Geometrically nonlinear analysis of shell structures using a flat triangular shell finite element

Gal, Erez; Levy, Robert

doi:10.1007/bf02736397

Cited by 40 publications

(21 citation statements)

References 216 publications

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“…From the vast numbers of papers dedicated for this purpose, we chose to present some reference works by Ramm (1977), Parisch (1978, Bathe and Bolourchi (1980), Surana (1983), Oliver and Onate (1984), Pietraszkiewicz (1984), Belytschko et al (1989), Buechter and Ramm (1992), Bucalem and Bathe (1993), Kratzig (1993), Wall et al (2000), Gal and Levy (2006) and Altenbach and Eremeyev (2014). These studies have used either the standard total or the updated Lagrangian formulations (TLF and ULF respectively), pertaining to the degenerate shell formulation and analysis.…”

Section: Introductionmentioning

confidence: 99%

Discrete-Mindlin finite element for nonlinear geometrical analysis of shell structures

et al. 2015

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A finite degenerated shell element based on Mindlin discrete approach is presented for nonlinear geometric analysis in large displacements and small deformations. The element, called DMQS (Discrete Mindlin Quadrilateral Shell) with four-nodes and 6 dof/node, includes a constant transverse displacement and rich quadratic rotations. Since the global kinematics of shell is dominated by a rigid body rotation and motion involving small displacements and rotations, an Updated Lagrangian Formulation at each Iteration is used. The tangent stiffness matrix has been treated as a sum of two parts: linear part related to the degenerated shell model (DMQS) as well as the initial stress part associated with the wellknown membrane standard element. Some standard nonlinear benchmarks are presented herein, where very good results have been obtained and show better accuracy than similar quadrilateral elements.

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Section: Introductionmentioning

confidence: 99%

Discrete-Mindlin finite element for nonlinear geometrical analysis of shell structures

et al. 2015

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“…The element is also widely used to formulate the flat shell element to analyze complicate plate structural problems as a result of its 776 P. BHOTHIKHUN AND P. DECHAUMPHAI simplicity and reliability [9][10][11][12][13][14]. However, these finite element formulations were developed for bending analysis only for the plates under mechanical loading.…”

Section: Introductionmentioning

confidence: 99%

Development of DKT Finite Element Formulation for Thermal Bending of Thin Plate

Bhothikhun

Dechaumphai

2015

Journal of Thermal Stresses

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The finite element formulation for thermal bending analysis of a thin plate due to the temperature gradient through its thickness is presented. The formulation is developed for the Discrete Kirchhoff Triangle (DKT) element to analyze the plate bending behavior under the thermal loading. The finite element load vector is derived in closedform expressions so that the numerical integration is not required. Solution accuracy of the developed DKT finite element is evaluated by several examples. Performance of the developed DKT finite element is also compared with the effective nonconforming triangular element (BCIZ element). Results show that the developed DKT finite element formulation provides high solution accuracy for analysis of plate bending problem under thermal loading.

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“…In the case of small deformation, the stretching deformation and bending deformation of a flat element can be considered independent of each other and hence it is the superposition of a membrane problem and a plate bending problem. Accordingly, one approach for developing flat shell elements is to combine a membrane element and a plate bending element [4,5]. The main advantage of this 1415…”

Section: Introductionmentioning

confidence: 99%

A 3‐node flat triangular shell element with corner drilling freedoms and transverse shear correction

Zhang¹,

Zhou²,

Li³

et al. 2011

Numerical Meth Engineering

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SUMMARYThe formulation, implementation and testing of simple, efficient and robust shell finite elements have challenged investigators over the past four decades. A new 3-node flat triangular shell element is developed by combination of a membrane component and a plate bending component. The ANDES-based membrane component includes rotational degrees of freedom, and the refined nonconforming element methodbased bending component involves a transverse shear correction. Numerical examples are carried out for benchmark tests. The results show that compared with some popular shell elements, the present one is simple but exhibits excellent all-around properties (for both membrane-and bending-dominated situations), such as free of aspect ratio locking, passing the patch test, free of shear locking, good convergence and high suitability for thin to moderately thick plates. The developed element has already been adopted in a warpage simulation package for injection molding.

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Geometrically nonlinear analysis of shell structures using a flat triangular shell finite element

Cited by 40 publications

References 216 publications

Discrete-Mindlin finite element for nonlinear geometrical analysis of shell structures

Discrete-Mindlin finite element for nonlinear geometrical analysis of shell structures

Development of DKT Finite Element Formulation for Thermal Bending of Thin Plate

A 3‐node flat triangular shell element with corner drilling freedoms and transverse shear correction

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