Torsional warping eigenmodes of FGM beams with longitudinally varying material properties

Muŕın, Just́ın; Aminbaghai, Mehdi; Hrabovský, Juraj; Balduzzi, Giuseppe; Dorn, Michaël; Mang, Herbert A.

doi:10.1016/j.engstruct.2018.08.048

Cited by 14 publications

(5 citation statements)

References 21 publications

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“…Aribas etal. [21] investigated the static and dynamic analyses of noncircular composite helical bars considering the exact helix geometry and warping effect. Nguyen etal.…”

Section: Literature Reviewmentioning

confidence: 99%

Exact finite beam element for open thin walled doubly symmetric members under torsional and warping moments

Hjaji¹,

Nagiar²,

Krar³

et al. 2021

JSEAM

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Starting with total potential energy variational principle, the governing equilibrium coupled equations for the torsional-warping static analysis of open thin-walled beams under various torsional and warping moments are derived. The formulation captures shear deformation effects due to warping. The exact closed form solutions for torsional rotation and warping deformation functions are then developed for the coupled system of two equations. The exact solutions are subsequently used to develop a family of shape functions which exactly satisfy the homogeneous form of the governing coupled equations. A super-convergent finite beam element is then formulated based on the exact shape functions. Key features of the beam element developed include its ability to (a) eliminate spatial discretization arising in commonly used finite elements, and (e) eliminate the need for time discretization. The results based on the present finite element solution are found to be in excellent agreement with those based on exact solution and ABAQUS finite beam element solution at a small fraction of the computational and modelling cost involved.

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“…Aribas etal. [21] investigated the static and dynamic analyses of noncircular composite helical bars considering the exact helix geometry and warping effect. Nguyen etal.…”

Section: Literature Reviewmentioning

confidence: 99%

Exact finite beam element for open thin walled doubly symmetric members under torsional and warping moments

Hjaji¹,

Nagiar²,

Krar³

et al. 2021

JSEAM

View full text Add to dashboard Cite

show abstract

“…In the following, the equilibrium equations for TMM will be formulated. They are obtained as According to [10,11]…”

Section: Non-uniform Torsion Of the Fgm Beams With Stmdementioning

confidence: 99%

“…The polynomial ) ( E x I  is obtained by multiplication of the warping constant I  with the polynomial representation of Young's modulus, ) ( E x . After mathematical manipulation, [10][11][12], the following differential equation of fourth order, with the load polynomial…”

Section: Non-uniform Torsion Of the Fgm Beams With Stmdementioning

confidence: 99%

“…. 8The variable polynomial coefficients and establishing of the local finite element are given in [10]. The local finite element equations for non-uniform torsion (in particular for free torsional vibrations) read as follows (considering the definitions of positive quantities in the framework of the FEM, resulting in…”

Section: Non-uniform Torsion Of the Fgm Beams With Stmdementioning

confidence: 99%

“…is the first derivative of the angle of twist (the bicurvature) that is very often used as a 7th degree of freedom in the usual non-uniform torsion formulations [13 -14, 16].A detailed description of the matrix coefficients in (9) for modal analysis is presented in [10].The local finite element matrix Bin (9) is symmetric and the indices determine position of the relevant terms in the complete local finite element matrix (11).…”

Section: Non-uniform Torsion Of the Fgm Beams With Stmdementioning

confidence: 99%

See 2 more Smart Citations

Extension of the FGM Beam Finite Element by Warping Torsion

Muŕın

Hrabovský

Aminbaghai

et al. 2019

Strojnícky Časopis - Journal of Mechanical Engineering

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In the contribution, our 3D FGM Timoshenko beam finite element with 12x12 stiffness and mass matrices for doubly symmetric open and closed cross-section [1] is extended by warping torsion effect (non-uniform torsion) to 14x14 finite element matrices. A longitudinal continuous variation of effective material properties is considered by the finite element equations derivation, which can be obtained by homogenization of the spatial varying material properties in real FGM beam. Results of numerical elastostatic non-uniform torsional analysis of the FGM cantilever beam of I-cross-section are presented and the accuracy and effectiveness of the new FGM beam finite element is discussed and evaluated.

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Effect of Longitudinal Variation of Material Properties in Warping Torsion of FGM Beams

Muŕın¹,

Hrabovský²,

Kugler

et al. 2020

Analysis of Shells, Plates, and Beams

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Torsional warping eigenmodes of FGM beams with longitudinally varying material properties

Cited by 14 publications

References 21 publications

Exact finite beam element for open thin walled doubly symmetric members under torsional and warping moments

Exact finite beam element for open thin walled doubly symmetric members under torsional and warping moments

Extension of the FGM Beam Finite Element by Warping Torsion

Effect of Longitudinal Variation of Material Properties in Warping Torsion of FGM Beams

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