Positional Finite Element Method, whose fundamental variables are the nodal positions of the finite element. For the processing time, the numerical results indicate a better performance of the iterative methods compared to direct methods, especially for large orders problems, which are most commonly found in the structural area.