Snap‐Through and Bifurcation in a Simple Structure

Pecknold, David A.; Ghaboussi, Jamshid; Healey, Timothy J.

doi:10.1061/(asce)0733-9399(1985)111:7(909)

Cited by 81 publications

(32 citation statements)

References 9 publications

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“…This example has been treated by several authors, e.g. Pecknold et al 24 and Krenk. 25; 26 In the last reference, Krenk also presents an analytical result.…”

Section: ·3147mentioning

confidence: 96%

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Numerical treatment of complete load-deflection curves

Magnusson

Svensson

1998

Int. J. Numer. Meth. Engng.

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A method for direct computation of complete load-de ection curves, including both primary and secondary branches, as well as exact calculation of singular points is presented. The method used for path following is the cylindrical arc-length method in accordance with Crisÿeld.1 To calculate singular points, an extended system, as proposed by Keener and Keller, 2 has been adopted. The numerical problems arising from illconditioned sti ness matrices near the singular points, are circumvented using a de ation technique. By a modiÿcation of the constraint equation used in the arc-length method, a reliable method for branch switching has been obtained. This leads to a uniÿed approach to complete path following of structures with limit and bifurcation points.The use of this approach is demonstrated both on a simple two-bar truss as well as on a star-shaped shallow truss dome which exhibits complex stability characteristics. Comparisons are made with calculations found in the literature. ?

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“…This example has been treated by several authors, e.g. Pecknold et al 24 and Krenk. 25; 26 In the last reference, Krenk also presents an analytical result.…”

Section: ·3147mentioning

confidence: 96%

“…where (24) are the directional derivatives of the sti ness matrix with respect to the displacement and the load parameter, respectively. The dimension of the matrix K T is (2N + 1) × (2N + 1), and since K T is non-symmetric, it is expensive to factorize.…”

Section: Calculation Of Singular Pointsmentioning

confidence: 99%

Numerical treatment of complete load-deflection curves

Magnusson

Svensson

1998

Int. J. Numer. Meth. Engng.

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“…Since PLEA is the axial strain of a column, the third term in the blacket of Eq. (20) can be negligible compared with the other two terms, as long as the small strain assumption holds. Therefore the tangent stiffness matrix is almost symmetric and has the ordinary form of the sum of linear and geometric stiffness matrices.…”

Section: Elasticamentioning

confidence: 99%

“…(19) into the tangent stiffness equation (13) yields df =[kBE+kG+ 0 (P/EA)]ad (20) from which the buckling load can be obtained as its eigenvalue and where kBE is the linear stiffness matrix of the Bernoulli-Euler beam, and kG the geometric stiffness. kBE and kG correspond to kL and kNL in Eq.…”

Section: Elasticamentioning

confidence: 99%

Principle and Numerical Check of a Stiffness Equation for Plane Frames

Iwakuma

Hasegawa

Nishino

et al. 1987

Doboku Gakkai Ronbunshu

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A stiffness equation of plane frames is formulated in finite displacements by the total Lagrangian approach. The formulation is based on the physical interpretation of the polar decomposition theorem and does not use any variational principle. The corresponding differential equations are also given to show which theoretical solutions the discretized ones converge to. For the Bernoulli-Euler beam, the postbuckling behavior can be analysed accurately without the geometric stiffness matrix which helps to accelerate the convergence of solutions. On the other hand, the Timoshenko beam element must have the geometric stiffness in order to obtain the correct solutions. Finally the typical stability problems which have the bifurcation points in their equilibrium paths are solved to demonstrate the ability of the stiffness equation.

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“…Snap-through can also be studied qualitatively using a truss system [6]. Simplifying assumptions are usually needed in finding the analytical estimates.…”

Section: Introductionmentioning

confidence: 99%

Numerical pathologies in snap-through simulations

Chandra

Stanciulescu

Eason

et al. 2012

Engineering Structures

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Aircraft structures operating in severe environments may experience snap-through, causing the curvature on part or all of the structure to invert inducing fatigue damage. This paper examines the performance of beam and continuum nonlinear finite element formulations in conjunction with several popular implicit time stepping algorithms to assess the accuracy and stability of numerical simulations of snap-through events. Limitations for the structural elements are identified and we provide examples of interaction between spatial and temporal discretizations that affect the robustness of the overall scheme and impose strict limits on the size of the time step. These limitations need to be addressed in future works in order to develop accurate, robust and efficient simulation methods for response prediction of structures encountering extreme environments.

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Snap‐Through and Bifurcation in a Simple Structure

Cited by 81 publications

References 9 publications

Numerical treatment of complete load-deflection curves

Numerical treatment of complete load-deflection curves

Principle and Numerical Check of a Stiffness Equation for Plane Frames

Numerical pathologies in snap-through simulations

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