An assessment of two fundamental flat triangular shell elements with drilling rotations

Providas, E.; Kattis, M. A.

doi:10.1016/s0045-7949(99)00215-1

Cited by 32 publications

(24 citation statements)

References 21 publications

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“…A 3-node triangular shell element can be formulated by combining a membrane element and a bending element [9][10][11][12], or by relying on three-dimensional continuum mechanics with the Reissner-Mindlin kinematic hypothesis and the plane-stress assumption [8,13]. Existing 3-node triangular shell elements can be categorized into 4 types: Type 1 with only 3 displacement degrees-of-freedom (dofs) per node [14][15][16][17][18][19][20][21][22]; Type 2 with 3 displacement dofs and 2 rotational dofs per node [23][24][25]; Type 3 with 3 displacement dofs at the vertices and the rotational dofs at side nodes [26][27]; Type 4 with 3 displacement dofs and 3 rotational dofs per node [28][29][30][31][32][33].…”

Section: Introductionmentioning

confidence: 99%

“…A flat shell element with 5 degrees-of-freedom per corner node can be obtained by combining a conventional triangular membrane element with a standard 9-dof triangular bending element. On the other hand, if several elements of this type sharing the same node are coplanar, it is difficult to achieve inter-element compatibility between membrane and transverse displacements, and the assembled global stiffness matrix is singular in shell analysis due to the absence of in-plane rotation degrees-of-freedom [9][10][11][12]34]. In addition, flat shell elements with 5 degrees-of-freedom per node lack proper nodal degrees of freedom to model folded plate/shell structures, making the assembly of elements troublesome [35].…”

Section: Introductionmentioning

confidence: 99%

“…This type of elements cannot, however, be easily matched with other types of elements in modeling of complex structures. Alternatively, some researchers [9][10][11][12] added a sixth degree of freedom (the drilling rotation) at each node of flat triangular shell elements by combining a bending element and a membrane element with drilling rotational degrees-of-freedom. Such shell elements are very convenient for engineering applications since no special connection scheme is necessary at the shell edges and intersections, and no particular care needs to be taken when coupling shell and rod elements [36].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

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%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

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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“…As discussed in many references [10,11,12,13,14,15], flat elements have been often and widely used owing to the ease to mix these with other types of element, the simplicity in their formulation and the effectiveness in performing computation.…”

Section: Introductionmentioning

confidence: 99%

Buckling and vibration analysis of laminated composite plate/shell structures via a smoothed quadrilateral flat shell element with in-plane rotations

Nguyen‐Van

Mai‐Duy

Karunasena

et al. 2011

Computers & Structures

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This paper presents buckling and free vibration analysis of composite plate/shell structures of various shapes, modulus ratios, span-to-thickness ratios, boundary conditions and lay-up sequences via a novel smoothed quadrilateral flat element. The element is developed by incorporating a strain smoothing technique into a flat shell approach. As a result, the evaluation of membrane, bending and geometric stiffness matrices are based on integration along the boundary of smoothing elements, which leads to accurate numerical solutions even with badly-shaped elements. Numerical examples and comparison with other existing solutions show that the present element is efficient, accurate and free of locking.

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“…Another problem with this method is that triangular elements with drilling degrees of freedom encounter poor response for membrane action [14][15][16], especially in spherical shells and twisted beam structures [17]. Recently, an approach for adding true drilling rotations to the triangular thin flat shell element was studied by Provias and Kattis [18]. Triangular, discrete Reissner-Mindlin plate and shell elements were studied by Sydenstricker and Landau [19], however the spherical shell and twisted beam problem are not considered.…”

Section: Introductionmentioning

confidence: 99%

Refined triangular discrete Mindlin flat shell elements

Zeng-jie

Wanji

2003

Computational Mechanics

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In this paper flat shell elements are formed by the assemblage of discrete Mindlin plate elements RDKTM and either the constant strain membrane element CST or the Allman's membrane element with drilling degrees of freedom LST. The element RDKTM is a robust Mindlin plate element, which can perform uniformly thick and thin plate bending analysis. It also passes the patch test for thin plate bending, and its convergence for very thin plates can be ensured theoretically. The singularity of the stiffness matrix and membrane locking are studied for the present elements. Numerical examples are presented to show that the present models indeed possess properties of simple formulations, high accuracy for thin and thick shells, and it is free from shear locking for thin plate/shell analysis.Keywords Mindlin plate theory, Shear locking, Drilling degrees of freedom, Displacement functions of a Timoshenko beam IntroductionIn the formulations of shell elements there are three distinct choices: (1) The flat shell element, that is obtained by combining a membrane element for plane elasticity and a bending element for flat plates; (2) The curved shell element, that is formulated according to shell theory; and (3) The degenerated shell element, that is formed based on the three dimensional solid theory. Among those formulations, the flat shell element is considered simplest and avoids complex shell equations. Therefore, the application of flat shell elements is widespread in engineering.Triangular flat shell elements may be used to represent an arbitrarily shaped shell as a faceted surface for curved shell structures. In this case, convergence to the exact geometry is obtained when the mesh is refined. Usually, triangular flat shell elements consist of triangular constant strain membrane elements and triangular bending plate elements. To study this type of shell element, the first step is the choice of an applicable plate element and an applicable membrane element. However, shear locking has been a major problem for the Mindlin plate element. It is well known that for Mindlin plates that only C 0 continuity is required and that the difficulties of C 1 continuity for thin plate elements can be avoided. Moreover both thin plate and thick plate analysis can be integrated in the element model. Initially, Mindlin plate elements use strain-displacement relations to obtain bending and transverse shear strain. In this case, bending energy is written in terms of nodal rotations only, whereas shear strain energy is given in terms of both nodal rotations and deflections. When the plate becomes thin, transverse shear effects are reduced and nodal deflections become associated only with the vanishing shear energy. This is a difficult situation to uphold and shear locking is soon observed. In order to avoid this, reduced integration [1, 2] and selective integration [3,4] technique are widely used. In the 3-noded triangular element, a single Gauss point integration is used for calculating the shear strain energy. However, it is found that such el...

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An assessment of two fundamental flat triangular shell elements with drilling rotations

Cited by 32 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

Buckling and vibration analysis of laminated composite plate/shell structures via a smoothed quadrilateral flat shell element with in-plane rotations

Refined triangular discrete Mindlin flat shell elements

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