Some Finite Element Methods for Linear Thin Shell Problems

Abstract-The objective in this paper is to present fundamental considerations regarding the finite element analysis of shell structures. First, we review some well-known results regarding the asymptotic behaviour of a shell mathematical model. When the thickness becomes small, the shell behaviour falls into one of two dramatically different categories; namely, the membrane-dominated and bending-dominated cases. The shell geometry and boundary conditions decide into which category the shell structure falls, and a seemingly small change in these conditions can result into a change of category and hence into a drama.tically different shell behaviour.An effective finite element scheme should be applicable to both categories of shell behaviour and the rate of convergence in either case should be optimal and independent of the shell thickness. Such a finite element scheme is difficult to achieve but it is important that existing procedures be analysed and measured with due regard to these considerations. To this end, we present theoretical considerations and we propose appropriate shell analysis test cases for numerical evaluations. 0 1997 Elsevier Science Ltd

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“…which is a penalized problem similar to Equation (9). Here, both o* and a, are convergent, according to Prop.…”

Section: Injluence Of the Loadingmentioning

confidence: 99%

Fundamental considerations for the finite element analysis of shell structures

Chapelle¹,

Bathe²

1998

Computers & Structures

198

178

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“…The proof follows from the properties of the elliptic part, the first integral, of (12) stated in [8]. The input operator, the second integral, is similar to that in [11].…”

Section: Shells With Piezoelectric Actuatorsmentioning

confidence: 96%

“…An expansion of the electric field with respect to the deviation from the reference surface is also necessary. Let Q be a point of the plate, M orthogonal projection of Q onto the middle surface, u 1 , u 2 longitudinal displacements of M and w the transversal displacement of M. According to the Kirchhoff-Love-Koiter hypothesis (see, e.g., [8]), the components of the strain tensor at the point Q are given by…”

Section: Elimination Of the Thicknessmentioning

confidence: 99%

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Real-Time Optimization and Stabilization of Distributed Parameter Systems with Piezoelectric Elements

Hoffmann

Botkin

2001

Online Optimization of Large Scale Systems

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The investigation of this paper is related to the design of active real-time controls which provide the desired performance of flexible constructions subjected to varying disturbances. Physical controllers are piezoelectric elements that transform applied voltages into mechanical forces and moments. Control voltages are computed on the base of signals measured on piezoelectric sensors. The underlying structure is a thin plate or shell. The piezoelectric elements are either surface mounted or embedded within the structure. Conventional averaging procedures are used to eliminate the thickness in mathematical models. A homogenization procedure is used to reduce structures with large number of piezoelectric elements to the case of continuously distributed input or output signals.

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“…They are commonly analyzed with the Finite Element Method (FEM) using two-dimensional (2D) surface elements (i.e. shell Finite Elements (FE)) which consist of a combination of a plane stress (membrane) and a plate element (bending) (Bernadou 1996, Bandyopadhyay 1998. They have been optimized in one of three ways: 1) The thickness of the shell was optimized, whilst maintaining the original shape of the structure (Rao and Hinton 1993, Li et al 1999, Lam et al 2000; 2) The shape of the shell was optimized by moving the control points which defined it, but keeping its thickness unchanged (Bletzinger and Ramm 1993, Lindby and Santos 1999, Uysal et al 2007; and 3) The topology of the shell was optimized using topology optimization where both its shape and thickness could be modified (Luo and Gea 1998, Li et al 1999, Belblidia and Bulman 2002, Ansola et al 2002.…”

Section: Introductionmentioning

confidence: 99%

The effects of membrane thickness and asymmetry in the topology optimization of stiffeners for thin-shell structures

Victoria¹,

Querin²,

Díaz³

et al. 2013

Engineering Optimization

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ReuseUnless indicated otherwise, fulltext items are protected by copyright with all rights reserved. The copyright exception in section 29 of the Copyright, Designs and Patents Act 1988 allows the making of a single copy solely for the purpose of non-commercial research or private study within the limits of fair dealing. The publisher or other rights-holder may allow further reproduction and re-use of this version -refer to the White Rose Research Online record for this item. Where records identify the publisher as the copyright holder, users can verify any specific terms of use on the publisher's website. TakedownIf you consider content in White Rose Research Online to be in breach of UK law, please notify us by emailing eprints@whiterose.ac.uk including the URL of the record and the reason for the withdrawal request. 1 The Effects of Membrane Thickness and Asymmetry in the Topology Optimization of Stiffeners for Thin Shell Structures Mariano Victoria Study into the Effects of Membrane Thickness and Asymmetry in the Topology Optimization of Stiffeners for Thin Shell StructuresThin walled shell structures are extensively used in architecture and engineering due to their lightweight and ease of shaping. But they suffer from poor overall stiffness, something addressed by the strategic addition of stiffeners. The optimization of stiffeners is divided between those which include shell membrane in the optimization and those which do not. However, no studies were found which indicate when it is necessary or valid to use either approach. In most cases it was also found that symmetry was forced in the optimization of stiffening layers. These two effects were investigated, concluding that: For membranes with thicknesses less than 20% of the structure, they do not affect the final topology; and for membrane thicknesses greater than 20%, they must be included in the optimization as they have a considerable effect. When bending and membrane loadings are present, symmetry should not be forced, otherwise sub-optimal designs are generated.

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Some Finite Element Methods for Linear Thin Shell Problems

Cited by 41 publications

References 8 publications

Fundamental considerations for the finite element analysis of shell structures

Fundamental considerations for the finite element analysis of shell structures

Real-Time Optimization and Stabilization of Distributed Parameter Systems with Piezoelectric Elements

The effects of membrane thickness and asymmetry in the topology optimization of stiffeners for thin-shell structures

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