Conversion from imperfection-sensitive into imperfection-insensitive elastic structures. II: Numerical investigation

Schranz, Christian; Krenn, Burkhard; Mang, Herbert A.

doi:10.1016/j.cma.2005.05.025

Cited by 29 publications

(25 citation statements)

References 5 publications

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“…9), respectively, and the reduction of the rise of the undeformed structure [34]. The results of this investigation include different modes of conversion from imperfection-sensitive into imperfection-insensitive structures as well as failure to achieve such a conversion.…”

Section: Conversion From Imperfection-sensitive Into Imperfection-insmentioning

confidence: 98%

“…This mode of analysis primarily serves the purpose of deducing important theoretical results which facilitate the verification of specific numerical results. New mathematical conditions for symmetric bifurcation from nonlinear prebuckling paths are presented [34].…”

Section: Conversion From Imperfection-sensitive Into Imperfection-insmentioning

confidence: 99%

“…Increasing the stiffness of an elastic spring, suitably attached to the structure, however, usually enables its conversion from an imperfectionsensitive into an imperfection-insensitive structure. Hence, additional supports of a structure may be effective means to achieve the desired conversion [34].…”

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%

See 3 more Smart Citations

Computational mechanics of materials and structures

Mang¹,

Eberhardsteiner²,

Hellmich³

et al. 2009

Engineering Structures

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Section: Conversion From Imperfection-sensitive Into Imperfection-insmentioning

confidence: 98%

Section: Conversion From Imperfection-sensitive Into Imperfection-insmentioning

confidence: 99%

Section: Conversion From Imperfection-sensitive Into Imperfection-insmentioning

confidence: 99%

Section: Conversion From Imperfection-sensitive Into Imperfection-insmentioning

confidence: 99%

See 2 more Smart Citations

Computational mechanics of materials and structures

Mang¹,

Eberhardsteiner²,

Hellmich³

et al. 2009

Engineering Structures

Self Cite

View full text Add to dashboard Cite

show abstract

“…Also, the geometrical nonlinearity, the post-buckling and qualitative improvement of sensitive structures (Gao et al, 2003;Schranz et al, 2006;Steinboeck et al, 2008) have become more and more attractive. Shon et al (2002) analyzed the effect of global instability caused by joint rigidity, and Lopez et al (2007) carried out analytic and experimental research into the Euler buckling of a member and snap-through at the node.…”

Section: Introductionmentioning

confidence: 99%

Characteristics of bifurcation and buckling load of space truss in consideration of initial imperfection and load mode

Shon

Lee

2013

J. Zhejiang Univ. Sci. A

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Abstract:This study investigated characteristics of bifurcation and critical buckling load by shape imperfection of space truss, which were sensitive to initial conditions. The critical point and buckling load were computed by the analysis of the eigenvalues and determinants of the tangential stiffness matrix. The two-free-nodes example and star dome were selected for the case study in order to examine the nodal buckling and global buckling by the sensitivity to the eigen buckling mode and the analyses of the influence, and characteristics of the parameters as defined by the load ratio of the center node and surrounding node, as well as rise-span ratio were performed. The sensitivity to the imperfection of the initial shape of the two-free-nodes example, which occurs due to snapping at the critical point, resulted in bifurcation before the limit point due to the buckling mode, and the buckling load was reduced by the increase in the amount of imperfection. The two sensitive buckling patterns of the numerical model are established by investigating the displaced position of the free nodes, and the asymmetric eigenmode greatly influenced the behavior of the imperfection shape whether it was at limit point or bifurcation. Furthermore, the sensitive mode of the two-free-nodes example was similar to the in-extensional basis mechanism of a simplified model. The star dome, which was used to examine the influence among several nodes, indicated that the influence of nodal buckling was greater than that of global buckling as the rise-span ratio was higher. Besides, global buckling is occurred with reaching bifurcation point as the value of load ratio was higher, and the buckling load level was about 50%-70% of load level at limit point.

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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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Conversion from imperfection-sensitive into imperfection-insensitive elastic structures. II: Numerical investigation

Cited by 29 publications

References 5 publications

Computational mechanics of materials and structures

Computational mechanics of materials and structures

Characteristics of bifurcation and buckling load of space truss in consideration of initial imperfection and load mode

Remarkable postbuckling paths analyzed by means of the consistently linearized eigenproblem

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