Plane Anisotropy by the Polar Method*

Vannucci, Paolo

doi:10.1007/s11012-005-2132-z

Cited by 94 publications

(127 citation statements)

References 14 publications

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“…the laminate polar parameters, see [26]). At the second level of the strategy we determine the optimal skins lay-up (the skin meso-scale) meeting the values of the material and geometrical parameters issued from the rst level of the strategy.…”

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confidence: 99%

“…At the second level of the strategy we determine the optimal skins lay-up (the skin meso-scale) meeting the values of the material and geometrical parameters issued from the rst level of the strategy. The whole strategy is based on the use of the polar formalism [26,28] and on the Genetic Algorithm (GA) BIANCA [20,21]. For more details on the polar formalism and the related advantages the reader is addressed to Part II of the present work.…”

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confidence: 99%

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A multi-scale approach for the optimum design of sandwich plates with honeycomb core. Part I: homogenisation of core properties

Catapano

Montemurro

2014

Composite Structures

122

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This work deals with the problem of the optimum design of a sandwich panel. The design process is based on a general two-level optimisation strategy involving di erent scales: the meso-scale for both the unit cell of the core and the constitutive layer of the laminated skins and the macro scale for the whole panel. Concerning the meso-scale of the honeycomb core, an appropriate model of the unit cell able to properly provide its e ective elastic properties (to be used at the macro-scale) must be conceived. To this purpose, in this rst paper, we present the numerical homogenisation technique as well as the related nite element model of the unit cell which makes use of solid elements instead of the usual shell ones. A numerical study to determine the e ective properties of the honeycomb along with a comparison with existing models and a sensitive analysis in terms of the geometric parameters of the unit cell have been conducted. Numerical results show that shell-based models are no longer adapted to evaluate the core properties, mostly in the context of an optimisation procedure where the parameters of the unit cell can get values that go beyond the limits imposed by a 2D model.

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A multi-scale approach for the optimum design of sandwich plates with honeycomb core. Part I: homogenisation of core properties

Catapano

Montemurro

2014

Composite Structures

122

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“…The polar invariants are directly linked to the elastic symmetries, allow for a simple expression of the elastic properties in a rotated frame and of the elastic bounds by invariants. A deeper insight in the matter can be found in [9], here only the essential points for the rest of the paper are briefly recalled.…”

Section: Basic Equationsmentioning

confidence: 99%

“…But with the polar formalism, the bounds are rather simple and concern invariant quantities. For an orthotropic tensor, the bounds are, [9], T 0 −R 0 >0,…”

Section: Elastic and Geometrical Boundsmentioning

confidence: 99%

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A Note on the Elastic and Geometric Bounds for Composite Laminates

Vannucci

2012

J Elast

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Invariant formulation of phenomenological failure criteria for orthotropic sheets and optimisation of their strength

Catapano

Desmorat

Vannucci

2012

Math Methods in App Sciences

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The strength optimisation of orthotropic materials is an open problem. The majority of the studies conducted on strength optimisation of anisotropic materials have been performed with the help of a phenomenological failure criterion that describe the conditions to obtain a limit state identified with the ultimate strength of the material. This paper is a study concerning the bidimensional linear case. Our approach concerns the formulation of a failure criterion through tensors invariants, in order to reduce the optimisation variables to only one: the orientation of material properties of the continuum. Finally, the analytical approach is introduced in order to minimise the failure index and results obtained with the use of three different failure criteria that are compared in order to understand the role of the three formulations with respect to the strength's behaviour. Copyright © 2012 John Wiley & Sons, Ltd.

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Plane Anisotropy by the Polar Method*

Cited by 94 publications

References 14 publications

A multi-scale approach for the optimum design of sandwich plates with honeycomb core. Part I: homogenisation of core properties

A multi-scale approach for the optimum design of sandwich plates with honeycomb core. Part I: homogenisation of core properties

A Note on the Elastic and Geometric Bounds for Composite Laminates

Invariant formulation of phenomenological failure criteria for orthotropic sheets and optimisation of their strength

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