Nonlinear Analysis of Space Trusses Using Modified Normal Flow Algorithm

Saffari, Hamed; Fadaee, Mohammad Javad; Tabatabaei, R.

doi:10.1061/(asce)0733-9445(2008)134:6(998)

Cited by 38 publications

(22 citation statements)

References 23 publications

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“…In this paper a modified normal flow algorithm [21] is used to trace the equilibrium paths. The theory of this method is described in the following sections.…”

Section: Three-point Scheme In Structural Analysismentioning

confidence: 99%

“…A detailed discussion and the process of the normal flow algorithm have been represented in reference [21].…”

Section: Modified Normal Flow Algorithmmentioning

confidence: 99%

“…(25) which is unique among an infinite number of solutions obtainable [21]. A particular solution {V } should be obtained from: (27) in which:…”

Section: Modified Normal Flow Algorithmmentioning

confidence: 99%

“…Normal flow GDC Arc-length MRD algorithm [21] method [6] method [20] method [7 From Table 6, the minimum number of iterations is associated with the three-point scheme.…”

Section: Examplementioning

confidence: 99%

“…Eriksson [13] described a general setting for the evaluation of onedimensional generalized solution paths to augmented structural equilibrium problems. Saffari et al [21] introduced a new algorithm for passing the equilibrium path, known as modified normal flow algorithm, for geometrically nonlinear analysis of space trusses. This algorithm can reduce both number of iterations and computing time.…”

Section: Introductionmentioning

confidence: 99%

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An accelerated incremental algorithm to trace the nonlinear equilibrium path of structures

Saffari

Mirzai

Mansouri

2012

Lat. Am. j. solids struct.

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This paper deals with the convergence acceleration of iterative nonlinear methods. An effective iterative algorithm, named the three-point method, is applied to nonlinear analysis of structures. In terms of computational cost, each iteration of the three-point method requires three evaluations of the function. In this study the effective functions have been proposed to accelerate the convergence process. The proposed method has a convergence order of eight, and it is important to note that its implementation does not require the computation of higher order derivatives compared to most other methods of the same order. To trace the equilibrium path beyond the limit point, a normal flow algorithm is implemented into a computer program. The three-point method is applied as an inner step in the normal flow algorithm. The procedure can be used for structures with complex behavior, including: unloading, snap-through, elastic post-buckling and inelastic post-buckling analyses. Several numerical examples are given to illustrate the efficiency and performance of the new method. Results show that the new method is comparable with the well-known existing methods and gives better results in convergence speed.

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“…In this paper a modified normal flow algorithm [21] is used to trace the equilibrium paths. The theory of this method is described in the following sections.…”

Section: Three-point Scheme In Structural Analysismentioning

confidence: 99%

“…A detailed discussion and the process of the normal flow algorithm have been represented in reference [21].…”

Section: Modified Normal Flow Algorithmmentioning

confidence: 99%

“…(25) which is unique among an infinite number of solutions obtainable [21]. A particular solution {V } should be obtained from: (27) in which:…”

Section: Modified Normal Flow Algorithmmentioning

confidence: 99%

“…Normal flow GDC Arc-length MRD algorithm [21] method [6] method [20] method [7 From Table 6, the minimum number of iterations is associated with the three-point scheme.…”

Section: Examplementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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An accelerated incremental algorithm to trace the nonlinear equilibrium path of structures

Saffari

Mirzai

Mansouri

2012

Lat. Am. j. solids struct.

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Advanced energy‐based analyses of trusses employing hybrid metaheuristics

Bekdaş

Kayabekir

Niğdeli

et al. 2019

Structural Design Tall Build

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Summary Total potential optimization using metaheuristic algorithm (TPO/MA) is an alternative method in structural analyses, and it is a black‐box application for nonlinear analyses. In the study, an advanced TPO/MA using hybridization of several metaheuristic algorithms is investigated to solve large‐scale structural analyses problems. The new generation algorithms considered in the study are flower pollination algorithm (FPA), teaching learning‐based optimization, and Jaya algorithm (JA). Also, the proposed methods are compared with methodologies using classic and previously used algorithms such as differential evaluation, particle swarm optimization, and harmony search. Numerical investigations were carried out for structures with four to 150 degrees of freedoms (design variables). It has been seen that in several runs, JA gets trapped into local solutions. For that reason, four different hybrid algorithms using fundamentals of JA and phases of other algorithms, namely, JA using Lévy flights, JA using Lévy flights and linear distribution, JA with consequent student phase, and JA with probabilistic student phase (JA1SP), are developed. It is observed that among the variants tried, JA1SP is seen to be more effective on approaching to the global optimum without getting trapped in a local solution.

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