Development of MITC isotropic triangular shell finite elements

Lee, Phill-Seung; Bathe, Klaus‐Jürgen

doi:10.1016/j.compstruc.2004.02.004

Cited by 229 publications

(174 citation statements)

References 21 publications

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“…Shell finite elements play an important role in analyzing, designing and optimizing shell structures. An optimal shell element should (1) be applicable to arbitrary shell geometries for both thick and thin structures, (2) provide accurate displacements and stresses with low computational cost, and (3) be robust with low sensitivity to element distortion [1][2][3][4][5][6][7]. Formulations for flat 3-node triangular shell elements are simpler, and computationally more efficient, than for curved triangular elements with more than 3 nodes.…”

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

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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.

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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

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“…Of course, we are still continuing our research to improve these shell elements [ 111. We also work to improve, as well, the effectiveness of triangular elements [12] and to include three-dimensional through-the-thickness effects [13]. In metal forming, it can be important to include the through-the-kckness stress and strain effects, and shell elements with quadratic displacement interpolations through the thickness are then effective 1131.…”

Section: Mathematical Conditions On Finite Elementsmentioning

confidence: 99%

On the State of Finite Element Procedures for Forming Processes

Bathe¹

2004

AIP Conference Proceedings

149

154

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Abstract. The solution of forming processes requires reliable and efficient finite element methods to model the various complex physical phenomena encountered. The objective in this presentation is to focus on the current state of finite element methods with respect to reliability and efficiency in modeling forming processes. The finite element procedures pertain to the simulation of sheet metal forming, bulk forming, extrusion and drawing, rolling, welding, cutting processes, etc. It is emphasized that the appropriate finite element methods for a specific problem should be used, and that indeed procedures are available which are effective in many situations. The presentation briefly considers the state of modeling of solids, shell structures, contact conditions, friction, inelastic material response in large strains, thermomechanical coupling and fluid-solid interactions, as encountered in forming process simulations. The solutions of the governing finite element models are obtained using sparse direct or iterative solvers. The oral presentation will include the results of various example simulations.

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“…1 are modeled. We will use in the tests the MITC quadrilateral and triangular shell elements [21][22][23][24][25]. The sequence of meshes used is given in Table 2 (but for Fig.…”

Section: Meshingmentioning

confidence: 99%

“…1 using the convergence measures given in Section 3.3. In the finite element discretizations, we use the quadrilateral MITC4 [21] and 'improved' MITC9 shell elements [22] and the triangular MITC3 [23] and 'improved' MITC6 shell elements [24], see also Ref. [25].…”

Section: Illustrative Solutionsmentioning

confidence: 99%

Measuring the convergence behavior of shell analysis schemes

Bathe

Lee

2011

Computers & Structures

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a b s t r a c tWhile shells have been analyzed abundantly for many years in engineering and the sciences, improved finite element and related analysis methods are still much desired and researched. More general and effective finite element procedures are needed for complex shell structures, including for the analysis of composite shells and the optimization of shells. In this paper we discuss how finite element methods, and other analysis techniques, should be tested in order to identify their reliability and effectiveness. We summarize some important theoretical results, present appropriate test problems and convergence measures, and we illustrate our discussion through some novel numerical results. An important conclusion is that the testing has to be performed very carefully in order to obtain relevant results, and we show how this is accomplished in detail.

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Development of MITC isotropic triangular shell finite elements

Cited by 229 publications

References 21 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

On the State of Finite Element Procedures for Forming Processes

Measuring the convergence behavior of shell analysis schemes

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