Evaluation of some shear deformable shell elements

Laulusa, A.; Bauchau, Olivier A.; Choi, Jou-Young; Tan, V.B.C.; Li, Linhu

doi:10.1016/j.ijsolstr.2005.08.006

Cited by 32 publications

(19 citation statements)

References 23 publications

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“…Its material properties are E=10.5×10 6 and μ=0.3125, respectively. The cylindrical shell is pulled by two diametrically opposite point forces F (Figure 11).…”

Section: Pull-out Of Open Cylindrical Shellmentioning

confidence: 99%

“…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%

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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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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“…Its material properties are E=10.5×10 6 and μ=0.3125, respectively. The cylindrical shell is pulled by two diametrically opposite point forces F (Figure 11).…”

Section: Pull-out Of Open Cylindrical Shellmentioning

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

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show abstract

“…Hong and Kim [21] presented a triangular solid element based on a partial assumed strain formulation. Laulusa et al [22] proposed a heterosis triangular element, T6H. Up to now, there does not exist, however, a satisfying locking-free triangular shell element.…”

Section: Introductionmentioning

confidence: 99%

An efficient co‐rotational formulation for curved triangular shell element

Vu‐Quoc

2007

Numerical Meth Engineering

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SUMMARYA 6-node curved triangular shell element formulation based on a co-rotational framework is proposed to solve large-displacement and large-rotation problems, in which part of the rigid-body translations and all rigid-body rotations in the global co-ordinate system are excluded in calculating the element strain energy. Thus, an element-independent formulation is achieved. Besides three translational displacement variables, two components of the mid-surface normal vector at each node are defined as vectorial rotational variables; these two additional variables render all nodal variables additive in an incremental solution procedure. To alleviate the membrane and shear locking phenomena, the membrane strains and the out-of-plane shear strains are replaced with assumed strains in calculating the element strain energy. The strategy used in the mixed interpolation of tensorial components approach is employed in defining the assumed strains. The internal force vector and the element tangent stiffness matrix are obtained from calculating directly the first derivative and second derivative of the element strain energy with respect to the nodal variables, respectively. Different from most other existing co-rotational element formulations, all nodal variables in the present curved triangular shell formulation are commutative in calculating the second derivative of the strain energy; as a result, the element tangent stiffness matrix is symmetric and is updated by using the total values of the nodal variables in an incremental solution procedure. Such update procedure is advantageous in solving dynamic problems. Finally, several elastic plate and shell problems are solved to demonstrate the reliability, efficiency, and convergence of the present formulation.

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“…The improvement is even more significant when lower-order shape functions are used, such as in linear and quadratic beam elements. It should be also noticed that, unlike a classical displacement-based finite element, an element adopting MITC correction strategy no longer assures a monotonic convergence "from below", as shown in Laulusa et al [38]. Following the previous convergence analyses, 121 nodes and MITC B4 elements are used for the plot results, whereas 121 nodes and MITC B2, B3, and B4 elements are compared in the table results at a fixed load parameter.…”

Section: Numerical Resultsmentioning

confidence: 99%

Geometrically Nonlinear Analysis of Beam Structures via Hierarchical One-Dimensional Finite Elements

Hui

Pietro

Giunta

et al. 2018

Mathematical Problems in Engineering

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The formulation of a family of advanced one-dimensional finite elements for the geometrically nonlinear static analysis of beam-like structures is presented in this paper. The kinematic field is axiomatically assumed along the thickness direction via a Unified Formulation (UF). The approximation order of the displacement field along the thickness is a free parameter that leads to several higher-order beam elements accounting for shear deformation and local cross-sectional warping. The number of nodes per element is also a free parameter. The tangent stiffness matrix of the elements is obtained via the Principle of Virtual Displacements. A total Lagrangian approach is used and Newton-Raphson method is employed in order to solve the nonlinear governing equations. Locking phenomena are tackled by means of a Mixed Interpolation of Tensorial Components (MITC), which can also significantly enhance the convergence performance of the proposed elements. Numerical investigations for large displacements, large rotations, and small strains analysis of beam-like structures for different boundary conditions and slenderness ratios are carried out, showing that UF-based higher-order beam theories can lead to a more efficient prediction of the displacement and stress fields, when compared to two-dimensional finite element solutions.

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Evaluation of some shear deformable shell elements

Cited by 32 publications

References 23 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

An efficient co‐rotational formulation for curved triangular shell element

Geometrically Nonlinear Analysis of Beam Structures via Hierarchical One-Dimensional Finite Elements

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