A homotopy method applied to elastica problems

Watson, Layne T.; Wang, Chang Y.

doi:10.1016/0020-7683(81)90044-5

Cited by 51 publications

(11 citation statements)

References 19 publications

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“…Contrary to that, there is a much less of works studying large deflection analysis of initially curved beams, see e.g., [9][10][11][12][13][14][15][16], or publications dealing with large deflections of beam composed of several initially curved members subjected to arbitrary loading state, e.g., [17][18][19][20][21][22][23][24]. In work done by Faulkner et al [18], the segmental shooting technique is presented.…”

Section: Introductionmentioning

confidence: 99%

“…Lee et al [19] showed post-buckling analysis of elastic frame using elliptic integral formulation. Furthermore, a homotopy method and its comparison with some other numerical methods is discussed by Watson and Wang [16]. A discrete approach is proposed by Bunce and Brown [9] and Srpčič and Saje [14], where a finite difference solutions to the governing differential equations are obtained.…”

Section: Introductionmentioning

confidence: 99%

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A simple method for determining large deflection states of arbitrarily curved planar elastica

2013

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The paper discusses a relatively simple method for determining large deflection states of arbitrarily curved planar elastica, which is modeled by a finite set of initially straight flexible segments. The basic equations are built using Euler-Bernoulli and large displacement theory. The problem is solved numerically using RungeKutta-Fehlberg integration method and Newton method for solving systems of nonlinear equations. This solution technique is tested on several numerical examples. From a comparison of the results obtained and those found in the literature, it can be concluded that the developed method is efficient and gives accurate results. The solution scheme displayed can serve as reference tool to test results obtained via more complex algorithms.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A simple method for determining large deflection states of arbitrarily curved planar elastica

2013

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“…(3)(4)(5) with boundary conditions (6,7,(10)(11)(12)(13); to solve this, we need values for F, , G, and .…”

Section: Methodsmentioning

confidence: 99%

“…The equilibrium shape of an elastica can then be described by a set of nonlinear differential equations, which can be integrated numerically or expressed in terms of elliptic functions. We shall not discuss the large deflections of simple members such as the cantilever under a tip load or the pulling apart of circular and square rings, where the deformation behaviors are well understood (see e.g., [3][4][5][6]). …”

Section: Introductionmentioning

confidence: 99%

Effect of flexible joints on the stability and large deflections of a triangular frame

2008

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SummaryAn isosceles triangular frame with rotationally resistive joints under a tip load is studied. The large in-plane deformation elastica equations are formulated. Stability analysis shows the frame can buckle symmetrically or asymmetrically. Post-buckling behavior showing limit load and hysteresis are obtained by shooting and homotopy numerical algorithms. The behavior of a frame with rigid joints is studied in detail. The effects of joint spring constant and base length are found.

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“…In this paper, the idea of homotopy optimization [18][19][20] is applied to dynamical systems and, in particular, those that are chaotic in nature. By augmenting the system equations with observer-like terms, the homotopy optimization technique avoids diverging when simulating chaotic systems, but does so using single-shooting rather than the more complicated multiple-shooting approach.…”

Section: Introductionmentioning

confidence: 99%

Single-shooting homotopy method for parameter identification in dynamical systems

Vyasarayani

McPhee

2012

Phys. Rev. E

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An algorithm for identifying parameters in dynamical systems is developed in this work using homotopy transformations and the single-shooting method. The equations governing the dynamics of the mathematical model are augmented with observer-like homotopy terms that smooth the objective function. As a result, premature convergence to a local minimum is avoided and the obtained parameter estimates are globally optimal. Numerical examples are presented to demonstrate the application of the proposed approach to chaotic systems.

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A homotopy method applied to elastica problems

Cited by 51 publications

References 19 publications

A simple method for determining large deflection states of arbitrarily curved planar elastica

A simple method for determining large deflection states of arbitrarily curved planar elastica

Effect of flexible joints on the stability and large deflections of a triangular frame

Single-shooting homotopy method for parameter identification in dynamical systems

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