Abstract
This paper deals with the convergence acceleration of iterative nonlinear methods. An effective iterative algorithm, named the three-point method, is applied to nonlinear analysis of structures. In terms of computational cost, each iteration of the three-point method requires three evaluations of the function. In this study the effective functions have been proposed to accelerate the convergence process. The proposed method has a convergence order of eight, and it is important to note that its implementation does not require the computation of higher order derivatives compared to most other methods of the same order. To trace the equilibrium path beyond the limit point, a normal flow algorithm is implemented into a computer program. The three-point method is applied as an inner step in the normal flow algorithm. The procedure can be used for structures with complex behavior, including: unloading, snap-through, elastic post-buckling and inelastic post-buckling analyses. Several numerical examples are given to illustrate the efficiency and performance of the new method. Results show that the new method is comparable with the well-known existing methods and gives better results in convergence speed.
Highlights
A lot of research has focused on presenting formulations for the nonlinear analysis of structures
A stress– strain relationship proposed by Hill et al.[15] is adopted to predict the inelastic post–buckling behavior of the trusses
The three–point technique can be applied to analysis of structures with complex behaviors, including unloading, snap–through, elastic post–buckling and inelastic post–buckling analyses
Summary
A lot of research has focused on presenting formulations for the nonlinear analysis of structures. Saffari et al.[21] introduced a new algorithm for passing the equilibrium path, known as modified normal flow algorithm, for geometrically nonlinear analysis of space trusses This algorithm can reduce both number of iterations and computing time. This method is originally proposed by Yang and Shieh[27]; (b) the work control method which was proposed by Bathe and Dvorkin[5] to enforce a constant value of work done in each iteration This method avoids the limitations of the load control and displacement control methods in tracing the equilibrium path; (c) Chan [7] proposed the minimum residual displacement method (MRD) to remove the residual displacement or the unbalanced force in each iteration.A new approach for nonlinear analysis of structures, which accelerates the convergence rate, has been presented by Saffari and Mansouri[22]. Results show that the proposed method is efficient in different kinds of path–following algorithms
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