An assumed strain formulation of efficient solid triangular element for general shell analysis

Kim, Jong Hoon; Kim, Yong Hyup; Lee, Sung Won

doi:10.1002/(sici)1097-0207(20000320)47:8<1481::aid-nme841>3.0.co;2-b

Cited by 14 publications

(14 citation statements)

References 29 publications

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“…Spatially isotropic behavior is an important requirement for the triangular elements. The element behavior should not depend on the sequence of node numbering, that is, the element orientation [9,[15][16][17][18]. The proposed solid-shell element passes this test.…”

Section: Basic Numerical Testsmentioning

confidence: 93%

“…We perform three patch tests: the membrane, bending, and transverse shearing patch tests; see Refs. for the patch tests. The geometry of the mesh is shown in Figure (a).…”

Section: Basic Numerical Testsmentioning

confidence: 99%

“…The plate bending problem is shown in Figure . The square plate with dimensions of 2 L × 2 L and thickness t is subjected to uniform pressure q = 1.0.…”

Section: Classical Benchmark Testsmentioning

confidence: 99%

“…In addition to conventional shell theories, solid-shell elements can represent extended physics with the inclusion of stretch in the thickness direction. Solid-shell elements have only translational degrees of freedom (DOFs), leading to the following advantages: the elements can easily simulate the thickness change of shell structures, merge well with solid finite elements, and avoid complex rotation updates in geometric nonlinear analyses [1][2][3][4][5][6][7][8][9][10][11][12][13]. The general threedimensional (3D) material law can be directly employed, which is beneficial in material nonlinear analyses [3][4][5][6][7].…”

Section: Introductionmentioning

confidence: 99%

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A 6‐node triangular solid‐shell element for linear and nonlinear analysis

Lee

2017

Numerical Meth Engineering

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Summary In this paper, we present an effective 6‐node triangular solid‐shell element (MITC‐S6), with particular attention on shear locking and thickness locking. To alleviate shear locking, the assumed transverse strain field of the MITC3+ shell element is used while modifying the bending enhancement mechanism. Thickness locking is treated using the assumed and enhanced strain methods for thickness strain. Two independent enhancements of strains are applied: The in‐plane and transverse shear strain fields are enhanced using the strain fields obtained from a bubble interpolation function for in‐plane translations, and the thickness strain field is enhanced for linear variation in the thickness direction. The general three‐dimensional material law is employed. The proposed element passes all the basic tests including zero‐energy mode, patch, and isotropy tests. Excellent performance is observed in various linear and nonlinear benchmark tests, wherein its performance is compared with that of existing 6‐node triangular and 8‐node quadrilateral solid‐shell elements. Copyright © 2016 John Wiley & Sons, Ltd.

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Section: Basic Numerical Testsmentioning

confidence: 93%

“…We perform three patch tests: the membrane, bending, and transverse shearing patch tests; see Refs. for the patch tests. The geometry of the mesh is shown in Figure (a).…”

Section: Basic Numerical Testsmentioning

confidence: 99%

“…The plate bending problem is shown in Figure . The square plate with dimensions of 2 L × 2 L and thickness t is subjected to uniform pressure q = 1.0.…”

Section: Classical Benchmark Testsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A 6‐node triangular solid‐shell element for linear and nonlinear analysis

Lee

2017

Numerical Meth Engineering

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“…The resulting element stiffness matrix has one incompatible spurious energy mode which disappears when two elements are assembled [Hughes and Taylor (1982), Kim et al (2000)]. The proof of the incompatibility of the zero energy mode will be discussed later.…”

Section: Strains On the Area Coordinate Systemmentioning

confidence: 99%

Three-node macro triangular shell element based on the assumed natural strains

Kim

2002

Computational Mechanics

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Finite element models with simple triangular geometry facilitate pre-processing for the finite element analysis. In the present study, a robust shear deformable triangular shell element formulation is presented for general plate and shell analysis, using three-node mesh discretization. The present formulation is developed on the basis of the assumed natural strain (ANS) formulation to attenuate the shear locking effect. Furthermore, this study proposes macro triangular element scheme by dividing a three-node triangular mesh into three parts to produce three individual ANS triangular elements and then merges these by condensing out the virtual center node. The performance of the macro ANS element is highly enhanced by reducing the number of sampling locations of three sub triangular element, but still utilizes three-node mesh discretization same as does the mesh used for three-node triangular elements. The macro ANS element has invariant stiffness, possesses no commutable zero energy mechanism. Numerical tests are presented to illustrate the high performance nature of the macro ANS element in general shell analysis. In particular, the numerical study demonstrates that the macro ANS element completely removes the shear locking effect that has been detrimental in shear deformable linear triangular elements so far.Keywords Finite element method (FEM), Three-node linear triangular element, Macro element, Shear locking effect, Assumed natural strain, Plate and shell analysis IntroductionThe finite element method is becoming a more powerful numerical tool, which is being conveniently utilized in the engineering community to simulate structure behavior. While the main computing process becomes very fast with the aid of growing computational power, the pre-processing of the complicated geometry of practical structures is still tedious and time-consuming. Specifically, mesh generation is one of great burdens for most engineers involved in the numerical simulation of practical structures. Automatic mesh generation techniques have been popularly utilized as a substitute for manual mesh generation. As far as mesh generation and its automatic processing are concerned, the simple triangular element with only three corner nodes has definite topological advantages over other element configurations.However, most simple triangular plate and shell elements suffer from low computational performance primarily due to the shear locking. Various approaches have been investigated to develop an efficient three-node triangular element formulation, which reduces the locking effect. Discrete Kirchhoff triangular (DKT) elements [Batoz (1980)] eradicate the shear locking effect by removing the shear deformation from element kinematics. However, the applicability of such elements is limited to thin structures, since transverse shear flexibility cannot be neglected in the analysis of thick or moderately thick shells. The discrete shear triangular plate element represents an improvement, whereby the shear deformation energy is included, and assume...

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An assumed strain triangular solid shell element with bubble function displacements for analysis of plates and shells

Hong

Kim

Lee

2001

Numerical Meth Engineering

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SUMMARYBubble function displacements are used in conjunction with the assumed strain formulation to construct e cient triangular solid shell elements tailored for shell analysis. Two versions of 36-DOF triangular elements are presented with di erent bubble function displacements and the corresponding assumed strain ÿelds. In the ÿrst version the bubble function displacement is independent of the thickness while in the second version the bubble function varies linearly in the thickness direction. The assumed strain ÿelds are carefully selected to alleviate locking e ect. The ÿrst version models curved shells with at triangular elements. The second version is e ective in alleviating the membrane locking and thus allows more accurate modelling of curved shells. Various numerical examples demonstrate the validity and e ectiveness of the present assumed strain formulation elements with the bubble function displacements.

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An assumed strain formulation of efficient solid triangular element for general shell analysis

Cited by 14 publications

References 29 publications

A 6‐node triangular solid‐shell element for linear and nonlinear analysis

A 6‐node triangular solid‐shell element for linear and nonlinear analysis

Three-node macro triangular shell element based on the assumed natural strains

An assumed strain triangular solid shell element with bubble function displacements for analysis of plates and shells

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