Geometrically Nonlinear Analysis of Structures Using Various Higher Order Solution Methods: A Comparative Analysis for Large Deformation

作     者：Ali Maghami Farzad Shahabian Seyed Mahmoud Hosseini 

作者机构：Civil Engineering DepartmentFaculty of EngineeringFerdowsi University of MashhadMashhadIran Industrial Engineering DepartmentFaculty of EngineeringFerdowsi University of MashhadMashhadIran 

出 版 物：《Computer Modeling in Engineering & Sciences》 (工程与科学中的计算机建模（英文）)

年 卷 期：2019年第121卷第12期

页      面：877-907页

核心收录：

学科分类：07[理学] 0835[工学-软件工程] 0701[理学-数学] 0811[工学-控制科学与工程] 0812[工学-计算机科学与技术（可授工学、理学学位）] 070101[理学-基础数学] 

基　　金：The authors would like to express their gratitude to anonymous reviewers for their in-depth comments that significantly strengthened this article 

主　　题：Geometrically nonlinear analysis higher order methods predictor-corrector algorithms convergence rate sensitivity to the increment size 

摘      要：The suitability of six higher order root solvers is examined for solving the nonlinear equilibrium equations in large deformation analysis of *** applied methods have a better convergence rate than the quadratic Newton-Raphson *** six methods do not require higher order derivatives to achieve a higher convergence *** algorithms are developed to use the higher order methods in place of the Newton-Raphson method to solve the nonlinear equilibrium equations in geometrically nonlinear analysis of *** higher order methods are applied to both continuum and discrete problems(spherical shell and dome truss).The computational cost and the sensitivity of the higher order solution methods and the Newton-Raphson method with respect to the load increment size are comparatively *** numerical results reveal that the higher order methods require a lower number of iterations that the Newton-Raphson method to *** is also shown that these methods are less sensitive to the variation of the load increment *** it is indicated in numerical results,the average residual reduces in a lower number of iterations by the application of the higher order methods in the nonlinear analysis of structures.