A macro plane triangle element from the individual element test

Eom, Jeong-Sik; Ko, Jin-Hwan; Lee, Byung Chai

doi:10.1016/j.finel.2008.12.001

Cited by 9 publications

(12 citation statements)

References 12 publications

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“…ALL-LS : Allman 88 element, least-square strain fit (Allman, 1988;Felippa, 2003a). Allman: Allman's element with spurious mode control (Allman, 1984;Cook, 1986;Choo et al, 2006;Eom et al, 2009). CST : Constant strain triangle CST-3/6C (Turner et al, 1956;Felippa, 2003a).…”

Section: Numerical Studiesmentioning

confidence: 99%

“…CST : Constant strain triangle CST-3/6C (Turner et al, 1956;Felippa, 2003a). CSTHybrid: Cook's plane hybrid triangle (Felippa, 2003a;Eom et al, 2009). FF84 : Free Formulation element of Bergan and Felippa (Bergan and Felippa, 1985;Felippa, 2003a).…”

Section: Numerical Studiesmentioning

confidence: 99%

“…The modified enhanced assumed strain triangle Lee, 1996, 1997;Choo et al, 2006; Latin American Journal of Solids and Structures 11 (2014) 2648-2671 Eom et al, 2009). OPT : Optimally fabricated assumed natural deviatoric strain triangle (Felippa, 2003a;Eom et al, 2009).…”

Section: Measmentioning

confidence: 99%

“…OPT : Optimally fabricated assumed natural deviatoric strain triangle (Felippa, 2003a;Eom et al, 2009). OPT*: Optimally fabricated assumed natural deviatoric strain triangle with alternative formulation for higher-order stiffness matrix (Paknahad et al, 2007).…”

Section: Measmentioning

confidence: 99%

“…In fact, the triangular elements are able to model the geometry of the structure more properly. On the other hand, numerical experiences have shown that the low-order triangular elements are less accurate than the quadrilateral ones (Eom et al, 2009). To solve irregular meshes, various means of constructing triangular elements have been proposed by the researchers (Felippa, 2003a;Choo et al, 2006;Huang et al, 2010;Pan and Wheel, 2011;Caylak and Mahnken, 2011;).…”

Section: Introductionmentioning

confidence: 99%

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A robust triangular membrane element

Rezaiee‐Pajand

Yaghoobi

2014

Lat. Am. j. solids struct.

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To analyze the plane problem with irregular mesh and complicated geometry, it is helpful to utilize the triangular element. In this study, several optimization criteria will be elaborated. By utilizing these provisions and satisfying the equilibrium conditions, a novel triangular element, named SST, is developed. To demonstrate the high accuracy and efficiency of the new element, a variety of structures will be solved. The findings will prove that the presented element has a low sensitivity to the geometric distortion. Moreover, the parasitic shear error will not arise when this element is employed. In addition to these, the proposed element is rotational invariant. Comparison studies will reveal that the SST element is more robust than the other well-known triangular ones.

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Section: Numerical Studiesmentioning

confidence: 99%

Section: Numerical Studiesmentioning

confidence: 99%

Section: Measmentioning

confidence: 99%

Section: Measmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A robust triangular membrane element

Rezaiee‐Pajand

Yaghoobi

2014

Lat. Am. j. solids struct.

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Development of a 4‐node hybrid stress tetrahedral element using a node‐based smoothed finite element method

Choi

Lee

2017

Numerical Meth Engineering

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Summary In this paper, a new 4‐node hybrid stress element is proposed using a node‐based smoothing technique of tetrahedral mesh. The conditions for hybrid stress field required are summarized, and the field should be continuous for better performance of a constant‐strain tetrahedral element. Nodal stress is approximated by the node‐based smoothing technique, and the stress field is interpolated with standard shape functions. This stress field is linear within each element and continuous across elements. The stress field is expressed by nodal displacements and no additional variables. The element stiffness matrix is calculated using the Hellinger‐Reissner functional, which guarantees the strain field from displacement field to be equal to that from the stress field in a weak sense. The performance of the proposed element is verified by through several numerical examples.

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Stress‐hybrid virtual element method on quadrilateral meshes for compressible and nearly‐incompressible linear elasticity

Chen,

Sukumar

2023

Numerical Meth Engineering

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In this article, we propose a robust low‐order stabilization‐free virtual element method on quadrilateral meshes for linear elasticity that is based on the stress‐hybrid principle. We refer to this approach as the stress‐hybrid virtual element method (SH‐VEM). In this method, the Hellinger–Reissner variational principle is adopted, wherein both the equilibrium equations and the strain‐displacement relations are variationally enforced. We consider small‐strain deformations of linear elastic solids in the compressible and near‐incompressible regimes over quadrilateral (convex and nonconvex) meshes. Within an element, the displacement field is approximated as a linear combination of canonical shape functions that are virtual. The stress field, similar to the stress‐hybrid finite element method of Pian and Sumihara, is represented using a linear combination of symmetric tensor polynomials. A 5‐parameter expansion of the stress field is used in each element, with stress transformation equations applied on distorted quadrilaterals. In the variational statement of the strain‐displacement relations, the divergence theorem is invoked to express the stress coefficients in terms of the nodal displacements. This results in a formulation with solely the nodal displacements as unknowns. Numerical results are presented for several benchmark problems from linear elasticity. We show that SH‐VEM is free of volumetric and shear locking, and it converges optimally in the norm and energy seminorm of the displacement field, and in the norm of the hydrostatic stress.

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A macro plane triangle element from the individual element test

Cited by 9 publications

References 12 publications

A robust triangular membrane element

A robust triangular membrane element

Development of a 4‐node hybrid stress tetrahedral element using a node‐based smoothed finite element method

Stress‐hybrid virtual element method on quadrilateral meshes for compressible and nearly‐incompressible linear elasticity

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