Conversion from imperfection-sensitive into imperfection-insensitive elastic structures I: Theory

Mang, Herbert A.; Schranz, Christian; Mackenzie‐Helnwein, Peter

doi:10.1016/j.cma.2005.05.024

Cited by 37 publications

(30 citation statements)

References 8 publications

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“…without an incremental analysis. Mang et al [7] extended the considerations to the postbuckling regime insofar as they investigated the possibility of converting an imperfection-sensitive system into an imperfection-insensitive system by means of minor structural modifications, which is the second aforementioned task.…”

Section: Motivationmentioning

confidence: 99%

Remarkable postbuckling paths analyzed by means of the consistently linearized eigenproblem

Steinboeck

Jia

Hoefinger

et al. 2008

Numerical Meth Engineering

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SUMMARYIn addition to the determination of load levels at critical points of stability problems, frequently the postbuckling behavior is of interest. For non-linear problems, the so-called consistently linearized eigenvalue problem is a suitable tangent linearization method, which facilitates determination of stability limits. The solution process of the eigenproblem is significantly simplified by appropriate coordinate transformations. Within this process, characteristic shapes of eigenvalue curves allow identification of bifurcation buckling modes, snap-through modes, and hilltop buckling modes. Mathematical properties of the eigenvalue curves are addressed and conclusions regarding the shape of postbuckling paths are drawn. Considerations also touch upon the conversion from imperfection sensitivity into insensitivity. The theoretical findings are corroborated by examples dealing with a von Mises truss and a similar discrete system, showing a remarkable postbuckling behavior such as a zero-stiffness equilibrium path. For both systems, the same approach of stiffness increase allows conversion from imperfection sensitivity into insensitivity.

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Section: Motivationmentioning

confidence: 99%

Remarkable postbuckling paths analyzed by means of the consistently linearized eigenproblem

Steinboeck

Jia

Hoefinger

et al. 2008

Numerical Meth Engineering

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“…are calculated [1]. It is self-evident that ((ũ(λ(η))), λ(η)) has to exist as equlibrium point on the primary path for all values of η in a neighborhood of 0.…”

Section: Limitations For Koiter's Postbuckling Analysismentioning

confidence: 99%

Is hilltop buckling imperfection sensitive or insensitive?

Hoefinger

Jia

Mang

2009

Proc Appl Math and Mech

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Hilltop buckling is the coincidence of a snap‐through point with a bifurcation point on the primary equilibrium path. An originally imperfection sensitive structure cannot be modified such that it shows both hilltop buckling and imperfection insensitivity. This is a rule for designing structures for imperfection insensitivity and guarantees validity of Koiter's postbuckling analysis, which would fail for imperfection insensitive hilltop buckling. (© 2009 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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“…Koiter's initial postbuckling analysis is applied in the framework of the Finite Element Method (FEM) to deduce mathematical relations associated with the transition from imperfection sensitivity to insensitivity [33]. This mode of analysis primarily serves the purpose of deducing important theoretical results which facilitate the verification of specific numerical results.…”

Section: Conversion From Imperfection-sensitive Into Imperfection-insmentioning

confidence: 99%

“…. Load-displacement path for a perfect as well as for an imperfect cylindrical shell (a) without and (b) with a spring attached to the shell [33] An important ingredient of the numerical investigation are accompanying linear eigenvalue analyses based on the so-called consistently linearized eigenproblem [33,34]. At the transition from imperfection sensitivity to insensitivity, the resulting eigenvalue curve, in general, has specific geometric properties (saddle points or planar points) at the bifurcation point.…”

Section: Conversion From Imperfection-sensitive Into Imperfection-insmentioning

confidence: 99%

Computational mechanics of materials and structures

Mang¹,

Eberhardsteiner²,

Hellmich³

et al. 2009

Engineering Structures

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Conversion from imperfection-sensitive into imperfection-insensitive elastic structures I: Theory

Cited by 37 publications

References 8 publications

Remarkable postbuckling paths analyzed by means of the consistently linearized eigenproblem

Remarkable postbuckling paths analyzed by means of the consistently linearized eigenproblem

Is hilltop buckling imperfection sensitive or insensitive?

Computational mechanics of materials and structures

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