Extension of the FGM Beam Finite Element by Warping Torsion

AbstractIn 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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Numerical Analysis and Experimental Verification of Eigenfrequencies of Overhead ACSR Conductor

Transactions on Electrical Engineering ◽

10.14311/tee.2016.4.116 ◽

2020 ◽

Vol 5 (4) ◽

pp. 116-121

Author(s):

Juraj Hrabovský ◽

Roman Gogola ◽

Vladimír Goga ◽

František Janíček

Keyword(s):

Finite Element Method ◽

Finite Element ◽

Modal Analysis ◽

Cross Section ◽

Material Properties ◽

Numerical Experiments ◽

Volume Element ◽

Experimental Measurements ◽

The Finite Element Method ◽

Fgm Beam

This contribution deals with the modal analysis of ACSR conductor using the finite element method (FEM) and experimental measurements of eigenfrequencies. In numerical experiments for the modelling of the conductor the material properties of the chosen conductor cross-section are homogenized by the Representative Volume Element (RVE) method. The spatial modal analysis of the power line is carried out by means of our new 3D FGM beam finite element and by standard beam finite element of the commercial software ANSYS. Experimental measurements are also carried out for verification of the numerical calculation accuracy.

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Analysis of Timoshenko beam with Koch snowflake cross-section and variable properties in different boundary conditions using finite element method

Advances in Mechanical Engineering ◽

10.1177/16878140211060982 ◽

2021 ◽

Vol 13 (11) ◽

pp. 168781402110609

Author(s):

Hossein Talebi Rostami ◽

Maryam Fallah Najafabadi ◽

Davood Domiri Ganji

Keyword(s):

Finite Element Method ◽

Finite Element ◽

Boundary Conditions ◽

Natural Frequency ◽

Cross Section ◽

Timoshenko Beam ◽

Natural Frequencies ◽

Variable Properties ◽

The Third ◽

Koch Snowflake

This study analyzed a Timoshenko beam with Koch snowflake cross-section in different boundary conditions and for variable properties. The equation of motion was solved by the finite element method and verified by Solidworks simulation in a way that the maximum error was about 2.9% for natural frequencies. Displacement and natural frequency for each case presented and compared to other cases. Significant research achievements illustrate that if we change the Koch snowflake cross-section of the beam from the first iteration to the second, the area and moment of inertia will increase, and we have a 5.2% rise in the first natural frequency. Similarly, by changing the cross-section from the second iteration to the third, a 10.2% growth is observed. Also, the hollow cross-section is considered, which can enlarge the natural frequency by about 26.37% compared to a solid one. Moreover, all the clamped-clamped, hinged-hinged, clamped-free, and free-free boundary conditions have the highest natural frequency for the Timoshenko beam with the third iteration of the Koch snowflake cross-section in solid mode. Finally, examining important physical parameters demonstrates that variable density from a minimum value to the standard value along the beam increases the natural frequencies, while variable elastic modulus decreases it.

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Derivation of Effective Material Properties of Reinforced Braid Layer Using Detailed 3-D Finite Element Model

Transactions of the Korean Society of Mechanical Engineers A ◽

10.3795/ksme-a.2004.28.11.1752 ◽

2004 ◽

Vol 28 (11) ◽

pp. 1752-1759

Keyword(s):

Finite Element ◽

Finite Element Model ◽

Material Properties ◽

Element Model ◽

Effective Material Properties

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Effect of Fiber Geometry and Representative Volume Element on Elastic and Thermal Properties of Unidirectional Fiber-Reinforced Composites

Journal of Composites ◽

10.1155/2014/629175 ◽

2014 ◽

Vol 2014 ◽

pp. 1-12 ◽

Cited By ~ 19

Author(s):

Siva Bhaskara Rao Devireddy ◽

Sandhyarani Biswas

Keyword(s):

Thermal Conductivity ◽

Finite Element ◽

Thermal Properties ◽

Elastic Modulus ◽

Cross Section ◽

Representative Volume Element ◽

Material Properties ◽

Volume Element ◽

Unidirectional Fiber ◽

Representative Volume

The aim of present work is focused on the evaluation of elastic and thermal properties of unidirectional fiber-reinforced polymer composites with different volume fractions of fiber up to 0.7 using micromechanical approach. Two ways for calculating the material properties, that is, analytical and numerical approaches, were presented. In numerical approach, finite element analysis was used to evaluate the elastic modulus and thermal conductivity of composite from the constituent material properties. The finite element model based on three-dimensional micromechanical representative volume element (RVE) with a square and hexagonal packing geometry was implemented by using finite element code ANSYS. Circular cross section of fiber and square cross section of fiber were considered to develop RVE. The periodic boundary conditions are applied to the RVE to calculate elastic modulus of composite. The steady state heat transfer simulations were performed in thermal analysis to calculate thermal conductivity of composite. In analytical approach, the elastic modulus is calculated by rule of mixture, Halpin-Tsai model, and periodic microstructure. Thermal conductivity is calculated analytically by using rule of mixture, the Chawla model, and the Hashin model. The material properties obtained using finite element techniques were compared with different analytical methods and good agreement was achieved. The results are affected by a number of parameters such as volume fraction of the fibers, geometry of fiber, and RVE.

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Effect of Dead Load on Dynamic Characteristics of Rotating Timoshenko Beams

Mathematical Problems in Engineering ◽

10.1155/2015/582192 ◽

2015 ◽

Vol 2015 ◽

pp. 1-10 ◽

Cited By ~ 1

Author(s):

Yan-Qi Yin ◽

Bo Zhang ◽

Yue-ming Li ◽

Wei-Zhen Lu

Keyword(s):

Finite Element ◽

Cantilever Beam ◽

Dynamic Characteristics ◽

Timoshenko Beam ◽

Natural Frequencies ◽

Experimental Result ◽

Dead Load ◽

Rotating Speed ◽

Experimental Apparatus ◽

The Dead

The dynamic characteristics of a rotating cantilever Timoshenko beam under dead load are investigated in this paper. Considering the predeformation caused by dead load and centrifugal force, governing equation of rotating cantilever Timoshenko beam is derived based on Hamilton’s principle, and the influence of the load on natural vibration is revealed. A suit of modal experimental apparatus for cantilever beam is designed and used to test the natural frequencies under the dead load, and the natural frequencies under rotation condition are calculated with a commercial finite element code. Both the experimental result and numerical result are utilized to compare with the present theoretical result, and the results obtained by present modeling method show a good agreement with those obtained from the experiment and finite element method. It is found that the natural frequencies of cantilever beam increase with both the dead load and the rotating speed.

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On a Finite Element Formulation of Dynamical Torsion of Beams Including Warping Inertia and Shear Deformation Due to Nonuniform Warping

Journal of Vibration and Acoustics ◽

10.1115/1.3269131 ◽

1983 ◽

Vol 105 (4) ◽

pp. 476-483

Author(s):

A. Potiron ◽

D. Gay

Keyword(s):

Finite Element ◽

Shear Deformation ◽

Cross Section ◽

Experimental Results ◽

Finite Element Formulation ◽

Element Formulation ◽

Secondary Effects ◽

Mass Matrices ◽

Warping Displacement ◽

Thin Walled

We start from the energetical expressions of dynamical torsion of beams in terms of angular and warping displacement and velocity. We derive the stiffness and two mass matrices including both secondary effects for torsion: the shear deformation due to nonuniform warping and the warping inertia. The suitability of these matrices for evaluation modified torsional frequencies is investigated in the case of thick, as well as thin-walled, cross section beams by comparison with analytical and experimental results.

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Buckling of Standing Tapered Timoshenko Columns with Varying Flexural Rigidity Under Combined Loadings

International Journal of Structural Stability and Dynamics ◽

10.1142/s0219455415500170 ◽

2016 ◽

Vol 16 (06) ◽

pp. 1550017 ◽

Cited By ~ 8

Author(s):

D.-L. Sun ◽

X.-F. Li ◽

C. Y. Wang

Keyword(s):

Cross Section ◽

Timoshenko Beam ◽

Material Properties ◽

Flexural Rigidity ◽

Axial Loading ◽

Beam Theory ◽

Shear Rigidity ◽

Initial Value ◽

Buckling Loads ◽

The Stability

The stability of a nonuniform column subjected to a tip force and axially distributed loading is investigated based on the Timoshenko beam theory. An emphasis is placed on buckling of a standing column with varying cross-section and variable material properties under self-weight and tip force. Four kinds of columns with different taper ratios are analyzed. A new initial value method is suggested to determine critical tip force and axial loading at buckling. The effectiveness of the method is confirmed by comparing our results with those for Euler–Bernoulli columns for the case of sufficiently large shear rigidity. The effects of shear rigidity, taper ratio, and gravity loading on the buckling loads of a heavy standing or hanging column are examined.

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Closed-Form Approximate Formulas for Torsional Analysis of Hollow Tubes with Straight and Circular Edges

Journal of Mechanics ◽

10.1017/s1727719100002884 ◽

2009 ◽

Vol 25 (4) ◽

pp. 401-409 ◽

Cited By ~ 7

Author(s):

A. Doostfatemeh ◽

M. R. Hematiyan ◽

S. Arghavan

Keyword(s):

Finite Element Method ◽

Finite Element ◽

Closed Form ◽

Cross Section ◽

Stress Function ◽

Analytical Formulas ◽

The Cross ◽

Torsional Analysis ◽

Approximate Formulas ◽

Element Method

ABSTRACTSome analytical formulas are presented for torsional analysis of homogeneous hollow tubes. The cross section is supposed to consist of straight and circular segments. Thicknesses of segments of the cross section can be different. The problem is formulated in terms of Prandtl's stress function. The derived approximate formulas are so simple that computations can be carried out by a simple calculator. Several examples are presented to validate the formulation. The accuracy of formulas is verified by accurate finite element method solutions. It is seen that the error of the formulation is small and the formulas can be used for analysis of thin to moderately thick-walled hollow tubes.

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