A robust non-linear mixed hybrid quadrilateral shell element

Wagner, Werner; Gruttmann, Friedrich

doi:10.1002/nme.1387

Cited by 107 publications

(149 citation statements)

References 40 publications

(52 reference statements)

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“…In this paper the strain energy is chosen as a quadratic function of the independent shell strains. Based on a previous publication [16], where appropriate interpolation functions for the independent stress resultants and strains are formulated, we present several new theoretical developments.…”

Section: Introductionmentioning

confidence: 99%

Structural analysis of composite laminates using a mixed hybrid shell element

Gruttmann

Wagner

2005

Comput Mech

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The structural analysis of thin composite structures requires robust and effective shell elements. In this paper the variational formulation is based on a Hu-Washizu functional with independent displacements, stress resultants and shell strains. For the independent shell strains an enhanced interpolation part is introduced. This yields an improved convergence behaviour especially for laminated shells with coupled membrane and bending stiffness. The developed mixed hybrid shell element possesses the correct rank and fulfills the in-plane and bending patch test. The formulation is tested by several nonlinear examples including bifurcation and post-buckling response. The essential feature of the new element is the robustness in nonlinear computations with large rigid body motions. It allows very large load steps in comparison to standard displacement models.

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Section: Introductionmentioning

confidence: 99%

Structural analysis of composite laminates using a mixed hybrid shell element

Gruttmann

Wagner

2005

Comput Mech

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“…The deformation u of the inward loaded point is used to compare the presented shell formulation to shell formulations with standard rotational concepts as applied e.g. in [2,8]. The deformation results are given in Fig.…”

Section: Shell Theory and Discretizationmentioning

confidence: 99%

An efficient and robust Reissner–Mindlin shell formulation for isogeometric analysis

Dornisch

Müller

Klinkel

2015

Proc Appl Math and Mech

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The novel idea of isogeometric analysis is to use the basis functions of the geometry description of the design model also for the analysis. Thus, the geometry is represented exactly on element level. A closer integration of design and analysis is fostered by the usage of one common geometry model for design and analysis. A prevalent choice for the geometry description in isogeometric shell analysis are Non-Uniform Rational B-spline (NURBS) surfaces, which are commonly used in industrial design software to model thin structures. In order to directly compute structures defined by NURBS surfaces, an efficient isogeometric shell formulation is required. In this contribution an isogeometric Reissner-Mindlin shell formulation derived from the continuum theory is presented. The shell body is described by a shell reference surface, which is defined by NURBS surfaces, and a director vector. The director vector in the current configuration is computed by an orthogonal rotation using Rodrigues' tensor in every integration point. The axial vector of the rotation is interpolated. A multiplicative update formulation for the rotations accounts for finite rotations. A benchmark example shows the superior accuracy of the presented shell formulation for nonlinear computations.

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“…8.4, usually drilling rotation stabilization has to be utilized. The ability of the proposed formulation to handle multi-patch geometries with kinks is shown with the help of the channel section beam proposed in [26]. The cantilevered beam is clamped at one side and a point load F is applied at the intersection of web and upper flange at the other side.…”

Section: Gravity-loaded L-shaped Platementioning

confidence: 99%

Treatment of Reissner–Mindlin shells with kinks without the need for drilling rotation stabilization in an isogeometric framework

Dornisch

Klinkel

2014

Computer Methods in Applied Mechanics and Engineering

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This work presents a framework for the computation of complex geometries containing intersections of multiple patches with Reissner-Mindlin shell elements. The main objective is to provide an isogeometric finite element implementation which neither requires drilling rotation stabilization, nor user interaction to quantify the number of rotational degrees of freedom for every node. For this purpose, the following set of methods is presented. Control points with corresponding physical location are assigned to one common node for the finite element solution. A nodal basis system in every control point is defined, which ensures an exact interpolation of the director vector throughout the whole domain. A distinction criterion for the automatic quantification of rotational degrees of freedom for every node is presented. An isogeometric Reissner-Mindlin shell formulation is enhanced to handle geometries with kinks and allowing for arbitrary intersections of patches. The parametrization of adjacent patches along the interface has to be conforming. The shell formulation is derived from the continuum theory and uses a rotational update scheme for the current director vector. The nonlinear kinematic allows the computation of large deformations and large rotations. Two concepts for the description of rotations are presented. The first one uses an interpolation which is commonly used in standard Lagrange-based shell element formulations. The second scheme uses a more elaborate concept proposed by the authors in prior work, which increases the accuracy for arbitrary curved geometries. Numerical examples show the high accuracy and robustness of both concepts. The applicability of the proposed framework is demonstrated.

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A robust non-linear mixed hybrid quadrilateral shell element

Cited by 107 publications

References 40 publications

Structural analysis of composite laminates using a mixed hybrid shell element

Structural analysis of composite laminates using a mixed hybrid shell element

An efficient and robust Reissner–Mindlin shell formulation for isogeometric analysis

Treatment of Reissner–Mindlin shells with kinks without the need for drilling rotation stabilization in an isogeometric framework

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