The treatment of shell normals in finite element analysis

MacNeal, Richard H.; Wilson, Charles T.; Harder, R. L.; Hoff, Claus

doi:10.1016/s0168-874x(98)00035-3

Cited by 13 publications

(18 citation statements)

References 7 publications

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“…solution failed to converge with the mesh refinement) of the QUAD4 element of the MSC/NASTRAN FE code. In [24], it was found that the problem was caused by the treatment of the shell normals and resulted in an inability to transfer correctly the twisting moments. This failure introduced significant transverse shears whose effect was greater with the mesh refinement since the drill rotation was less and less restrained by the bending stiffness of an adjacent element.…”

Section: Raasch Hookmentioning

confidence: 99%

A New Shell Finite Element With Drilling Degrees of Freedom and Its Relation to Existing Formulations

Winkler¹,

Plakomytis²

2016

Proceedings of the VII European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS Congress 2016)

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This contribution deals with shell element formulations involving three rotational degrees of freedom. Its purpose is twofold. Firstly, a review of relevant non-linear shell theories as well as finite element implementations is given and corresponding defects are addressed. Secondly, a geometrically linear shell element formulation is presented which is free of any of these defects. Conventional shell theories involve two rotational degrees of freedom, the drilling rotation being excluded. Three standard methods of incorporating the drilling degree of freedom are considered: (a) The application of a proper rotation constraint condition, (b) shell theories intrinsically involving three rotational degrees of freedom (here called 'micropolar theories') and (c) introducing the drilling degree of freedom at the level of the finite element discretization (Allman-type shape functions). Here, reference implementations relying on approaches (a) to (c) as well as their reasonable combinations are considered. It is demonstrated that each of these implementations reveals at least one questionable feature: Formulations based on a micropolar approach involve ad hoc assumptions related to the constitutive law. Formulations involving a rotation constraint imply the application of a problem-dependent penalty or regularization parameter. Finally, Allman-type shell elements suffer from a lower convergence rate for bending dominated problems compared to isoparametric ones. The proposed shell element relies on a conventional (nonpolar) shell theory and applies a drill rotation constraint via a penalty formulation. A crucial point is the application of properly designed enhanced strain fields to avoid in-plane locking phenomena. It is demonstrated numerically that the resulting implementation overperforms existing shell elements. Most importantly, the way of incorporating the rotation constraint proves to constitute a proper penalty formulation in the sense that for sufficiently large values of the penalty parameter the results are independent of the latter. Moreover, this threshold is independent of the problem. The relation to existing implementations of the drill rotation constraint, all of them requiring the application of problem dependent penalty parameters, is discussed. Concluding, it is explicated how the present formulation derives from a micropolar approach.

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Section: Raasch Hookmentioning

confidence: 99%

A New Shell Finite Element With Drilling Degrees of Freedom and Its Relation to Existing Formulations

Winkler¹,

Plakomytis²

2016

Proceedings of the VII European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS Congress 2016)

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“…Plate bending elements such as the type shown in Fig. 2 have been developed by several researchers [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21]. An element such as the type shown in Fig.…”

Section: Plane Stress Elementmentioning

confidence: 99%

“…MacNeal et al [21] described a new method to treat the nodal components of rotation in shell analysis. In shell analysis, strains are derivative functions of three components of translation and two components of rotation.…”

Section: Plane Stress Elementmentioning

confidence: 99%

A rectangular finite element formulation

Öztorun

2006

Finite Elements in Analysis and Design

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“…Zienkiewicz [317], for example, suggests the use of an arbitrary value of the rotational sti!ness at that node. The approach is based on determining a unique normal at each node and ensuring that the attached elements produce no moments about it [318]. The original approach was found to give erroneous results in the case of, for example the linear analysis of a hook problem, termed the Raasch Challenge [319] problem.…”

Section: Composite Shell Finite Elementsmentioning

confidence: 99%

“…The original approach was found to give erroneous results in the case of, for example the linear analysis of a hook problem, termed the Raasch Challenge [319] problem. This approach was subsequently modi"ed [318] and has been implemented in the commercial "nite element program NASTRAN.…”

Section: Composite Shell Finite Elementsmentioning

confidence: 99%

A survey of recent shell finite elements

Yang

Saigal

Masud

et al. 2000

Int. J. Numer. Meth. Engng.

264

126

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Since the mid-1960s when the forms of curved shell "nite elements were originated, including those pioneered by Professor Gallagher, the published literature on the subject has grown extensively. The "rst two present authors and Liaw presented a survey of such literature in 1990 in this journal. Professor Gallagher maintained an active interest in this subject during his entire academic career, publishing milestone research works and providing periodic reviews of the literature. In this paper, we endeavor to summarize the important literature on shell "nite elements over the past 15 years. It is hoped that this will be a be"tting tribute to the pioneering achievements and sustained legacy of our beloved Professor Gallagher in the area of shell "nite elements. This survey includes: the degenerated shell approach; stress-resultant-based formulations and Cosserat surface approach; reduced integration with stabilization; incompatible modes approach; enhanced strain formulations; 3-D elasticity elements; drilling d.o.f. elements; co-rotational approach; and higher-order theories for composites.

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The treatment of shell normals in finite element analysis

Cited by 13 publications

References 7 publications

A New Shell Finite Element With Drilling Degrees of Freedom and Its Relation to Existing Formulations

A New Shell Finite Element With Drilling Degrees of Freedom and Its Relation to Existing Formulations

A rectangular finite element formulation

A survey of recent shell finite elements

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