Nitsche method for isogeometric analysis of Reissner–Mindlin plate with non-conforming multi-patches

Du, Xiaoxiao; Zhao, Gang; Wang, Wei

doi:10.1016/j.cagd.2015.03.005

Cited by 48 publications

(12 citation statements)

References 41 publications

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“…An alternative approach to a continuous approximation of the solution is the discontinuous Galerkin method [1], which admits a discontinuous interpolation of the solution among the mesh elements and naturally handles arbitrary meshes, high-order basis functions and contiguous mesh elements with different order of approximation. Several dG schemes have been developed for plate theories: within the family of plate theories based on the CLPT, Wells et al [43] developed a rotation-free dG scheme for Kirchhoff plates, Noel and Radovitzky [28] presented a dG model for linear Kirchhoff-Love shells and Becker and Noel [3] extended it to non-linear elasto-plastic finite deformation including fracture; on the other hand, dG schemes for plate theories based on the FSDT include the work of Arnold et al [2], who introduced a family of dG schemes for the Reissner-Mindlin plates in which the rotation vector, the transverse displacement and the transverse shear are all approximated, the work of Bösing et al [4], who introduced an Interior Penalty formulation that recovers the thin-plate limit as the thickness tends to zero, and the work of Du et al [14], who exploied the flexibility of the dG method to develop a multi-patch isogeometric analysis for non-conforming plate domains.…”

Section: Introductionmentioning

confidence: 99%

A high-resolution layer-wise discontinuous Galerkin formulation for multilayered composite plates

Gulizzi

Benedetti

Milazzo

2020

Composite Structures

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Section: Introductionmentioning

confidence: 99%

A high-resolution layer-wise discontinuous Galerkin formulation for multilayered composite plates

Gulizzi

Benedetti

Milazzo

2020

Composite Structures

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“…It is applied to both trimmed and untrimmed non-conforming Kirchhoff-Love shells. Other examples of coupling non-conforming NURBS patches can be found in [16,17], where C 0 -continuity is enforced for Reissner-Mindlin plates. Dornisch et al in [16] propose the weak substitution method, a mortar-type technique that expresses the equality of mutual deformations using a variational equation.…”

Section: Introductionmentioning

confidence: 99%

“…This results in a master-slave relationship between the interface variables. In [17] on the other hand, Du et al employ Nitsche's method, altering the variational formulation to take into account the coupling conditions. Other examples of C 0 -coupled non-conforming patches in linear elasticity can be found in [18][19][20][21][22].…”

Section: Introductionmentioning

confidence: 99%

A robust patch coupling method for NURBS-based isogeometric analysis of non-conforming multipatch surfaces

Coox

Greco

Atak

et al. 2017

Computer Methods in Applied Mechanics and Engineering

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“…Nitsche's method was originally proposed by J. Nitsche [67,79] to impose weakly essential boundary conditions and more recently has regained popularity to deal with interface conditions with non-conforming discretizations (see, e.g., [9,44,2]). Nowadays Nitsche's method has also found a number of natural applications in IGA [40,64,4,71,42,36]. Nitsche's formulation makes use of an appropriate conjugate pair such as displacement-force or rotation-moment, in such a way that the method remains both primal (no extra DoFs) and consistent.…”

Section: Introductionmentioning

confidence: 99%

Skew-symmetric Nitsche’s formulation in isogeometric analysis: Dirichlet and symmetry conditions, patch coupling and frictionless contact

Chouly

et al. 2018

Computer Methods in Applied Mechanics and Engineering

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A simple skew-symmetric Nitsche's formulation is introduced into the framework of isogeometric analysis (IGA) to deal with various problems in small strain elasticity: essential boundary conditions, symmetry conditions for Kirchhoff plates, patch coupling in statics and in modal analysis as well as Signorini contact conditions. For linear boundary or interface conditions, the skew-symmetric formulation is parameter-free.For contact conditions, it remains stable and accurate for a wide range of the stabilization parameter.Several numerical tests are performed to illustrate its accuracy, stability and convergence performance. We investigate particularly the effects introduced by Nitsche's coupling, including the convergence performance and condition numbers in statics as well as the extra "outlier" frequencies and corresponding eigenmodes in structural dynamics. We present the Hertz test, the block test, and a 3D self-contact example showing that the skew-symmetric Nitsche's formulation is a suitable approach to simulate contact problems in IGA.have the ability to exactly describe geometries: thus, no geometrical approximation error is introduced.Moreover NURBS are widely adopted in commercial computer-aided design (CAD) packages, and this CAD data can directly be used to construct approximations. In boundary element method (BEM), this translates into the ability to solve directly from the field variables at the control points defining the geometry [78,77,74,59,10,60,58,68]. In FEM, a 3D parameterization of the volume is still necessary [87,88], except when solving shell-like problems [53,13,14,38,49]. The present paper focuses on two following issues. One first issue in IGA is related to boundary conditions, especially essential boundary conditions. Indeed, since NURBS are non-interpolatory, enforcing boundary conditions and constraints cannot be done as simply as in Lagrange FEM: they require tackling difficulties which are similar to those encountered in meshless methods [66] and implicit/immersed boundary methods [37,46]. One second issue in IGA comes from interface conditions and patch coupling: for complex geometries, patch-wise CAD modeling is necessary, and transmission conditions need to be satisfied. The same also arises when gluing heterogeneous materials.Various methods already exist to treat boundary or interface conditions weakly, that have been firstly designed for instance in the FEM context. They are applicable, or have already been applied, for IGA.The most widespread ones are the penalty method, mixed/mortar methods and Nitsche's method. The penalty method [7, 54] is simple but not consistent. Therefore the value of the penalty parameter has to be chosen with great care to achieve the best balance between accuracy and stability. As a matter of fact, if the penalty parameter is chosen too small the boundary or interface conditions are imposed inaccurately, whereas if it is chosen much larger than needed the penalized problem becomes ill-conditioned. Mixed methods for boundary conditions [6] introd...

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Nitsche method for isogeometric analysis of Reissner–Mindlin plate with non-conforming multi-patches

Cited by 48 publications

References 41 publications

A high-resolution layer-wise discontinuous Galerkin formulation for multilayered composite plates

A high-resolution layer-wise discontinuous Galerkin formulation for multilayered composite plates

A robust patch coupling method for NURBS-based isogeometric analysis of non-conforming multipatch surfaces

Skew-symmetric Nitsche’s formulation in isogeometric analysis: Dirichlet and symmetry conditions, patch coupling and frictionless contact

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