The Finite Element Model Study of the Pre-Twisted Timoshenko Beam

2012 ◽  
Vol 446-449 ◽  
pp. 3587-3590
Author(s):  
Chang Hong Chen ◽  
Ying Huang ◽  
Jian Shan
Keyword(s):  
Finite Element ◽  
Timoshenko Beam ◽  
Stiffness Matrix ◽  
Angular Displacement ◽  
Element Model ◽  
Beam Element ◽  
Element Stiffness Matrix ◽  
Straight Beam ◽  
The Relationship ◽  
Timoshenko Beam Element

The paper studies a new mechanical model of pre-twisted Timoshenko beam. But it is different from the conventional Timoshenko straight beam; the proposed new Timoshenko beam element takes separate interpolation polynomial functions both flexure bending displacement and angular displacement. According to the relationship between bending moment and shear, the relationship between of bending displacement and angle displacement is derived, more accurate to consider the effects of shear deformation, come up with a new initial reverse Timoshenko beam element stiffness matrix. Finally, by calculating the pre-twisted rectangle section beam example, and contrasting three-dimensional solid finite element using ANSYS, the comparative analysis results show that pre-twisted Timoshenko beam element stiffness matrix has good accuracy.

The Finite Element Model Research of the Pre-Twisted Beam

2012 ◽  
Vol 188 ◽  
pp. 31-36 ◽  
Author(s):  
Chang Hong Chen ◽  
Ying Huang ◽  
Jian Shan
Keyword(s):  
Finite Element ◽  
Timoshenko Beam ◽  
Element Model ◽  
Beam Element ◽  
Euler Beam ◽  
Systematic Analysis ◽  
Straight Beam ◽  
The Relationship ◽  
Twisted Beam ◽  
Timoshenko Beam Element

Based on the traditional mechanical model of straight beam element, the paper makes a systematic analysis and research on the pre-twisted beam finite element numerical model. Firstly, the paper proposed the pre-twisted Euler beam element mode, the mode uses 2 node and 12 freedom degrees, the element axial and torsion displacements use 2 nodes Lagrange interpolation function, bending displacement still use the cubic displacement. Secondly, the paper studies a new pre-twisted Timoshenko beam element mode, the proposed new Timoshenko beam element takes separate interpolation polynomial functions both flexure bending and rotation displacement. According to the relationship between bending moment and shear, the relationship between of bending displacement and angle displacement is derived, which is more accurate to consider the effects of shear deformation. Finally, by calculating the pre-twisted rectangle cantilever beam example, and contrasting three-dimensional solid finite element using ANSYS, the comparative analysis results show that pre-twisted Timoshenko beam element mode has good accuracy.

The Pre-Twisted Thin-Walled Beam Element Stiffness Matrix Considering the Saint-Venant Warping Deformation

2013 ◽  
Vol 871 ◽  
pp. 129-134
Author(s):  
Chang Hong Chen ◽  
Ying Huang
Keyword(s):  
Finite Element ◽  
Mechanical Model ◽  
Stiffness Matrix ◽  
Three Dimensional ◽  
Beam Element ◽  
Systematic Analysis ◽  
Element Stiffness Matrix ◽  
Straight Beam ◽  
Elliptical Section ◽  
Thin Walled

Based on the traditional mechanical model of thin-walled straight beam, the paper makes a systematic analysis and research on the pre-twisted thin-walled beam finite element numerical model. Firstly, based on the geometric deformation differential relationship, the paper deduces the pre-twisted thin-walled beam Saint-Venant warping strain. According to traditional thin-walled straight beam finite element mechanical model, the paper establishes its finite element stiffness matrix considering the Saint-Venant warping deformations. Finally, by calculating the pre-twisted elliptical section beam example, and contrasting three-dimensional solid finite element using ANSYS, the comparative analysis results show that pre-twisted thin-walled beam element stiffness matrix considering Saint-Venant warping deformation has good accuracy.

The Finite Element Model Study of the Pre-Twisted Euler Beam

2012 ◽  
Vol 446-449 ◽  
pp. 3615-3618
Author(s):  
Ying Huang ◽  
Chang Hong Chen ◽  
Jian Shan
Keyword(s):  
Finite Element ◽  
Stiffness Matrix ◽  
Degrees Of Freedom ◽  
Element Model ◽  
Displacement Function ◽  
Interpolation Function ◽  
Euler Beam ◽  
Systematic Analysis ◽  
Element Stiffness Matrix ◽  
Straight Beam

Based on the traditional mechanical model of straight beam, the paper makes a systematic analysis and research on the pre-twisted Euler beam finite element numerical model. The paper uses two-node model of 12 degrees of freedom, axial displacement interpolation function using 2-node Lagrange interpolation function, beam transverse bending displacements (u and υ) still use the cubic displacement, bending with torsion angle displacement function using cubic polynomial displacement function. Firstly, based on the author previous literature on the flexure strain relationship, the paper deduces the element stiffness matrix of the pre-twisted beam. Finally, by calculating the pre-twisted rectangle section beam example, and contrasting three-dimensional solid finite element using ANSYS, the comparative analysis results show that pre-twisted Euler beam element stiffness matrix has good accuracy.

scholarly journals Finite element model of circularly curved Timoshenko beam for in-plane vibration analysis

2021 ◽  
Vol 49 (3) ◽  
pp. 615-626
Author(s):  
Azin Nadi ◽  
Mehdi Raghebi
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
Timoshenko Beam ◽  
Natural Frequencies ◽  
Element Model ◽  
Beam Element ◽  
Polar Coordinate System ◽  
Curved Beam ◽  
Plane Vibration ◽  
Curved Timoshenko Beam

Curved beams are used so much in the arches and railway bridges and equipments for amusement parks. There are few reports about the curved beam with the effects of both the shear deformation and rotary inertias. In this paper, a new finite element model investigates to analyze In-Plane vibration of a curved Timoshenko beam. The Stiffness and mass matrices of the curved beam element was obtained from the force-displacement relations and the kinetic energy equations, respectively. Assembly of the elemental property matrices is simple and without need to transformation matrix because of using the local polar coordinate system. The natural frequencies of curved Euler-Bernoulli beam with large thickness are not sufficiently accurate. In this case, using the curved Timoshenko beam element is necessary. Moreover, the influence of vibration absorber is discussed on the natural frequencies of the curved beam.

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.

Finite Element Analysis of the ESTELA M1 Airplane Firewall (Representative Specimen)

2011 ◽  
Author(s):  
V. Ramirez-Elias ◽  
E. Ledesma-Orozco ◽  
H. Hernandez-Moreno
Keyword(s):  
Finite Element ◽  
Federal Aviation Administration ◽  
Element Model ◽  
Maximum Load ◽  
Load Factor ◽  
Representative Specimen ◽  
Maximum Displacement ◽  
Element Analysis ◽  
Element Simulation ◽  
The Relationship

This paper shows the finite element simulation of a representative specimen from the firewall section in the AEROMARMI ESTELA M1 aircraft. This specimen is manufactured in glass and carbon / epoxy laminates. The specimen is subjected to a load which direction and magnitude are determined by a previous dynamic loads study [10], taking into account the maximum load factor allowed by the FAA (Federal Aviation Administration) for utilitarian aircrafts [11]. A representative specimen is manufactured with the same features of the firewall. Meanwhile a fix is built in order to introduce the load directions on the representative specimen. The relationship between load and displacement is plotted for this representative specimen, whence the maximum displacement at the specific load is obtained, afterwards it is compared with the finite element model, which is modified in its laminate thicknesses in order to decrease the deviation error; subsequently this features could be applied to perform the whole firewall analysis in a future model [10].

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