Static and dynamic applications of a high- precision triangular plate bending element

Cowper, G.R.; Kosko, E.; Lindberg, Garry M.; Olson, M. D.

doi:10.2514/3.5488

Cited by 136 publications

(30 citation statements)

References 8 publications

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“…In [6] it is referred to as "one of the most interesting and ingenious of all finite elements" and it states that "a series of careful numerical experiments has given first prize to this remarkable element", referring to the studies in reference [10]. The example problems presented in this paper support the notion that this element offers many advantages for extended MHD calculations.…”

Section: Summary and Discussionsupporting

confidence: 60%

“…5. Again, we verify that at least N -5 scaling is obtained, and that reasonable accuracy (10 -5 ) can be obtained for values of κ || /κ as large as 10 8 for values of N as low as 60. Note that the mesh shown in Fig.…”

Section: A a Simple Elliptic Problemsupporting

confidence: 51%

“…With these constraints, and that of C 1 continuity, the reduced quintic element emerges. While this element has been used in structural engineering studies since the late 1960s [10], it has apparently been overlooked by the extended MHD community. Here we show that it has some real advantages, and should be seriously considered as a basis for contemporary computational models of extended MHD in magnetized plasmas.…”

Section: Introductionmentioning

confidence: 99%

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A Triangular Finite Element with First-derivative Continuity Applied to Fusion MHD Applications

Jardin

2004

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We describe properties of the reduced quintic triangular finite element. The expansion used in the element will represent a complete quartic polynomial in two dimensions, and thus the error will be of order h 5 if the solution is sufficiently smooth. The quintic terms are constrained to enforce C 1 continuity across element boundaries, allowing their use with partial differential equations involving derivatives up to fourth order. There are only three unknowns per node in the global problem, which leads to lower rank matrices when compared with other high-order methods with similar accuracy but lower order continuity. The integrations to form the matrix elements are all done in closed form, even for the nonlinear terms. The element is shown to be well suited for elliptic problems, anisotropic diffusion, the Grad-Shafranov-Schlüter equation, and the timedependent MHD or extended MHD equations. The element is also well suited for 3D calculations when the third (angular) dimension is represented as a Fourier series.

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Section: Summary and Discussionsupporting

confidence: 60%

Section: A a Simple Elliptic Problemsupporting

confidence: 51%

Section: Introductionmentioning

confidence: 99%

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A Triangular Finite Element with First-derivative Continuity Applied to Fusion MHD Applications

Jardin

2004

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“…In a similar manner, Di Sciuva [16] has upgraded the high precision triangular element of Cowper et al [17] as triangular element has the advantage of modelling a plate having irregular shape. Extending the concept of Bogner et al [15], Icardi [18] has developed an eight-noded curvilinear element base on RHSDT [10] where different degrees of freedom (DOF) are taken at the different nodes.…”

Section: Introductionmentioning

confidence: 99%

A new triangular element to model inter‐laminar shear stress continuous plate theory

Chakrabarti¹,

Sheikh

2004

Numerical Meth Engineering

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SUMMARYAn efficient triangular element based on an inter-laminar shear stress continuous plate theory is developed and applied to the analysis of composite and sandwich plates under different situations to study the performance of the element. The plate theory represents parabolic through thickness variation of transverse shear stresses where the continuity condition of these stresses are satisfied at the layer interfaces. It also satisfies transverse shear stress free condition at the top and bottom surfaces of the plate. The most attractive feature of the plate theory is that the basic unknowns are same as those used in first-order shear deformation theory. The only problem lies with this elegant plate theory is found in its finite element implementation, as it requires C 1 continuity of transverse displacement at the element interfaces. This is a well-known problem of thin plate elements, which is also found in some other refined plate theories. Although there are some elements based on these refined plate theories but the number of such elements is very few and they possess certain drawbacks in general. Keeping these aspects in view, an attempt has been made in this study to develop a six-noded triangular element having equal degrees of freedom at each node.

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“…[18][19][20]),but they too are quite complicated and involve nodal derivative degrees-of-freedom of order greater than one, which complicates the specification of boundary conditions.…”

Section: Introductionmentioning

confidence: 99%

Finite Element Formulation and Solution of Contact-Impact Problems in Continuum Mechanics - IV

Hughes¹,

Taylor²,

Sackman³

et al. 1976

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In Section I w: present theory and algorithms for large displacement contact-impact analysis in two limensions (i.e. plane stress, plane strain and axisymmetric).The theory encompasses a wide range of contact-impact problems and allows for a completely arbitrary contact surface development, stick, slip and frictional slidinf conditions, and inpact-release conditions covering the full range of contact possibilities.In Tection II we describe some new developments regarding the Hertzian algorithm. SectiCn III contains sample problems which employ the algorithms described in Section I and also some studies involving the Hertzian algorithm.Anticipating the need for an efficient shell element for crash configuration modelling, we have performed a pilot study of a plate bending element. 'he results of this study, which are encouraging, are contained in Section IV.17.

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Static and dynamic applications of a high- precision triangular plate bending element

Cited by 136 publications

References 8 publications

A Triangular Finite Element with First-derivative Continuity Applied to Fusion MHD Applications

A Triangular Finite Element with First-derivative Continuity Applied to Fusion MHD Applications

A new triangular element to model inter‐laminar shear stress continuous plate theory

Finite Element Formulation and Solution of Contact-Impact Problems in Continuum Mechanics - IV

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