A new MITC4+ shell element

Ko, Yeongbin; Lee, Phill-Seung; Bathe, Klaus-Jrgen

doi:10.1016/j.compstruc.2016.11.004

Cited by 67 publications

(24 citation statements)

References 31 publications

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“…Therefore, the present method can be effectively used to analyze shell structures using quadrilateral‐based shell meshes generated by the paving and cutting method. The performance of the pentagonal shell element could be improved by using formulations in MITC3+ and MITC4+ shell elements to avoid membrane locking behavior, which will be investigated in the forthcoming paper in detail.…”

Section: Resultsmentioning

confidence: 99%

“…() The MITC method has been successfully used to avoid the transverse shear locking of quadrilateral and triangular shell elements. () Some studies(–) showed that MITC shell elements are almost optimal in their convergence behavior. The results of numerical examples show that the present method can provide a novel approach to FE analysis of shell structures using trimmed quadrilateral shell meshes generated using the paving and cutting algorithm.…”

Section: Introductionmentioning

confidence: 99%

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A new strategy for finite‐element analysis of shell structures using trimmed quadrilateral shell meshes: A paving and cutting algorithm and a pentagonal shell element

Ho-Nguyen-Tan

Kim

2018

Numerical Meth Engineering

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Summary In this paper, we present a novel scheme to generate trimmed quadrilateral shell meshes using a paving and cutting algorithm. Paving with well‐shaped quadrilateral shell elements is initiated from a seed element placed in the interior of a geometric surface and proceeds around the boundary of the paved mesh in all directions. The paved all‐quadrilateral mesh covering the entire domain is cut by the boundaries of a geometric surface. Pentagonal shell elements are created by cutting the corners of quadrilateral shell elements at the domain boundaries. Pentagonal shape functions are constructed using Wachspress coordinates, and assumed natural strains in the form of the mixed interpolation of tensorial components approach are employed to avoid the transverse shear locking of pentagonal shell elements. Several numerical examples are investigated to show the effectiveness of the present method.

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Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A new strategy for finite‐element analysis of shell structures using trimmed quadrilateral shell meshes: A paving and cutting algorithm and a pentagonal shell element

Ho-Nguyen-Tan

Kim

2018

Numerical Meth Engineering

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“…A natural extension of the present work should consider other types of MITC elements with higher-order interpolations and/or improved tying rules and geometries which are known to better perform with respect to membrane locking [see e.g. 46,53,18]. Developing automated tools to perform classical tests such as the patch test or the test of the inf-sup stability conditions, would be a further appropriate extension that could meet the expectations of the community working on finite element engineering.…”

Section: Discussionmentioning

confidence: 99%

“…A possible explanation is that membrane locking is not cured in our MITC implementation. Further developments should attempt to implement in FEniCS-Shells more advanced MITC techniques that are known to better perform with respect to membrane locking [53,29,46,16]. However, we conclude that the PSRI technique introduced in FEniCS-Shells is a very efficient discretisation to cure both shear and membrane locking in the weakly nonlinear regime.…”

Section: Lenticular Plate With Inelastic Curvaturementioning

confidence: 99%

Simple and extensible plate and shell finite element models through automatic code generation tools

Hale

Brunetti

Bordas

et al. 2018

Computers & Structures

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A large number of advanced finite element shell formulations have been developed, but their adoption is hindered by complexities of transforming mathematical formulations into computer code. Furthermore, it is often not straightforward to adapt existing implementations to emerging frontier problems in thin structural mechanics including nonlinear material behaviour, complex microstructures, multi-physical couplings, or active materials. We show that by using a high-level mathematical modelling strategy and automatic code generation tools, a wide range of advanced plate and shell finite element models can be generated easily and efficiently, including: the linear and non-linear geometrically exact Naghdi shell models, the Marguerre-von Kármán shallow shell model, and the Reissner-Mindlin plate model. To solve shear and membrane-locking issues, we use: a novel re-interpretation of the Mixed Interpolation of Tensorial Component (MITC) procedure as a mixed-hybridisable finite element method, and a high polynomial order Partial Selective Reduced Integration (PSRI) method. The effectiveness of these approaches and the ease of writing solvers is illustrated through a large set of verification tests and demo codes, collected in an open-source library, FEniCS-Shells, that extends the FEniCS Project finite element problem solving environment.

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“…Shell elements have been the subject of extensive research over several recent decades. Many different formulations capable of representing nonlinear behaviour of shells with different geometric configurations have been proposed for both triangular (Lee, Lee and Bathe, 2014) and quadrilateral (Dvorkin and Bathe, 1984;Swamy Naidu and Sateesh, 2015;Ko, Lee and Bathe, 2017) elements. The most common formulations are based around Reissner-Mindlin plate theory with modifications to the shear strain fields to alleviate locking problems.…”

Section: Introductionmentioning

confidence: 99%

Realistic modelling of irregular slabs under extreme loading

Grosman

Izzuddin

2018

Proceedings of the Institution of Civil Engineers - Engineering

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This paper presents a new triangular flat shell element for composite and reinforced concrete slabs of complex planar configuration subjected to extreme loading. The element is developed within a co-rotational framework, and it incorporates the effects of geometric as well as material nonlinearities. To improve the approximation of the solution and deal with shear locking, additional hierarchic parameters are introduced within the local system of the element, providing an option to activate higher-order quadratic approximation for the element shape functions. The element formulation allows for composite action between different layers under the assumption of perfect bond between the slab concrete material, the reinforcement layers and the steel deck for composite slabs. To account for floor slabs of irregular geometric configurations, due allowance is made for uniaxial reinforcement to be oriented arbitrarily within the slab plane. Furthermore, an algorithm for automatic rebar orientation is developed for irregular slabs with realistic reinforcement distributions. The paper briefly describes the element formulation followed by several numerical verification examples. The applicability of the element to modelling concrete slabs is demonstrated via several validation studies against existing experimental results. The versatility of the element is further exemplified with a realistic large-scale floor slab model subjected to extreme loading scenarios. It is shown that the developed element provides a good balance between accuracy and efficiency in the modelling of irregular floor slabs subject to extreme loading conditions.

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A new MITC4+ shell element

Cited by 67 publications

References 31 publications

A new strategy for finite‐element analysis of shell structures using trimmed quadrilateral shell meshes: A paving and cutting algorithm and a pentagonal shell element

A new strategy for finite‐element analysis of shell structures using trimmed quadrilateral shell meshes: A paving and cutting algorithm and a pentagonal shell element

Simple and extensible plate and shell finite element models through automatic code generation tools

Realistic modelling of irregular slabs under extreme loading

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