Using residual areas for geometrically nonlinear structural analysis

Rezaiee‐Pajand, Mohammad; Naserian, Rahele

doi:10.1016/j.oceaneng.2015.06.043

Cited by 15 publications

(6 citation statements)

References 42 publications

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“…Truss systems are commonly implemented in several structural systems including space structures, high-span bridge systems and bracing the skeleton buildings. Recently, it is reported that the implementation of the linear analysis to investigate the structural applications is not sufficiently reliable without considering nonlinearities [1][2][3][4]. Instead, the development of engineering science and growth in computer processing power have made it possible to conduct an efficient nonlinear analysis.…”

Section: Introductionmentioning

confidence: 99%

Improved Homotopy Perturbation Method for Geometrically Nonlinear Analysis of Space Trusses

et al. 2020

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The objective of this study is to explore a noble application of the improved homotopy perturbation procedure bases in structural engineering by applying it to the geometrically nonlinear analysis of the space trusses. The improved perturbation algorithm is proposed to refine the classical methods in numerical computing techniques such as the Newton–Raphson method. A linear of sub-problems is generated by transferring the nonlinear problem with perturbation quantities and then approximated by summation of the solutions related to several sub-problems. In this study, a nonlinear load control procedure is generated and implemented for structures. Several numerical examples of known trusses are given to show the applicability of the proposed perturbation procedure without considering the passing limit points. The results reveal that perturbation modeling methodology for investigating the structural performance of various applications has high accuracy and low computational cost of convergence analysis, compared with the Newton–Raphson method.

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Section: Introductionmentioning

confidence: 99%

Improved Homotopy Perturbation Method for Geometrically Nonlinear Analysis of Space Trusses

et al. 2020

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“…Rezaiee-Pajand and Naserian 26 developed an iterative method with three steps and fourth-order convergence for solving nonlinear equations of type f ( x ) = 0. Given initial point x (0) , the iterative equations for this method are given by:…”

Section: Structural Problem and Solution Methodsmentioning

confidence: 99%

“…for every k = 0,1,2,…, and τ i ∈ [0,1], f′ is the first derivative of the function f and w i is the weight that verifies the consistency condition 26 :…”

Section: Structural Problem and Solution Methodsmentioning

confidence: 99%

New fourth-order convergent algorithm for analysis of trusses with material and geometric nonlinearities

Souza

Santos

Kawamoto

et al. 2021

The Journal of Strain Analysis for Engineering Design

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This paper presents a new algorithm to solve the system of nonlinear equations that describes the static equilibrium of trusses with material and geometric nonlinearities, adapting a three-step method with fourth-order convergence found in the literature. The co-rotational formulation of the Finite Element Method is used in the discretization of structures. The nonlinear behavior of the material is characterized by an elastoplastic constitutive model. The equilibrium paths with limit points of load and displacement are obtained using the linearized Arc-Length path-following technique. The numerical results obtained with the free program Scilab show that the new algorithm converges faster than standard procedures and modified Newton-Raphson, since the approximate solution of the problem is obtained with a smaller number of accumulated iterations and less CPU time. The equilibrium paths show that the structures exhibit a completely different behavior when the material nonlinearity is considered in the analysis with large displacements.

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“…Especially, MIP Newton method can be well applied to high slenderness structures. Because of the importance of nonlinear solvers with respect to computational mechanics and their wide application, many solvers have been proposed to reduce number of iterations per load step and computation as the following: optimization-based iterative technique 6 and residual areas-based iterative technique, 7 dynamic relaxation techniques, [8][9][10] multipoint methods-based path following techniques, 11 a novel method to transform the discretized governing equations, 12 a data-driven nonlinear solver (DDNS), 13 an improved predictor-corrector method, 14 Koiter-Newton method with a superior performance for nonlinear analyses of structures, 15,16 etc. It is observed that employing time series prediction to reduce number of iterations of nonlinear solvers is very rare except the DDNS.…”

Section: Introductionmentioning

confidence: 99%

Deep learned one‐iteration nonlinear solver for solid mechanics

Nguyen

Lee

Dinh‐Tien

et al. 2022

Numerical Meth Engineering

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Nowadays, there are a lot of iterative algorithms which have been proposed for nonlinear problems of solid mechanics. The existing biggest drawback of iterative algorithms is the requirement of numerous iterations and computation to solve these problems. This can be found clearly when the large or complex problems with thousands or millions of degrees of freedom are solved. To overcome completely this difficulty, the novel one‐iteration nonlinear solver (OINS) using time series prediction and the modified Riks method (M‐R) is proposed in this paper. OINS is established upon the core idea as follows: (1) Firstly, we predict the load factor increment and the displacement vector increment and the convergent solution of the considering load step via the predictive networks which are trained by using the load factor and the displacement vector increments of the previous convergence steps and group method of data handling (GMDH); (2) Thanks to the predicted convergence solution of the load step is very close to or identical with the real one, the prediction phase used in any existing nonlinear solvers is eliminated completely in OINS. Next, the correction phase of the M‐R is adopted and the OINS iteration is started at the predicted convergence point to reach the convergent solution. The training process and the applying process of GMDH are continuously conducted and repeated during the nonlinear analysis in order to predict the convergence point at the beginning of each load step. Through numerical investigations, we prove that OINS is powerful, highly accurate and only needs about one iteration per load step. Thus, OINS significantly saves number of iterations and a huge amount of computation compared with the conventional methods. Especially, OINS not only can detect limit, inflection, and other special points but also can predict exactly various types of instabilities of structures.

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Using residual areas for geometrically nonlinear structural analysis

Cited by 15 publications

References 42 publications

Improved Homotopy Perturbation Method for Geometrically Nonlinear Analysis of Space Trusses

Improved Homotopy Perturbation Method for Geometrically Nonlinear Analysis of Space Trusses

New fourth-order convergent algorithm for analysis of trusses with material and geometric nonlinearities

Deep learned one‐iteration nonlinear solver for solid mechanics

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