FE Modeling and Analysis of Isotropic and Orthotropic Beams Using First Order Shear Deformation Theory

Elshafei, M. Adnan

doi:10.4236/msa.2013.41010

Cited by 10 publications

(15 citation statements)

References 26 publications

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“…From equations (4-5) and (8) into equation 14, the strain energy can be stated as: The potential energy V of the applied harmonic axial and flexural forces, as shown in Fig (2), can be given by:…”

Section:  mentioning

confidence: 99%

“…Most of the models are based on two approaches. In the first approach, formulations are based on approximate shape functions such as the work of [1]- [7], and recently [8]. In the second approach, exact shape functions which are based on the static solution of the governing equilibrium equations, such as the work of [9].…”

Section: Introductory Review On Finite Element Formulationmentioning

confidence: 99%

“…Their formulations incorporate the effects of Poisson's ratio, shear deformation, rotary inertia and coupling of extensional-bending and bending-torsional deformations. Recently, [8] developed a finite element model to predict the static and free vibration analyses for isotropic and orthotropic beams with different boundary conditions and length-to-thickness ratios. Based on higher-order shear deformation theory, [5] used the conventional finite element to analyze the free vibration behavior of laminated composite beams by considering the effects of rotary inertia, Poisson's effect, and coupled extensional and bending deformations.…”

Section: Introductory Review On Finite Element Formulationmentioning

confidence: 99%

See 2 more Smart Citations

Super-Convergent Finite Element for Dynamic Analysis of Symmetric Composite Shear-deformable Beams under Harmonic Forces

Hjaji¹,

Nagiar²,

Allaboudi³

et al. 2016

IOSR

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A super-convergent finite element is formulated for the dynamic flexural response of symmetric laminated composite beams subjected to various transverse harmonic forces. Based on the assumptions of Timoshenko beam theory, a one-dimensional finite beam element with two-nodes and four degrees of freedom per element is developed. The new beam element is applicable to symmetric laminated composite beams and accounts for the effects of shear deformation, rotary inertia, and Poison's ratio. The exact closed-form solution for flexural displacement functions developed in this study is employed to develop exact shape functions. Although the present finite element formulation is developed to obtain the steady state dynamic response but can be also used to capture the quasi-static analysis of the symmetric laminated composite beams. Moreover, it is also used to extract the natural frequencies and mode shapes for flexural response. The accuracy and efficiency of the present finite beam element are shown through comparisons with other established exact and Abaqus finite element solutions. The new element is demonstrated to be free from shear locking and mesh discretization errors occurring in conventional finite element solutions and illustrates an excellent agreement with those based on finite element solutions at a fraction of the computational and modeling cost.

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Section:  mentioning

confidence: 99%

Section: Introductory Review On Finite Element Formulationmentioning

confidence: 99%

Section: Introductory Review On Finite Element Formulationmentioning

confidence: 99%

See 1 more Smart Citation

Super-Convergent Finite Element for Dynamic Analysis of Symmetric Composite Shear-deformable Beams under Harmonic Forces

Hjaji¹,

Nagiar²,

Allaboudi³

et al. 2016

IOSR

View full text Add to dashboard Cite

show abstract

“…The Timoshenko beam theory deals with two differential equations of motion in terms of deflection and cross-section rotation. The Timoshenko beam theory has come into focus with considerable developments of the finite element method and its application in practice [7][8][9].…”

Section: Introductionmentioning

confidence: 99%

Spectral element analysis of free - vibration of Timoshenko beam

Hamioud

Khalfallah

2018

IJEM

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The paper describes free vibration of Timoshenko beam by using spectral element method. Based on the partial differential equation of motion, the dynamic stiffness matrix in the frequency domain is formulated. In this case, natural frequencies for simply supported beam are obtained for each mode of vibration. In this study, three solutions are presented: (1) the analytical solution, (2) the finite element method, and (3) the spectral element method. In the last method, the beam is described by one element only, but in finite element modelling, the number of elements varies in order to improve the quality of the solution. Numerical results obtained by these three methods are collected. The spectral element method displays high performance compared to the finite element approach, and is considered as interesting tool in the structural dynamic field.

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“…[4] conducted a study of free vibration analyses of axially loaded laminated composite beams based on higher-order shear deformation theory using dynamic stiffness matrix method to solve the free vibration and buckling problems of axially loaded laminated composite beams with arbitrary lay-ups. Elshafei [5] used MATLAB code to compute the natural frequencies and the static deformation of isotropic and orthotropic beams using First Order Shear Deformation Theory. Thakur, A. S., & Patel, N. [6] provided a literature survey revealing that a large number of studies dealed with dynamic behaviors of laminated composite beams.…”

Section: Introductionmentioning

confidence: 99%

The Effect of Various Fiber Orientations and Boundary Conditions on Natural Frequencies of Laminated Composite Beam

Norman¹,

Zainuddin²,

Mahmud³

2018

IJET

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This paper investigates the free vibration characteristics of laminate composite beam for various lamination schemes and under various boundary conditions. A beam model with the aspect ratio (length to thickness) of 25 to 150 made of carbon/ epoxy laminates under free vibration were constructed using a commercially available finite element software (ANSYS). The varied parameters are the lamination schemes (cross ply, angle ply and unidirectional ply) and boundary conditions (Clamp-Free (C-F), Clamp-Clamp (C-C), Clamp-Hanger (C-H), Free-Free (F-F) and Hanger-Hanger (H-H) ). For each case, finite element simulations were performed and the natural frequencies were determined. Mode shapes were also analyzed to observe the beam’s deformation behavior. Results showed that increasing aspect ratio will decrease natural frequencies for the first seven mode shapes. In terms of lamination scheme, the unidirectional ply produced the highest frequency (34.26 Hz), followed by cross ply (34.05 Hz) and angle ply (13.60 Hz) at the aspect ratio of 25. In terms of boundary conditions, the Hanger-Hanger boundary condition produced the highest natural frequency (2272.52 Hz) at the aspect ratio of 25, while Clamped-Free boundary condition produced the lowest frequency (2.28 Hz) at the aspect ratio of 150. In general, it can be concluded that the current study is useful and has contributed significant knowledge to better understand of effect of various fiber orientations and boundary conditions on the natural frequencies of laminated composite beam.

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FE Modeling and Analysis of Isotropic and Orthotropic Beams Using First Order Shear Deformation Theory

Cited by 10 publications

References 26 publications

Super-Convergent Finite Element for Dynamic Analysis of Symmetric Composite Shear-deformable Beams under Harmonic Forces

Super-Convergent Finite Element for Dynamic Analysis of Symmetric Composite Shear-deformable Beams under Harmonic Forces

Spectral element analysis of free - vibration of Timoshenko beam

The Effect of Various Fiber Orientations and Boundary Conditions on Natural Frequencies of Laminated Composite Beam

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