TY - EJOU
AU - Maghami, Ali
AU - Shahabian, Farzad
AU - Hosseini, Seyed Mahmoud
TI - Geometrically Nonlinear Analysis of Structures Using Various Higher Order Solution Methods: A Comparative Analysis for Large Deformation
T2 - Computer Modeling in Engineering \& Sciences
PY - 2019
VL - 121
IS - 3
SN - 1526-1506
AB - The suitability of six higher order root solvers is examined for solving the
nonlinear equilibrium equations in large deformation analysis of structures. The applied
methods have a better convergence rate than the quadratic Newton-Raphson method. These
six methods do not require higher order derivatives to achieve a higher convergence rate.
Six algorithms are developed to use the higher order methods in place of the NewtonRaphson
method to solve the nonlinear equilibrium equations in geometrically nonlinear
analysis of structures. The 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 investigated. The numerical results reveal that the
higher order methods require a lower number of iterations that the Newton-Raphson
method to converge. It is also shown that these methods are less sensitive to the variation
of the load increment size. As 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.
KW - Geometrically nonlinear analysis
KW - higher order methods
KW - predictor-corrector algorithms
KW - convergence rate
KW - sensitivity to the increment size
DO - 10.32604/cmes.2019.08019