Ali Maghami1, Farzad Shahabian1, Seyed Mahmoud Hosseini2,*
CMES-Computer Modeling in Engineering & Sciences, Vol.121, No.3, pp. 877-907, 2019, DOI:10.32604/cmes.2019.08019
Abstract 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… More >
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