Some results concerning the state of bending for transversely isotropic plates

Passarella, Francesca; Zampoli, Vittorio

doi:10.1002/mma.1113

Cited by 11 publications

(5 citation statements)

References 13 publications

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“…Nevertheless, as with the study carried out in [Passarella and Zampoli 2009a;2009b], we restrict our attention to the bending state characterized by…”

Section: Formulation Of the Problemmentioning

confidence: 99%

“…The work in this paper was performed under the auspices of the GNFM of the Italian INdAM.. The state of bending for a transversely isotropic plate of Mindlin-type has been analyzed by Passarella and Zampoli [2009a;2009b]. The first of these papers contains a uniqueness result and a Galerkin representation of the solution, without positive definiteness assumptions on the elasticity tensor.…”

Section: Introductionmentioning

confidence: 99%

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Decay properties of solutions of a Mindlin-type plate model for rhombic systems

Passarella

Tibullo

Zampoli

2010

JOMMS

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In the present paper, we investigate the spatial behavior of transient and steady-state solutions for the problem of bending applied to a linear Mindlin-type plate model; the plate is supposed to be made of a material characterized by rhombic isotropy, with the elasticity tensor satisfying the strong ellipticity condition. First, using an appropriate family of measures, we show that the transient solution vanishes at distances greater than cT from the support of the given data on the time interval [0, T ], where c is a characteristic material constant. For distances from the support less than cT , we obtain a spatial decay estimate of Saint-Venant type. Then, for a plate whose middle section is modelled as a (bounded or semiinfinite) strip, a family of measures is used to obtain an estimate describing the spatial behavior of the amplitude of harmonic vibrations, provided that the frequency is lower than a critical value.A list of symbols can be found on page 337.

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“…Nevertheless, as with the study carried out in [Passarella and Zampoli 2009a;2009b], we restrict our attention to the bending state characterized by…”

Section: Formulation Of the Problemmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Decay properties of solutions of a Mindlin-type plate model for rhombic systems

Passarella

Tibullo

Zampoli

2010

JOMMS

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“…where u i are the components of the displacement vector that vary smoothly with respect to x 3 . Nevertheless, as with the study carried out in [Passarella and Zampoli 2009a;2009b], we restrict our attention to the bending state characterized by…”

Section: Formulation Of the Problemmentioning

confidence: 99%

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2010

JOMMS

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Delamination in layered composites and debonding in adhesive joints are modeled and analyzed using interfacial mechanics, consisting of interface elements for the kinematical assumption and tractionseparation equations for the constitutive model. Material equations are presented for the inelastic behavior of pure and ductile-modified epoxy resins, used for the matrix phase of the composite and in a chemically modified form for the adhesive in bonded structures. Two different modeling approaches are proposed. The first is a brittle fracture model with a stressbased failure criterion and rate-dependent strength parameters together with a mixed-mode energy criterion for the interaction of the three different modes of failure. The second makes use of an elastic-plastic approach with a traction-separation equation for ductile materials and rate-dependent yield stresses. Standard tests for the delamination of layered composites under various modes of failure are simulated by making use of the interface element for bonding/debonding. The model for the inelastic behavior of a thin layer of the structural adhesive is validated up to fracture for various modes of failure due to pure and combined loading in the normal and shear directions. Therefore, the relevant part of the experimental setup for the testing is meshed with finite elements and the results of the simulation are compared to the corresponding test data.

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“…For a transversely isotropic plate described through the Mindlin-model and without positive definiteness assumptions on the elasticity tensor, Passarella and Zampoli (2007) have established a uniqueness result and a Galerkin representation of solution of the field equations. Furthermore, under the hypotheses of positive definiteness of the elasticity tensor, they prove a variational theorem of Gurtin 2 A C C E P T E D M A N U S C R I P T ACCEPTED MANUSCRIPT type and a minimum principle.…”

Section: Accepted M Manuscriptmentioning

confidence: 99%

Spatial estimates for transient and steady-state solutions in transversely isotropic plates of Mindlin-type

Passarella

Zampoli

2009

European Journal of Mechanics - A/Solids

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This paper concerns with a state of bending for a linear transversely isotropic plate model based on the Mindlin assumption on the displacement. By using appropriate families of lineintegral measures, we are able to establish results about the spatial behaviour of transient and steady-state solutions. All the results are obtained under relaxed hypotheses on the positive definiteness of the elasticity tensor.

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Some results concerning the state of bending for transversely isotropic plates

Cited by 11 publications

References 13 publications

Decay properties of solutions of a Mindlin-type plate model for rhombic systems

Decay properties of solutions of a Mindlin-type plate model for rhombic systems

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Spatial estimates for transient and steady-state solutions in transversely isotropic plates of Mindlin-type

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