An accelerated incremental algorithm to trace the nonlinear equilibrium path of structures

Latin American Journal of Solids and Structures

Hamed Saffari¹  Iman Mansouri¹  Nadia M. Mirzai² 

[1] Shahid Bahonar University of Kerman;Shiraz University;

关键词: Nonlinear analysis;    Convergence acceleration;    Normal flow algorithm;    Three-point method;   

DOI  :  10.1590/S1679-78252012000400001

来源: DOAJ

【 摘 要 】

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.

【 授权许可】

Unknown