Initial postbuckling behavior of thin-walled frames under mode interaction

Rizzi, Nicola Luigi; Varano, Valerio; Gabriele, Stefano

doi:10.1016/j.tws.2013.03.004

Cited by 71 publications

(42 citation statements)

References 16 publications

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“…Geometric nonlinearities have to be considered, as well, viz . by using the suggestions presented in , while a complete dynamic approach for the generalized beam theory has been addressed in and in the references cited therein.…”

Section: Resultsmentioning

confidence: 99%

An analytical assessment of finite element and isogeometric analyses of the whole spectrum of Timoshenko beams

2016

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The theoretical results relevant to the vibration modes of Timoshenko beams are here used as benchmarks for assessing the correctness of the numerical values provided by several finite element models, based on either the traditional Lagrangian interpolation or on the recently developed isogeometric approach. Comparison of results is performed on both spectrum error (in terms of the detected natural frequencies) and on the l2 relative error (in terms of the computed eigenmodes): this double check allows detecting for each finite element model, and for a discretization based on the same number of degrees‐of‐freedom, N, the frequency threshold above which some prescribed accuracy level is lost, and results become more and more unreliable. Hence a quantitative way of measuring the finite element performance in modeling a Timoshenko beam is proposed. The use of Fast Fourier Transform is finally employed, for a selected set of vibration modes, to explain the reasons of the accuracy decay, mostly linked to a poor separation of the natural frequencies in the spectrum, which is responsible of some aliasing of modes.

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Section: Resultsmentioning

confidence: 99%

An analytical assessment of finite element and isogeometric analyses of the whole spectrum of Timoshenko beams

2016

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“…Also the relevant effort of modeling out of plane deformation configurations and related buckling phenomena must be pursued, see the guidelines described, for example, in [18][19][20][21][22][23][24][25][26][27].…”

Section: Discussionmentioning

confidence: 99%

Fiber rupture in sheared planar pantographic sheets: Numerical and experimental evidence

Turco

Dell’Isola

Rizzi

et al. 2016

Mechanics Research Communications

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“…Other issues of relevance in the structural context are related to damage and fracture characterization (see for some examples [57][58][59][60][61][62]) and fluid-structure interaction, which is particularly delicate for these kinds of light systems and with heterogeneous material properties (see for further details [63][64][65][66]). These aspects can involve instability of the structure, which being very complex require unconventional computational methods (see, e.g., [67][68][69][70]). It is worth investigating the use of the Generalized Beam Theory in order to model in a more accurate way the fibers, in particular taking cross section distortions into account (see, e.g., [71][72][73]).…”

Section: Discussionmentioning

confidence: 99%

In plane shear and bending for first gradient inextensible pantographic sheets: numerical study of deformed shapes and global constraint reactions

Greco

Giorgio

Battista

2016

Mathematics and Mechanics of Solids

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The aim of the present paper is the analysis of a two-dimensional continuum with two families of inextensible fibers that are orthogonal in the initial configuration. In the first part of the work, a new formulation is presented, in which the problem is reduced to a standard nonlinear constrained minimization, while in the second part of the work several numerical investigations are presented considering different boundary conditions with respect to standard symmetric bias extensional tests. The conceptual framework can be recognized in the researches by Pipkin and Rivlin on inextensible nets. Furthermore, an implicit version of the Rivlin representation of the generic placement for a two-dimensional sheet with two families of inextensible fibers is provided by considering the angles of the fiber directors as degrees of the freedom of the formulation. In this way the first gradient formulation is given in terms of two angle fields only.

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Initial postbuckling behavior of thin-walled frames under mode interaction

Cited by 71 publications

References 16 publications

An analytical assessment of finite element and isogeometric analyses of the whole spectrum of Timoshenko beams

An analytical assessment of finite element and isogeometric analyses of the whole spectrum of Timoshenko beams

Fiber rupture in sheared planar pantographic sheets: Numerical and experimental evidence

In plane shear and bending for first gradient inextensible pantographic sheets: numerical study of deformed shapes and global constraint reactions

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