Insight into 3-node triangular shell finite elements: the effects of element isotropy and mesh patterns

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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“…The convergence curves are given in Figs. [17][18][19][20]. All elements show indeed the expected convergence behavior.…”

Section: The Shell Problem With Fixed-free Boundarysupporting

confidence: 56%

Measuring the convergence behavior of shell analysis schemes

Bathe

Lee

2011

Computers & Structures

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“…Furthermore, 3-node triangular mesh is the most robust and efficient option of mesh generation. As a result, reliable and computationally efficient 3-node triangular shell elements have important applications in modeling shell structures with arbitrary and complex geometries [8].…”

Section: Introductionmentioning

confidence: 99%

“…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%

“…In general, flat 3-node triangular shell element cannot well approximate the pure bending displacement field; thus, locking problems are serious and inevitable. 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%

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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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“…(see, e.g., References [29][30][31][32][33][34][35]). For the fluid boundary element, a four-node quadrilateral element is used, and as for the structural element, the isoparametric interpolation method is adopted for the fluid velocity potential and fluid boundary surface geometry.…”

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confidence: 99%

A direct coupling method for 3D hydroelastic analysis of floating structures

Kim

Lee

Park

2013

Numerical Meth Engineering

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SUMMARYThis paper presents a complete formulation for three-dimensional hydrodynamic analysis of floating flexible structures subjected to surface regular waves, as well as other excitation forces, by employing a direct tight coupling method. The continuum mechanics-based finite element method is employed to model floating structures with arbitrary geometries, which can account for the geometric nonlinearities and initial stress effects that result from the hydrostatic analysis, whereas the boundary element method is used for the fluid via total potential formulation. The simplicity and generality of the present formulation are revealed as compared with the conventional formulation. Numerical examples demonstrate the general capability of the formulation proposed.

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Insight into 3-node triangular shell finite elements: the effects of element isotropy and mesh patterns

Cited by 47 publications

References 12 publications

Measuring the convergence behavior of shell analysis schemes

Measuring the convergence behavior of shell analysis schemes

A 3-Node Co-Rotational Triangular Elasto-Plastic Shell Element Using Vectorial Rotational Variables

A direct coupling method for 3D hydroelastic analysis of floating structures

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