Study of the Discrete Shear Gap Technique in Timoshenko Beam Elements

Wong, Foek Tjong; Sugianto, Steven

doi:10.9744/ced.19.1.54-62

Cited by 3 publications

(3 citation statements)

References 15 publications

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“…The basic idea of this technique is to replace the assumed displacement-based transverse shear strain over an element, 𝛾 𝑒 = 𝑤, 𝑒 𝑥 -𝜃 𝑒 , with a substitute shear strain, 𝛾 𝑒 ̅̅̅ . This substitute strain field is obtained from the derivative of a substitute shear gap field [8,11]. In the previous work of Wong et al [8], the DSG technique was applied in the K-beam models to eliminate the shear locking.…”

Section: Discrete Shear Gap Techniquementioning

confidence: 99%

“…It is worth mentioning here that this constant bending test may be regarded as a type of patch test for beam finite elements [11]. A beam element passes the test if it can reproduce exact results (within computer accuracy).…”

Section: Pure Bending Testsmentioning

confidence: 99%

“…'Discrete' shear gaps are shear gaps at the nodal points. In the standard FEM for the Timoshenko beam model [11], the DSGs were evaluated at the element nodal points. In the K-FEM [8], however, the DSGs were evaluated at all nodes in a DOI and interpolated using Kriging shape functions to create a substitute shear gap field.…”

Section: Introductionmentioning

confidence: 99%

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Locking-free Kriging-based Timoshenko Beam Elements using an Improved Implementation of the Discrete Shear Gap Technique

Tjong¹,

Santoso²,

Sutrisno³

2022

ced

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Kriging-based finite element method (K-FEM) is an enhancement of the conventional finite element method using a Kriging interpolation as the trial solution in place of a polynomial function. In the application of the K-FEM to the Timoshenko beam model, the discrete shear gap (DSG) technique has been employed to overcome the shear locking difficulty. However, the applied DSG was only effective for the Kriging-based beam element with a cubic basis and three element-layer domain of influencing nodes. Therefore, this research examines a modified implementation of the DSG by changing the substitute DSG field from the Kriging-based interpolation to linear interpolation of the shear gaps at the element nodes. The results show that the improved elements of any polynomial degree are free from shear locking. Furthermore, the results of beam deflection, cross-section rotation, and bending moment are very accurate, while the shear force field is piecewise constant.

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Section: Discrete Shear Gap Techniquementioning

confidence: 99%

Section: Pure Bending Testsmentioning

confidence: 99%

See 1 more Smart Citation

Locking-free Kriging-based Timoshenko Beam Elements using an Improved Implementation of the Discrete Shear Gap Technique

Tjong¹,

Santoso²,

Sutrisno³

2022

ced

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Stress-Based FEM in the Problem of Bending of Euler–Bernoulli and Timoshenko Beams Resting on Elastic Foundation

Więckowski

Świątkiewicz

2021

Materials

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The stress-based finite element method is proposed to solve the static bending problem for the Euler–Bernoulli and Timoshenko models of an elastic beam. Two types of elements—with five and six degrees of freedom—are proposed. The elaborated elements reproduce the exact solution in the case of the piece-wise constant distributed loading. The proposed elements do not exhibit the shear locking phenomenon for the Timoshenko model. The influence of an elastic foundation of the Winkler type is also taken into consideration. The foundation response is approximated by the piece-wise constant and piece-wise linear functions in the cases of the five-degrees-of-freedom and six-degrees-of-freedom elements, respectively. An a posteriori estimation of the approximate solution error is found using the hypercircle method with the addition of the standard displacement-based finite element solution.

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On the Derivation of Exact Solutions of a Tapered Cantilever Timoshenko Beam

Wong

Gunawan²,

Agusta³

et al. 2019

ced

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A tapered beam is a beam that has a linearly varying cross section. This paper presents an analytical derivation of the solutions to bending of a symmetric tapered cantilever Timoshenko beam subjected to a bending moment and a concentrated force at the free end and a uniformly-distributed load along the beam. The governing differential equations of the Timoshenko beam of a variable cross section are firstly derived from the principle of minimum potential energy. The differential equations are then solved to obtain the exact deflections and rotations along the beam. Formulas for computing the beam deflections and rotations at the free end are presented. Examples of application are given for the cases of a relatively slender beam and a deep beam. The present solutions can be useful for practical applications as well as for evaluating the accuracy of a numerical method.

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Study of the Discrete Shear Gap Technique in Timoshenko Beam Elements

Cited by 3 publications

References 15 publications

Locking-free Kriging-based Timoshenko Beam Elements using an Improved Implementation of the Discrete Shear Gap Technique

Locking-free Kriging-based Timoshenko Beam Elements using an Improved Implementation of the Discrete Shear Gap Technique

Stress-Based FEM in the Problem of Bending of Euler–Bernoulli and Timoshenko Beams Resting on Elastic Foundation

On the Derivation of Exact Solutions of a Tapered Cantilever Timoshenko Beam

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