Beam finite element for modal analysis of FGM structures

Muŕın, Just́ın; Aminbaghai, Mehdi; Hrabovský, Juraj; Gogola, Roman; Kugler, Stephan

doi:10.1016/j.engstruct.2016.04.042

Cited by 40 publications

(20 citation statements)

References 56 publications

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“…In this example we consider a rectangular cross-section (height ) which is made from pure aluminum (Al6061-TO, 9 = 69 10 E  , = 0.33  ) in the core and pure titancarbid (TiC, 9 = 480 10 E  , = 0.33  ) at the outer surfaces. Due to Murin et al [3] the variation of the material properties is assumed to be linear in both transverse directions (see Fig. 2a where ten layers are used to approximate the continuous distribution).…”

Section: Rectangular Fgm Cross-sectionmentioning

confidence: 99%

“…the continuous variation is approximated by layers of one element horizontally and two elements vertically. It is shown in [3] that the application of ten layers delivers good accuracy regarding…”

Section: Rectangular Fgm Cross-sectionmentioning

confidence: 99%

“…Many achievements regarding the numerical analysis of such beam structures in the static and the dynamic regime are due to Murin et al [1,2,3,15] (and due to the references therein), where the authors focus on classical beam theory with a minimum number of degrees of freedom. There, the cross-section is assumed to be rigid in its projection plane, i.e.…”

Section: Introductionmentioning

confidence: 99%

“…In this text, we restrict ourselves to a linear isotropic elastic case at each point of the beam's domain where Young's modulus and Poisson's ratio may depend arbitrarily on the lateral and transverse direction. The cross-sectional shape and the constitutive relation is assumed to be constant along the beam's axis 3. Due to that, a simply supported reference beam is modeled for transverse loading, for axial loading the reference beam is unmovable at the middle, while regarding torsional loading both reference beam ends are fork supported.…”

mentioning

confidence: 99%

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On the Access to Transverse Shear Stiffnesses and to Stiffness Quantities for Non-Uniform Warping Torsion in FGM Beam Structures

Kugler

Peter

Muŕın

2019

Strojnícky Časopis - Journal of Mechanical Engineering

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The application of first order shear beam theory in the analysis of beam structures made of functionally graded materials requires the access to homogenized stiffness quantities. These quantities depend on the cross-sectional shape and on the spatial variation of constitutive parameters. Some of these stiffness quantities can be evaluated easily by simple integration, however, the access to transverse shear stiffnesses and to stiffness quantities regarding warping torsion is typically cumbersome. In this contribution a novel approach for their evaluation is proposed, which is based on a reference beam problem. Here, we restrict ourselves to double symmetric cross-sections, however, a generalization of the proposed method to the arbitrary case is obvious. Besides that, a novel approach to cover non-uniform warping torsion is included. The proposed method is efficient, since the discretization of the cross-section suffices, and accurate as can be shown in challenging bench mark problems.

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Section: Rectangular Fgm Cross-sectionmentioning

confidence: 99%

Section: Rectangular Fgm Cross-sectionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

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On the Access to Transverse Shear Stiffnesses and to Stiffness Quantities for Non-Uniform Warping Torsion in FGM Beam Structures

Kugler

Peter

Muŕın

2019

Strojnícky Časopis - Journal of Mechanical Engineering

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“…The element, respectively, used Lagrange and Hermite functions to interpolate the axial and transverse displacements, is accurate in evaluating the natural frequencies. Murin et al [26] took into account the effects of shear force deformation and variation of longitudinal inertia and rotary inertia in derivation of a finite element formulation for modal analysis of FGM structures. The accuracy of the formulation derived in the work has been confirmed by comparing the obtained results with the ones using the commercial finite element package ANSYS.…”

Section: Introductionmentioning

confidence: 99%

Dynamic Analysis of Functionally Graded Timoshenko Beams in Thermal Environment Using a Higher‐Order Hierarchical Beam Element

Nguyen¹,

Bui

2017

Mathematical Problems in Engineering

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A higher-order finite beam element for free and forced vibration analysis of functionally graded Timoshenko beams in thermal environment is formulated by using hierarchical functions to interpolate the kinematic variables. The shear strain is constrained to constant to improve the efficiency of the element. The effect of environmental temperature is taken into account in the element derivation by considering that the material properties are temperature-dependent and the temperature is nonlinear distribution in the beam thickness. The accuracy of the derived formulation is confirmed by comparing the results obtained in the present work with the published data. Numerical investigations show that the formulated element is efficient, and it is capable of giving accurate vibration characteristics by a small number of elements. A parametric study is carried out to highlight the effect of the material inhomogeneity, temperature rise, and loading parameter on the dynamic behaviour of the beams. The influence of the aspect ratio on the dynamic behaviour of the beam is also examined and highlighted.

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Beam Dynamics Using a Generalized Beam Theory Based on the Solution of a Reference Beam Problem

Kugler

Fotiu

Muŕın³

2020

Analysis of Shells, Plates, and Beams

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Beam finite element for modal analysis of FGM structures

Cited by 40 publications

References 56 publications

On the Access to Transverse Shear Stiffnesses and to Stiffness Quantities for Non-Uniform Warping Torsion in FGM Beam Structures

On the Access to Transverse Shear Stiffnesses and to Stiffness Quantities for Non-Uniform Warping Torsion in FGM Beam Structures

Dynamic Analysis of Functionally Graded Timoshenko Beams in Thermal Environment Using a Higher‐Order Hierarchical Beam Element

Beam Dynamics Using a Generalized Beam Theory Based on the Solution of a Reference Beam Problem

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