Stability of Structures with Small Imperfections

Roorda, J.

doi:10.1061/jmcea3.0000586

Cited by 103 publications

(9 citation statements)

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“…formulation for discrete elastic systems for which the perfect system has a unique buckling mode. The analysis is purely quasi-static and asymptotic for small imperfections, but did compare well with step buckling experiments on structural frames of the type built by Roorda [18]. For both unstable symmetric and asymmetric bifurcations, Thompson determined: (i) the relation between the static buckling load λ S (the max load) and the imperfection and (ii) the relation between the 'astatic load', λ N , and the imperfection.…”

Section: Buckling Under Step Loading With Spatially Uniform Pressurementioning

confidence: 93%

Nonlinear dynamics of spherical shells buckling under step pressure

2019

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Dynamic buckling is addressed for complete elastic spherical shells subject to a rapidly applied step in external pressure. Insights from the perspective of nonlinear dynamics reveal essential mathematical features of the buckling phenomena. To capture the strong buckling imperfection-sensitivity, initial geometric imperfections in the form of an axisymmetric dimple at each pole are introduced. Dynamic buckling under the step pressure is related to the quasi-static buckling pressure. Both loadings produce catastrophic collapse of the shell for conditions in which the pressure is prescribed. Damping plays an important role in dynamic buckling because of the time-dependent nonlinear interaction among modes, particularly the interaction between the spherically symmetric 'breathing' mode and the buckling mode. In general, there is not a unique step pressure threshold separating responses associated with buckling from those that do not buckle. Instead there exists a cascade of buckling thresholds, dependent on the damping and level of imperfection, separating pressures for which buckling occurs from those for which it does not occur. For shells with small and moderately small imperfections the dynamic step buckling pressure can be substantially below the quasi-static buckling pressure.

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Section: Buckling Under Step Loading With Spatially Uniform Pressurementioning

confidence: 93%

Nonlinear dynamics of spherical shells buckling under step pressure

2019

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“…In order to examine the ability of the Cosserat theory to model a frame with beams connected by Cosserat joints, attention is focused on the simple problem considered by Roorda [27,28]. In this problem the structure is made of two cantilevered beams, each having length O 5 and uniform rectangular cross-section with height K and width Z.…”

Section: Example Of a Simple Framementioning

confidence: 99%

“…In the problem considered by Roorda [27], the beams deform in the plane and the joint is loaded by a concentrated force of magnitude S applied in the negative h 4 (see Figure 12). Roorda [27] observed that the buckling of this structure is sensitive to changes in the point of application of the applied force. Here, three loads are considered.…”

Section: Example Of a Simple Framementioning

confidence: 99%

Post-Buckling Behavior of Nonlinear Elastic Beams and Three-Dimensional Frames Using the Theory of a Cosserat Point

Nadler

Rubin

2004

Mathematics and Mechanics of Solids

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The theory of a Cosserat point for rods has been developed to formulate the numerical solution of problems for nonlinear elastic rod and beams. This theory is fully nonlinear and can be used to model dynamic problems with large deformations and rotations. One objective of this paper is to show that this theory can be used to accurately predict the lateral buckling load and the three-dimensional post-buckling response of a cantilever beam with rectangular cross-section. The theory of a Cosserat point for homogeneous deformations is also used to formulate the theory of a flexible Cosserat joint which connects a finite set of beams at arbitrary orientations in three-space. Using this Cosserat joint and the Cosserat points for beam elements it is possible to formulate the numerical solution of problems of three-dimensional frames which are constructed by connecting beams by joints. A simple two-dimensional frame is considered, and both in-plane and out-of-plane large deformations are analyzed to test the Cosserat theory.

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“…where we note that positive values of k io imply destabilizing. Since the lowest power of θ o is 2, asymmetric postbifurcation of the kind experienced by the so-called Roorda Frame is not covered; see [Roorda 1965] and [Koiter 1966] for the elastic version, and [Byskov 1982-83] for the elastic-plastic version.…”

Section: Introductionmentioning

confidence: 99%

Untitled

2008

J. Mech. Mater. Struct.

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The mechanical threshold stress plasticity model of Follansbee and Kocks was designed to predict the flow stress of metals and alloys in the regime where thermally activated mechanisms are dominant and high temperature diffusion effects are negligible. In this paper we present a model that extends the original mechanical threshold stress to the high strain-rate regime (strain rates higher than 10 4 s −1 ) and attempts to allow for high temperature effects. We use a phonon drag model for moderate strain rates and an overdriven shock model for extremely high strain rates. A temperature dependent model for the evolution of dislocation density is also presented. In addition, we present a thermodynamically-based model for the evolution of temperature with plastic strain. Parameters for 6061-T6 aluminum alloy are determined and compared with experimental data. The strain-rate dependence of the flow stress of 6061-T6 aluminum is found to be in excellent agreement with experimental data. The amount of thermal softening is underestimated at high temperatures (greater than 500 K) but still is an improvement over the original model. We also find that the pressure dependence of the shear modulus does not completely explain the pressure dependence of the flow stress of 6061-T6 aluminum alloy.

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Stability of Structures with Small Imperfections

Cited by 103 publications

References 0 publications

Nonlinear dynamics of spherical shells buckling under step pressure

Nonlinear dynamics of spherical shells buckling under step pressure

Post-Buckling Behavior of Nonlinear Elastic Beams and Three-Dimensional Frames Using the Theory of a Cosserat Point

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