An edge-based smoothed finite element method (ES-FEM) with stabilized discrete shear gap technique for analysis of Reissner–Mindlin plates

Nguyen‐Xuan, H.; Liu, G.R.; Thai-Hoang, C.; Nguyen-Thoi, T.

doi:10.1016/j.cma.2009.09.001

Cited by 196 publications

(63 citation statements)

References 79 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…As the shell thickness decreases, the convergence of the finite element solution rapidly deteriorates [8]. Researchers developed methods to overcome locking phenomena in flat triangular shell elements, such as the Mixed Interpolation of Tensorial Components method used in the MITC3 element [8], the line integration method used in TRIA3 element [42], the mixed or hybrid formulation [43][44][45], incompatible displacement methods [46][47], stabilization methods [29,[48][49][50][51][52][53][54], assumed strain methods [19,28,55], etc.…”

Section: Introductionmentioning

confidence: 99%

A 3-Node Co-Rotational Triangular Elasto-Plastic Shell Element Using Vectorial Rotational Variables

Li¹,

Izzuddin²,

Vu‐Quoc³

et al. 2017

Volume 13 Number 3

View full text Add to dashboard Cite

A 3-node co-rotational triangular elasto-plastic shell element is developed. The local coordinate system of the element employs a zero-'macro spin' framework at the macro element level, thus reducing the material spin over the element domain, and resulting in an invariance of the element tangent stiffness matrix to the order of the node numbering. The two smallest components of each nodal orientation vector are defined as rotational variables, achieving the desired additive property for all nodal variables in a nonlinear incremental solution procedure. Different from other existing co-rotational finite-element formulations, both element tangent stiffness matrices in the local and global coordinate systems are symmetric owing to the commutativity of the nodal variables in calculating the second derivatives of strain energy with respect to the local nodal variables and, through chain differentiation with respect to the global nodal variables. For elasto-plastic analysis, the Maxwell-Huber-Hencky-von Mises yield criterion is employed together with the backward-Euler return-mapping method for the evaluation of the elasto-plastic stress state, where a consistent tangent modulus matrix is used. Assumed membrane strains and assumed shear strains---calculated respectively from the edge-member membrane strains and the edge-member transverse shear strains---are employed to overcome locking problems, and the residual bending flexibility is added to the transverse shear flexibility to improve further the accuracy of the element. The reliability and convergence of the proposed 3-node triangular shell element formulation are verified through two elastic plate patch tests as well as three elastic and three elasto-plastic plate/shell problems undergoing large displacements and large rotations.

show abstract

Section: Introductionmentioning

confidence: 99%

A 3-Node Co-Rotational Triangular Elasto-Plastic Shell Element Using Vectorial Rotational Variables

Li¹,

Izzuddin²,

Vu‐Quoc³

et al. 2017

Volume 13 Number 3

View full text Add to dashboard Cite

show abstract

“…Table 19 and Figure 18 show the buckling factors using the element QH8-R with regular mesh of 9 × 9 rectangular elements (280 nodes) when / = 1.0. The QH8-R results are also compared to the DSG3 and ES-DSG3 [47] (mesh of 16 × 16 elements and 289 nodes), S8R (mesh of 9 × 9 elements and 280 nodes), mesh-free method [48], and the pb-2 Ritz [46]. It is seen that the QH8-R exhibits a good agreement with the pb-2 Ritz method, and S8R is not suitable for plate / = 0.2.…”

Section: Boundary Conditionmentioning

confidence: 98%

A Refined Higher-Order Hybrid Stress Quadrilateral Element for Free Vibration and Buckling Analyses of Reissner-Mindlin Plates

Wanji

et al. 2017

Mathematical Problems in Engineering

View full text Add to dashboard Cite

This paper is devoted to develop a new 8-node higher-order hybrid stress element (QH8) for free vibration and buckling analysis based on the Mindlin/Reissner plate theory. In particular, a simple explicit expression of a refine method with an adjustable constant is introduced to improve the accuracy of the analysis. A combined mass matrix for natural frequency analysis and a combined geometric stiffness matrix for buckling analysis are obtained using the refined method. It is noted that numerical examples are presented to show the validity and efficiency of the present element for free vibration and buckling analysis of plates. Furthermore, satisfactory accuracy for thin and moderately thick plates is obtained and it is free from shear locking for thin plate analysis and can pass the nonzero shear stress patch test.

show abstract

“…It is worth mentioning here that although some researchers have employed the DSG technique with a stabilization parameter α to improve the accuracy and stability against mesh distortion [Bischoff et al (2003); Nguyen-Thoi et al (2012); Nguyen-Xuan et al (2010a, 2010b)], we do not resort to this approach because the parameter α is problem dependent and makes the role of the shear correction factor obscure.…”

Section: Introductionmentioning

confidence: 99%

“…The DSG technique has been applied not only in the conventional FEM but also in recent alternative computational methods such as the edge-based smoothed FEM [Nguyen-Xuan et al (2010a)] and node-based smoothed FEM [Nguyen-Xuan et al (2010b)]. The most recent application of the DSG approach is to combine the DSG three-node triangular element with the cell-based smoothed FEM to produce a three-node triangular plate element, which is claimed to have some superior properties compared to many existing plate elements of the same class [Nguyen-Thoi et al (2012].…”

Section: Introductionmentioning

confidence: 99%

Kriging-Based Timoshenko Beam Elements with the Discrete Shear Gap Technique

Wong

Sulistio

Syamsoeyadi³

2018

Int. J. Comput. Methods

View full text Add to dashboard Cite

PublishedKriging-based finite element method (K-FEM) is an enhancement of the FEM through the use of Kriging interpolation in place of the conventional polynomial interpolation. In this paper, the K-FEM is developed for static, free vibration, and buckling analyses of Timoshenko beams. The discrete shear gap technique is employed to eliminate shear locking. The numerical tests show that a Kriging-Based beam element with cubic basis and three element-layer domain of influencing nodes is free from shear locking. Exceptionally accurate displacements, bending moments, natural frequencies, and buckling loads and reasonably accurate shear force can be achieved using a relatively course mesh.

show abstract

An edge-based smoothed finite element method (ES-FEM) with stabilized discrete shear gap technique for analysis of Reissner–Mindlin plates

Cited by 196 publications

References 79 publications

A 3-Node Co-Rotational Triangular Elasto-Plastic Shell Element Using Vectorial Rotational Variables

A 3-Node Co-Rotational Triangular Elasto-Plastic Shell Element Using Vectorial Rotational Variables

A Refined Higher-Order Hybrid Stress Quadrilateral Element for Free Vibration and Buckling Analyses of Reissner-Mindlin Plates

Kriging-Based Timoshenko Beam Elements with the Discrete Shear Gap Technique

Contact Info

Product

Resources

About