Analysis of plates and shells with a simplified three node triangular element

Sabourin, Francis; Brunet, Michel

doi:10.1016/0263-8231(94)00001-g

Cited by 42 publications

(50 citation statements)

References 15 publications

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“…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%

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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show abstract

“…Sabourin and Brunet [30] related the rigid body rotation of the main element (e) sides to the out-ofplane nodal displacements, similar to the approach by Munro and Fonseca [12]. The rigid body rotations of the three elements surrounding element (e) on their common sides with element (e) were found similarly.…”

Section: Existing Rotation-free Triangular Plate Elementmentioning

confidence: 66%

“…Among the different alternatives to curvature calculations, the one that can be implemented in a manner closest to the spirit of the yield line analysis is the Sabourin and Brunet approach [30]. The main aspects of the element are presented below.…”

Section: Existing Rotation-free Triangular Plate Elementmentioning

confidence: 99%

“…The "S3" element derived by Sabourin and Brunet [30] has its roots in the Morley Triangle [29]. The out-of-plane deflection (w) within the triangle comes from a linear, rigid-body deflection (w r ) due to the nodal translations w 1 , w 2 , w 3 and from the quadratic "bending" deflection (w b ), Figs.…”

Section: Existing Rf Element "S3"mentioning

confidence: 99%

“…Examples of the performance of element S3 under different load conditions, including twisting moment, were presented by Sabourin and Brunet [30]. Comparisons were made with both analytical solutions and these obtained using other type of elements.…”

Section: Existing Rf Element "S3"mentioning

confidence: 99%

See 2 more Smart Citations

Finite element lower bound “yield line” analysis of isotropic slabs using rotation-free elements

Al‐Sabah

Falter

2013

Engineering Structures

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A new lower bound finite element method for slab analysis is presented as a practical substitute to full, non-linear, finite element methods that require expert knowledge and long running times. The method provides a general, safe and efficient lower bound solution for the analysis of reinforced concrete slabs up to failure. As it is finite element based, the method is more general than the yield line and strip methods currently in use. Furthermore, its lower bound nature makes it safer than the yield line method. The method uses a rotation-free, plate finite element modified to allow plastic "yield lines" to pass through at any direction. Yield lines are generated at the principal moment directions when the plastic moment capacity is attained. The material is assumed to be elastic perfectly-plastic. Following the general spirit of yield line analysis, the effects of a yield line are projected to the sides of the triangular element and then used to calculate the bending curvatures. The method's efficiency is achieved by using rotation-free plate elements with a single degree of freedom per node and by the incremental solution that does not require iterations. The method's accuracy and convergence are assessed by comparing standard cases with known results. In all cases, results were close to the theoretical values with difference of less than 1%. It is also used to solve a practical sized flat slab problem in order to demonstrate the method's efficiency, convergence, and speed.

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Refined non-conforming triangular elements for analysis of shell structures

Wanji

Cheung

1999

Int. J. Numer. Meth. Engng.

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SUMMARYBased on the re"ned non-conforming element method, simple #at triangular elements with standard nodal displacement parameters are proposed for the analysis of shell structures. For ensuring the convergence of the elements a new coupled continuity condition at the inter-element has been established in a weaker form. A common displacement for the inter-element, an explicit expression of re"ned constant strain matrix, and an adjustable constant are introduced into the formulation, in which the coupled continuity requirement at the inter-element is satis"ed in the average sense. The non-conforming displacement function of the well-known triangular plate element BCIZ [1] and the membrane displacement of the constant strain triangular element CST [2] are employed to derive the re"ned #at shell elements RTS15, and the re"ned #at shell elements RTS18 is derived by using the element BCIZ and the Allman's triangular plane element [3] with the drilling degrees of freedom. A simple reduced higher-order membrane strain matrix is proposed to avoid membrane locking of the element RTS18. An alternative new reduced higher-order strain matrix method is developed to improve the accuracy of the elements RTS15 and RTS18. Numerical examples are given to show that the present methods have improved the accuracy of the shell analysis.

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Analysis of plates and shells with a simplified three node triangular element

Cited by 42 publications

References 15 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

Finite element lower bound “yield line” analysis of isotropic slabs using rotation-free elements

Refined non-conforming triangular elements for analysis of shell structures

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