An improved two-node timoshenko beam finite element

Friedman, Zvi; Kosmatka, J. B.

doi:10.1016/0045-7949(93)90243-7

Cited by 241 publications

(164 citation statements)

References 15 publications

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“…The shear strains, however, are not identical; those obtained using the DSG techniques are much more accurate than those obtained using the SRI and full integration beam elements. For the cubic beam elements, as expected, all deflection results are exact since the homogeneous part of Timoshenko beam differential equation is a cubic polynomial function [22]. The bending moments obtained using the DSG and SRI cubic elements are not identical but their accuracy is comparable.…”

Section: Figure 6 Cantilever Beam Subjected To Linearly-distributed mentioning

confidence: 49%

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Study of the Discrete Shear Gap Technique in Timoshenko Beam Elements

Wong¹,

Sugianto²

2017

ced

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A major difficulty in formulating a finite element for shear-deformable beams, plates, and shells is the shear locking phenomenon. A recently proposed general technique to overcome this difficulty is the discrete shear gap (DSG) technique. In this study, the DSG technique was applied to the linear, quadratic, and cubic Timoshenko beam elements. With this technique, the displacement-based shear strain field was replaced with a substitute shear strain field obtained from the derivative of the interpolated shear gap. A series of numerical tests were conducted to assess the elements performance. The results showed that the DSG technique works perfectly to eliminate the shear locking. The resulting deflection, rotation, bending moment, and shear force distributions were very accurate and converged optimally to the corresponding analytical solutions. Thus the beam elements with the DSG technique are better alternatives than those with the classical selective-reduced integration.

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Section: Figure 6 Cantilever Beam Subjected To Linearly-distributed mentioning

confidence: 49%

“…The geometrical, material, and loading data were L=4 m, h=0.5 m, b=2 m, E=1000 kN/m 2 , v= 0.3, and q0 = 1 kN/m. The exact deflection at the free end, bending moment and shear force at the fixed end are given as [22] (1 ) 30 12…”

Section: Assessment Of Accuracy and Convergencementioning

confidence: 99%

Study of the Discrete Shear Gap Technique in Timoshenko Beam Elements

Wong¹,

Sugianto²

2017

ced

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“…In order to overcome this phenomenon, several authors have developed numerical models based on the use of higher-order interpolation functions or functions depending on the material properties [6]. The disadvantage of the latter ones is that they are not updated during the nonlinear computations.…”

Section: Use Of a New Timoshenko Element With Internal Degrees Of Frementioning

confidence: 99%

Enhancement of Multifiber Beam Elements in the Case of Reinforced Concrete Structures for Taking Into Account the Lateral Confinement of Concrete Due to Stirrup

Khoder¹,

Grange²,

Sieffert³

2017

Proceedings of the 6th International Conference on Computational Methods in Structural Dynamics and Earthquake Engineering (COM

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Abstract. To assess the seismic vulnerability of existing reinforced concrete structures, a large number of degrees of freedom is involved. Consequently, efficient numerical tools are required. In the case of slender elements, enhanced beam elements have been developed to try to introduce shear effects, but in these models, the transverse steel is sometimes taken into consideration with approximated manner or often not at all. However, as shown by some experimental tests, the amount of transverse reinforcement triggers significantly the behavior of beam elements, especially under cyclic loading. Thus, the main goal of this work is to investigate solutions for an enhanced multifiber beam element accounting for vertical stretching of the cross section, occurring due to the presence of transverse reinforcement. The efficiency of the proposed modeling strategies is tested with results obtained from tension and flexure tests conducted on an elastic linear material.

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“…Thus lead to a two-node, with two degree of freedom per node, Timoshenko beam element which is impervious to shear-locking, and it is called superconvergent element [7,8]. By assembling all the elemental equations one gets the global dynamic equation…”

Section: Finite Element Formulationmentioning

confidence: 99%

“…In situations where one is dealing with share deformable beams the effect of transverse shear deformation is significant and it may be necessary to use the more accurate shear deformation (Timoshenko) beam theory. In our previous work [6], a detailed shear-deformable mechanical model was formulated for a sandwich beam with face piezoelectric layers using a superconvergent finite element formulation, following the work of Friedman and Kosmatka [7], and Reddy [8]. The purpose of this paper is the application of this model to shape control of beams with classical and auxetic material.…”

Section: Introductionmentioning

confidence: 99%

The Use of Auxetic Materials in Smart Structures

Hadjigeorgiou¹,

Stavroulakis²

2004

CMST

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This paper presents a study of the implications of using auxetic materials in the design of smart structures. By using auxetic materials as core and piezoelectric actuators as face layers to provide control forces, the problem of the shape control of sandwich beams is analyzed under loading conditions. The mechanical model is based on the shear deformable theory for beams and the linear theory of piezoelectricity. The numerical solution of the model is based on superconvergent (locking-free) finite elements for the beam theory, using Hamilton's principle. The optimal voltages of the piezo-actuators for shape control of a cantilever beams with classical and auxetic material are determined by using a genetic optimization procedure. Related numerical solutions of static problems demonstrate the role of auxetic material in the deformation, shape control and stress distribution of the beam and related twodimensional composite elastic structures.

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An improved two-node timoshenko beam finite element

Cited by 241 publications

References 15 publications

Study of the Discrete Shear Gap Technique in Timoshenko Beam Elements

Study of the Discrete Shear Gap Technique in Timoshenko Beam Elements

Enhancement of Multifiber Beam Elements in the Case of Reinforced Concrete Structures for Taking Into Account the Lateral Confinement of Concrete Due to Stirrup

The Use of Auxetic Materials in Smart Structures

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