Efficient Numerical Method in Second-Order Inelastic Analysis of Space Trusses

Abstract

In this paper, the Newton-Raphson method is combined with three different algorithms. These algorithms are the generalized minimum residual (GMRES), the least squares (LSQR), and the biconjugate gradient (BCG). Of these algorithms, the most effective at reducing the number of iterations and the time required is identified. A common characteristic of these algorithms is that they replace the inversion of the tangent stiffness matrix with an iterative procedure to solve the linearized system of equations. A computer program based on three algorithms is developed to numerically solve a system of nonlinear equations. The procedure can be applied to analysis of structures with complex behaviors, including unloading, snap-through buckling, and inelastic postbuckling analyses. To demonstrate the efficiency and accuracy of the method developed here, some well-known trusses are investigated and analyzed using the various aforementioned algorithms. Results show that the biconjugate gradient algorithm is a more effective scheme to be coupled with the Newton-Raphson method when nonlinear structural problems are to be solved, having considerable savings in computational cost and time. Furthermore, the BCG algorithm is improved for solving a system of nonlinear equations. Finally, results reveal that the improved BCG method drastically reduces the computational time and the number of iterations while the accuracy of the results is maintained.