A spectral element model for thermal effect on vibration and buckling of laminated beams based on trigonometric shear deformation theory

2017 ◽  
Vol 133 ◽  
pp. 100-111 ◽  
Author(s):  
Li Jun ◽  
Jiang Li ◽  
Li Xiaobin
Keyword(s):  
Thermal Effect ◽  
Shear Deformation ◽  
Deformation Theory ◽  
Shear Deformation Theory ◽  
Element Model ◽  
Spectral Element ◽  
Laminated Beams

Finite element bending analysis of symmetric and non-symmetric functionally graded sandwich beams using a novel parabolic shear deformation theory

2021 ◽  
pp. 146442072110050
Author(s):  
Mohamed-Ouejdi Belarbi ◽  
Abdelhak Khechai ◽  
Aicha Bessaim ◽  
Mohammed-Sid-Ahmed Houari ◽  
Aman Garg ◽  
...  
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
Shear Deformation ◽  
Transverse Shear ◽  
Deformation Theory ◽  
Shear Deformation Theory ◽  
Element Model ◽  
Beam Element ◽  
Functionally Graded ◽  
Sandwich Beams

In this paper, the bending behavior of functionally graded single-layered, symmetric and non-symmetric sandwich beams is investigated according to a new higher order shear deformation theory. Based on this theory, a novel parabolic shear deformation function is developed and applied to investigate the bending response of sandwich beams with homogeneous hardcore and softcore. The present theory provides an accurate parabolic distribution of transverse shear stress across the thickness and satisfies the zero traction boundary conditions on the top and bottom surfaces of the functionally graded sandwich beam without using any shear correction factors. The governing equations derived herein are solved by employing the finite element method using a two-node beam element, developed for this purpose. The material properties of functionally graded sandwich beams are graded through the thickness according to the power-law distribution. The predictive capability of the proposed finite element model is demonstrated through illustrative examples. Four types of beam support, i.e. simply-simply, clamped-free, clamped–clamped, and clamped-simply, are used to study how the beam deflection and both axial and transverse shear stresses are affected by the variation of volume fraction index and beam length-to-height ratio. Results of the numerical analysis have been reported and compared with those available in the open literature to evaluate the accuracy and robustness of the proposed finite element model. The comparisons with other higher order shear deformation theories verify that the proposed beam element is accurate, presents fast rate of convergence to the reference results and it is also valid for both thin and thick functionally graded sandwich beams. Further, some new results are reported in the current study, which will serve as a benchmark for future research.

Nonlocal finite element model for the bending and buckling analysis of functionally graded nanobeams using a novel shear deformation theory

2021 ◽  
Vol 264 ◽  
pp. 113712 ◽  
Author(s):  
Mohamed-Ouejdi Belarbi ◽  
Mohammed-Sid-Ahmed Houari ◽  
Ahmed Amine Daikh ◽  
Aman Garg ◽  
Tarek Merzouki ◽  
...  
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
Shear Deformation ◽  
Deformation Theory ◽  
Shear Deformation Theory ◽  
Element Model ◽  
Buckling Analysis ◽  
Functionally Graded

Spectral Element Model for the Vibration of a Bending-Shear-Torsion Coupled Composite Timoshenko Beam

2010 ◽  
Author(s):  
Usik Lee ◽  
Injoon Jang
Keyword(s):  
Timoshenko Beam ◽  
Equations Of Motion ◽  
Shear Deformation Theory ◽  
Element Model ◽  
Spectral Element ◽  
Beam Model ◽  
Shape Functions ◽  
Laminated Beams ◽  
Composite Timoshenko Beam ◽  
Dynamic Shape

In this paper, a spectral element model is developed for axially loaded bending-shear-torsion coupled composite laminated beams. The composite laminated beams are represented by the Timoshenko beam model based on the first-order shear deformation theory. The spectral element model is formulated by using the variational method from frequency-dependent dynamic shape functions. The dynamic shape functions are derived from exact wave solutions to the governing differential equations of motion which are transformed into the frequency-domain by using the DFT theory. The numerical results show that the present spectral model provides extremely accurate natural frequencies for an example problem when compared to the results obtained by using the conventional finite element model which is also presented in this paper.

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