Frame buckling: An illustration of the perturbation technique

Roorda, J.; Chilver, A. H.

doi:10.1016/0020-7462(70)90021-1

Cited by 37 publications

(8 citation statements)

References 3 publications

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“…For $ = 0 and $ = 24", experimental results by Roorda As far as third-order terms are concerned (straight line in Figs. 3 and 4), these results coincide with those obtained-through rather different approaches-by Koiter [3] and Roorda and Chilver [4], which in turn exhibit very good agreement with experimental results. Also, the newly computed fourth-order terms contribution seems to share the trend noticeable in experimental results.…”

Section: Rizzi DI Carlo and Pignatarosupporting

confidence: 93%

A Parametric Postbuckling Analysis of an Asymmetric Two-Bar Frame

Rizzi¹,

Carlo²,

Pignataro³

1980

Journal of Structural Mechanics

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The modified potential energy approach of flexurally elastic, axially, and shear undeformable beams is emplo:yed to investigate the buckling and (asymmetric) postbuckling behavior of the two-bar frame which was experimentally tested by Roorda in 1965. Following a Koiter-type energy approach, a suitable perturbation formulation is derived from a "hybrid" functional which is obtained by adding to the potential energy certain extra terms which account for the energy associated with the internal joint forces acting on the beam. In this way the nonlinear constraints expressing continuity of displacement across the joints are accommodated by introducing jointforces acting as Lagrangian multipliers. The inherent simplicity of the model herein proposed allows a thorough parametric analysis to be performed without undue complications up to and including fourth-order terms. The general trend compares favorably with the experimental results. Previous analytical results limited to a third-order analysis are in agreement with the present results. 43i5

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Section: Rizzi DI Carlo and Pignatarosupporting

confidence: 93%

A Parametric Postbuckling Analysis of an Asymmetric Two-Bar Frame

Rizzi¹,

Carlo²,

Pignataro³

1980

Journal of Structural Mechanics

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“…The theoretical and experimental studies were performed by many scientists: Andersen and Thomson [1], Beck [5], Evensen [13], Przybylski [20,21] and Tomski [27]. In the seventies of the previous century Roodr and Chilver [24] have proposed new method of solution of the boundary problems corresponding to slender systems. This method has been presented in detailed form by Osiński [19].…”

Section: Fig 1 Regions Of Local and Global Instabilitymentioning

confidence: 99%

Instability and vibration of multi-member columns subjected to Euler’s load

Sokół

Uzny

2015

Arch Appl Mech

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In this paper the instability and vibration phenomena of columns composed of three elements with different bending and compression stiffnesses are presented. In the internal rod the crack is taken into consideration and is being modeled by means of a rotational spring with linear characteristic. The boundary problem has been formulated on the basis of the Hamilton's principle. The proposed general form of problem formulation allows one to create five different systems on the basis of one mathematical model. The final formulation of the boundary problem has been carried out by means of a small parameter method. The monitoring of the columns is done by the analysis of the characteristic curves and shape modes. The obtained results are compared to the ones calculated for the uncracked columns. The results of numerical calculation are concern on vibration frequency, bifurcation load magnitude and bifurcation load-crack size relationship.

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“…Para el caso del modelo de Maxwell, formado por por un resorte y un amortiguamiento viscoso, tiene la expresión: [17] Donde ) (σ φ es una función monótona creciente con derivada decreciente.…”

Section: B) Viscoplasticidadunclassified