A higher order model for thin-walled structures with deformable cross-sections

Vieira, Ricardo; Virtuoso, Francisco; Pereira, E. B. R.

doi:10.1016/j.ijsolstr.2013.10.023

Cited by 42 publications

(20 citation statements)

References 52 publications

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“…Other researchers have developed TTT introducing the eigenvalue-type crosssectional analysis [42]- [43] establishing deformation modes and permitting their sorting in order of significance. Ranzi and Luongo [44], Jönsson and Andreassen [45]- [48] and Vieira et al [49] have employed eigenvalue cross-sectional analysis highlighting the fact that with this approach it is not necessary to classify cross-sections according to their geometrical configuration (open-, close-shaped, branched or un-branched). Additionally, the resulting modes contain the most significant ones and form a more meaningful and insightful basis of functions as compared to GBT ones which exhibit a more local character [44].…”

Section: Higher Order Beam Theories Considering Warping and Distortionmentioning

confidence: 99%

Influence of in-Plane Deformation in Higher Order Beam Theories

Sapountzakis

Argyridi

2018

Strojnícky Časopis - Journal of Mechanical Engineering

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Comparing Euler-Bernoulli or Tismoshenko beam theory to higher order beam theories, an essential difference can be depicted: the additional degrees of freedom accounting for out-of plane (warping) and in-plane (distortional) phenomena leading to the appearance of respective higher order geometric constants. In this paper, after briefly overviewing literature of the major beam theories taking account warping and distortional deformation, the influence of distortion in the response of beams evaluated by higher order beam theories is examined via a numerical example of buckling drawn from the literature.

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Section: Higher Order Beam Theories Considering Warping and Distortionmentioning

confidence: 99%

Influence of in-Plane Deformation in Higher Order Beam Theories

Sapountzakis

Argyridi

2018

Strojnícky Časopis - Journal of Mechanical Engineering

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“…Additionally, their arrangements were in accordance with the sequence they appeared in, which showed the capability of a hierarchy. The proposed simplified approach, although involved with cross-section analysis, was different from both the theory of Camotim et al [28] for obtaining GBT deformation modes or that of Vieira et al [29] for formulating the higher order model. Both of these theories have to solve the generalized eigenvalue problem to uncouple the governing differential equations or the basis functions, which is quite demanding.…”

Section: Sectional Deformation Modesmentioning

confidence: 99%

“…Therefore, an ideal thin-walled model is crucially dependent on the reasonable description of deformation modes. In this section, cross-section analysis has been carried out to explore an approach to identify sectional deformation modes of thin-walled structures, in reference to Bebiano et al [28] and Vieira et al [29].…”

Section: Cross-section Analysismentioning

confidence: 99%

A Simplified Approach to Identify Sectional Deformation Modes of Thin-Walled Beams with Prismatic Cross-Sections

Zhang

Zhu

et al. 2018

Applied Sciences

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In this paper, a simplified approach to identify sectional deformation modes of prismatic cross-sections is presented and utilized in the establishment of a higher-order beam model for the dynamic analyses of thin-walled structures. The model considers the displacement field through a linear superposition of a set of basis functions whose amplitudes vary along the beam axis. These basis functions, which describe basis deformation modes, are approximated from nodal displacements on the discretized cross-section midline, with interpolation polynomials. Their amplitudes acting in the object vibration shapes are extracted through a modal analysis. A procedure similar to combining like terms is then implemented to superpose basis deformation modes, with equal or opposite amplitude, to produce primary deformation modes. The final set of the sectional deformation modes are assembled with primary deformation modes, excluding the ones constituting conventional modes. The derived sectional deformation modes, hierarchically organized and physically meaningful, are used to update the basis functions in the higher-order beam model. Numerical examples have also been presented and the comparison with ANSYS shell model showed its accuracy, efficiency, and applicability in reproducing three-dimensional behaviors of thin-walled structures.

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“…A comparable theory is the method of Generalized Eigenvectors [12], whose modes are obtained through a cross-section discretization using two-dimensional elements. It is also remarkable that Vieira et al [13,14] have proposed a high order one-dimensional model being an alternative to those theories. It is credible that these theories are powerful enough to deal with almost any arbitrary thinwalled cross-sections with an acceptable precision.…”

Section: Introductionmentioning

confidence: 99%

A new approach to the identification of distortion modes of thin-walled structures based on plate/shell theory

Zhang

Zhu

et al. 2019

MATEC Web Conf.

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In this paper, a new approach to identify cross-section deformation modes is presented and utilized in the establishment of a high-order beam model for dynamic analyses of thin-walled structures. Towards this end, a systematic procedure to extract cross-section in-plane vibration shapes for a thin-walled cross-section is developed based on elastic plate/shell theory. Then the distortion shapes are separated from vibration shapes by removing the components of classic modes involved with the minimum value problem of 2-norm. Sequentially, curve fitting method is utilized to approximate the distortion shape functions along the cross-section midline. It should be noticed that these distortion modes are arranged in hierarchy consistent with the order that they are identified and the number of distortions to be identified depends on the required model precision. Based on this, Hamilton's principle is applied to formulate the dynamic governing equations of the beam by constructing its displacement field with the linear superposition of the cross-section mode shapes including distortions. Numerical examples are also presented to validate the new approach and to demonstrate its efficiency in the reproduction of three-dimensional behaviours of thin-walled structures in dynamic analyses.

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A higher order model for thin-walled structures with deformable cross-sections

Cited by 42 publications

References 52 publications

Influence of in-Plane Deformation in Higher Order Beam Theories

Influence of in-Plane Deformation in Higher Order Beam Theories

A Simplified Approach to Identify Sectional Deformation Modes of Thin-Walled Beams with Prismatic Cross-Sections

A new approach to the identification of distortion modes of thin-walled structures based on plate/shell theory

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