Improvements in the membrane behaviour of the three node rotation-free BST shell triangle using an assumed strain approach

Flores, Fernando G.; Oñate, Eugenio

doi:10.1016/j.cma.2003.08.012

Cited by 52 publications

(96 citation statements)

References 12 publications

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“…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%

“…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]. Most existing 3-node rotation-free triangular shell elements are based on the Kirchhoff assumption, ignoring shear deformation, can therefore only be employed in modeling thin plate and shell problems [21].…”

Section: Introductionmentioning

confidence: 99%

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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%

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

“…As it is shown in Reference [15], at each mid-side point the gradient depends exclusively on the co-ordinates of the four nodes associated to the two elements adjacent to the side i (the upper-index surrounded by round brackets indicates now evaluated at the mid-point of side i), i.e. The EBST element is also non-conforming, but a stronger continuity of the normal is imposed than in the BST element.…”

Section: Computation Of the Angle Variation For The Ebst Elementmentioning

confidence: 98%

“…In Reference [15] a similar element to the BST element was developed under the framework of an assumed strain method. The main advantage of this new rotation-free shell element (termed EBST) is that its membrane performance is similar to the linear strain triangle, in contrast with the BST that has a constant strain membrane behaviour.…”

Section: Computation Of the Angle Variation For The Ebst Elementmentioning

confidence: 99%

A rotation‐free shell triangle for the analysis of kinked and branching shells

Flores

Oñate

2006

Numerical Meth Engineering

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SUMMARYThis paper extends the capabilities of previous BST and EBST rotation-free thin shell elements to the analysis of kinked and branching surfaces. The computation of the curvature tensor is first redefined in terms of the angle change between the normals at the adjacent elements. This allows to deal with arbitrary large angles between adjacent elements and to treat kinked surfaces. A relative stiffness between elements is introduced to consider non-homogeneous surfaces. This idea is latter generalized to deal with branching shells. Several linear and non-linear examples are presented showing that the formulation leads to the correct results.

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“…For the membrane behavior, we follow the solution adopted in [6]. First, the strains are computed on the element patch as for a 6 node triangular element.…”

Section: Membrane Behaviormentioning

confidence: 99%

Advanced Capabilities for the Simulation of Membrane and Inflatable Space Structures Using SAMCEF

Jetteur¹,

Bruyneel²

2008

Textile Composites and Inflatable Structures II

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Improvements in the membrane behaviour of the three node rotation-free BST shell triangle using an assumed strain approach

Cited by 52 publications

References 12 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 rotation‐free shell triangle for the analysis of kinked and branching shells

Advanced Capabilities for the Simulation of Membrane and Inflatable Space Structures Using SAMCEF

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