Framework for finite-element-based large increment method for nonlinear structural problems

Authors
Citation
Aj. Aref et Zy. Guo, Framework for finite-element-based large increment method for nonlinear structural problems, J ENG MEC, 127(7), 2001, pp. 739-746
Citations number
13
Categorie Soggetti
Mechanical Engineering
Journal title
JOURNAL OF ENGINEERING MECHANICS-ASCE
ISSN journal
07339399 → ACNP
Volume
127
Issue
7
Year of publication
2001
Pages
739 - 746
Database
ISI
SICI code
0733-9399(200107)127:7<739:FFFLIM>2.0.ZU;2-8
Abstract
This paper addresses the formulation and application of a finite-element-ba sed large increment method for solving nonlinear structural problems. In a step-by-step solution of a nonlinear problem based on the displacement meth od, the main unknown variables are the system displacements. Therefore, to represent the general force in terms of general deformation, the constituti ve relations have to be linearized. As such, a step-by-step incremental pro cedure is often used, where the solution at the current step is added to th e solution of the previous step, thereby, successive steps are eventuality used to achieve a solution. However, a flexibility-based large increment me thod can be useful to solve nonlinear problems if linearization of the cons titutive relationship can be avoided. This paper presents;a novel methodolo gy based on the flexibility method to solve nonlinear problems with a large increment methodology. The idea is built on using a nonlinear material mod el without the need for linearization and a step-by-step approach. In doing so, the mathematical background, governing equations, solution methodology , and framework to implement the method on a parallel computation platform are presented in detail. The methodology has been demonstrated using a simp le nonlinear problem. The demonstration example clearly reveals the accurac y and the efficiency of the method.