The Raasch challenge for shell elements

Knight, Jr Norman F.

doi:10.2514/6.1996-1369

Cited by 12 publications

(14 citation statements)

References 12 publications

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“…To obtain the assumed natural strain field in Eqs. (17) and (18), the strain-displacement matrices at each of these tying points are calculated first to construct the transverse shear strain tensor at tying points:…”

Section: Kinematicsmentioning

confidence: 99%

“…Figure 12 shows the top view of the hook, modeled by two circular segments connected at the tangent point. Geometric, material, boundary and loading conditions are given according to the work of [17]. A reference solution of 5.027, for the displacement in the load direction of the free edge, is employed [16,17].…”

Section: Raasch's Hook Problemmentioning

confidence: 99%

“…Geometric, material, boundary and loading conditions are given according to the work of [17]. A reference solution of 5.027, for the displacement in the load direction of the free edge, is employed [16,17]. Mesh topologies consisting of 1×9, 3×18, 5×36, 10×72 and 20×144 shell elements are analyzed.…”

Section: Raasch's Hook Problemmentioning

confidence: 99%

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One point quadrature shell elements: a study on convergence and patch tests

Cardoso

Yoon

2006

Comput Mech

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One point quadrature shell elements are being widely used in the numerical simulation of shell structures, including sheet forming, because essentially of their computational efficiency. Nowadays, the purpose of using one point quadrature shell elements is not only related to computational efficiency but also because these elements have shown to be simultaneously robust and accurate in the simulation of complex sheet metal forming processes. The main objective of this work is to study the convergence behavior of different onepoint quadrature shell elements and their ability to pass the membrane and bending patch tests. For comparison purposes, two new elements include a new formulation for the membrane strain field in order to further improve the membrane behavior of the element developed in previous work of (in Cardoso et al. Comput Meth Appl Mech Eng 191:5177, 2002). The original convective membrane strains of Cardoso et al. (Comput Meth Appl Mech Eng 191:5177, 2002) (in the stabilization matrices only) are thus replaced by new membrane strains, constructed directly at the co-rotational coordinate system (located at the element's center). It is thus proved that with this new membrane formulation the elements pass now all the patch tests but, for warped (or curved) element geometries, their accuracy is not as good as the original element of (Cardoso et al. in

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Section: Kinematicsmentioning

confidence: 99%

Section: Raasch's Hook Problemmentioning

confidence: 99%

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One point quadrature shell elements: a study on convergence and patch tests

Cardoso

Yoon

2006

Comput Mech

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“…One of the approaches to circumvent the singularity is to use a membrane element with rotational degrees of freedom. The existence of an in-plane rotational degree of freedom at every node is convenient in engineering applications in respect that the membrane response can be improved and the sensitivity to element distortion can be reduced [13].…”

Section: Introductionmentioning

confidence: 99%

Linear and Geometrically nonlinear analysis of plates and shells by a new refined non-conforming triangular plate/shell element

Zhang

Kim

2005

Comput Mech

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A refined non-conforming triangular plate/ shell element for linear and geometrically nonlinear analysis of plates and shells is developed in this paper based on the refined non-conforming element method (RNEM). A conforming triangle membrane element with drilling degrees of freedom in Cartesian coordinates and the refined non-conforming triangular plate-bending element RT9, in which Kirchhoff kinematic assumption was adopted, are used to construct the present element. The displacement continuity condition along the interelement boundary is satisfied in an average sense for plate analysis, and the coupled displacement continuity requirement at the interelement is satisfied in an average sense, thereby improving the performance of the element for shell analysis. Selectively reduced integration with stabilization scheme is employed in this paper to avoid membrane locking. Numerical examples demonstrate that the present element behaves quite satisfactorily either for the linear analysis of plate bending problems and plane problems or for the geometrically nonlinear analysis of thin plates and shells with large displacement, moderate rotation but small strain.

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“…These elements are stable and perform very well in non-linear problems. Knight (1997) [8] suggested that a very small value be specified for the stiffness of the drilling degrees of freedom so that the contribution to the strain energy equation from this term will be zero. Bathe and Ho (1981) [9] approximated the stiffness for drilling degrees of freedom by using a small approximate value.…”

Section: Introductionmentioning

confidence: 99%

Degenerated Four Nodes Shell Element with Drilling Degree of Freedom

Adam¹,

Mohamed²,

Hassaballa³

2013

IOSRJEN

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A four node degenerated shell element with drilling degree of freedom is presented in this paper. The problem of zero stiffness that appears with using the drilling degree of freedom and causes singularity in the structure stiffness matrix is solved by employing, one of the recommended remedies. That is, adding a fictitious rotational stiffness using a penalty parameter (torsional constant) to control the solution to insure good element performance. Examples are presented including comparisons of torsional constant with the maximum displacements by using different mesh sizes, which results on selecting a value equal to one for the torsional constant is suitable value used to insure rapid convergence to true solution.

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The Raasch challenge for shell elements

Cited by 12 publications

References 12 publications

One point quadrature shell elements: a study on convergence and patch tests

One point quadrature shell elements: a study on convergence and patch tests

Linear and Geometrically nonlinear analysis of plates and shells by a new refined non-conforming triangular plate/shell element

Degenerated Four Nodes Shell Element with Drilling Degree of Freedom

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