Combined techniques for the characterization of linear–hyperbranched hybrid poly(butylene adipate) copolymers

Linear–hyperbranched hybrid poly(butylene adipate) (HPBA) copolymers were synthesized through a branching reaction between the linear tailored prepolymer terminated with methyl ester groups and different mol percents of the 1,1,1‐tris(hydroxymethyl) propane (TMP) as branching agent, using the titanium(IV) isopropoxide as catalyst, at 180 °C under vacuum for different times. All samples were characterized by NMR and matrix assisted laser desorption/ionization time of flight mass spectrometry (MALDI‐TOF MS). In particular, MALDI‐TOF mass spectra of the unfractionated and size exclusion chromatography (SEC)‐fractionated hyperbranched (HB) samples gave information on their composition, on the end groups as well as on the TMP units present in each family of HB macromolecules. HB chains containing cyclic branches and ether bonds formed by intermolecular transesterification and intramolecular and intermolecular transetherification side reactions, respectively, were also revealed by MALDI‐TOF MS analysis. All samples were also investigated by SEC. The average molar masses (MMs) evaluated by SEC calibrated with the polystyrene (PS) narrow standards were overestimated with respect to those calculated by the SEC/MALDI‐TOF MS self‐ calibration method, which gave reliable values. Moreover, it also showed that the hydrodynamic volume of the HPBA polymers was higher than that of the linear PSs with similar MMs. © 2011 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2011     

On the statical unilateral contact problem with friction of rectangular plates resting on an elastic half-space

Summary In this paper the statical equilibrium problem of a rectangular plate unilaterally constrained against an elastic half-space is analyzed. The frictional contact hypothesis at the interface between plate and foundation is made. The assumed friction law represents a suitable regularization of Coulomb's classical law, which is particularly helpful in view of the theoretical and numerical developments.The problem is formulated and discussed from a theoretical point of view. Some numerical results are also given showing the influence on the solution of the frictional contact hypothesis.

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Sommario In questo lavoro si analizza il problema di equilibrio statico di una piastra rettangolare vincolata unilateralmente su un semispazio elastico. Viene fatta l'ipotesi di contatto con attrito all'interfaccia fra piastra e fondazione. La legge di attrito che si assume rappresenta una opportuna regolarizzazione della classica legge di Coulomb, la quale è particolarmente utile per gli sviluppi sia teorici che numerici. Il problema viene formulato e discusso da un punto di vista teorico; vengono inoltre forniti alcuni risultati numerici che mostrano l'influenza sulla soluzione dell'ipotesi di contatto con attrito.

     

Orlicz spaces with a o–O type structure

We study non reflexive Orlicz spaces \(L^\varPsi \) and their Morse subspace \(M^\varPsi \), i.e. the closure of \(L^\infty \) in \(M^\varPsi \) to determine when \((M^\varPsi ,L^\varPsi )\) can be described as having an o–O type structure with respect to an equivalent norm on \(L^\varPsi \). Examples of classes of Young functions for which the answer is affirmative are provided, but also examples are given to show that this is not possible for all non-reflexive Orlicz spaces. An equivalent expression of the distance in \(L^\varPsi \) to \(M^\varPsi \), induced by the new norm, is also provided.

     

Intermolecular π‐Electron Perturbations Generate Extrinsic Visible Contributions to Eumelanin Black Chromophore in Model Polymers with Interrupted Interring Conjugation

The key structural factors underlying the unique black chromophore of eumelanin biopolymers have so far defied elucidation. Capitalizing on the ability of 1% polyvinylalcohol (PVA) to prevent pigment precipitation during melanogenesis in vitro, we have investigated the visible chromophore properties of soluble eumelanin‐like polymers produced by biomimetic oxidation of 5,6‐dihydroxyindole (DHI) and 5,6‐dihydroxyindole‐2‐carboxylic (DHICA) in 1% PVA‐containing buffer at pH 7. Upon dilution DHI‐eumelanin solutions exhibited almost linear visible absorbance changes, whereas DHICA‐eumelanin displayed a remarkable deviation from linearity in simple buffer, but not in PVA‐containing buffer. It is suggested that in DHICA polymers, exhibiting repeated interruptions of interring conjugation due to lack of planar conformations, the black chromophore is not due to an overlap of static entities defined intrinsically by the conjugation length across the carbon frame, but results largely from aggregation‐related intermolecular perturbations of the π‐electron systems which are extrinsic in character.     

Unbonded contact of a Mindlin plate on an elastic half-space

Summary In this paper a penalty formulation of the frictionless unilateral contact problem between an elastic rectangular plate and an elastic half-space is presented. In order to take into account the effects of the shear stress, the Mindlin plate model is analyzed. Some numerical results, obtained via finite elements, are given.

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Sommario In questo lavoro viene presentata una formulazione penalty del problema di contatto unilaterale senza attrito tra una piastra rettangolare elastica ed un semispazio elastico. Per la piastra si utilizza il modello di Mindlin, che consente di tener conto dell'effetto delle tensioni da taglio. Si forniscono alcuni risultati numerici ottenuti mediante discretizzazione agli elementi finiti.

     

Unilateral contact between a plate and an elastic foundation

Summary The unilateral frictionless contact between a plate and an elastic subgrade is examined. The foundation is modeled as an elastic half-space or as a Winkler subgrade. The variational formulations more convenient to get approximate solutions are presented. Furthermore the results of a numerical investigation relative to an axisymmetric circular plate are given.

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Sommario Si analizza il problema di contatto unilaterale senza attrito tra una piastra e una fondazione elastica. Per la fondazione si esaminano i modelli di semispazio elastico e di suolo alla Winkler.Vengono presentate le formulazioni variazionali più convenienti ai fini dell'approssimazione delle soluzioni col metodo degli elementi finiti e si illustrano alcuni risultati di un'indagine numerica per il caso di piastra circolare con carico assialsimmetrico.

     

Buckling of an elastic plate subjected to unilateral constraints

Summary In this paper we show how it is possible to extend the well-known variational properties of the critical loads for elastic structures to the case of unilateral constraints. In particular we examine the buckling of an elastic plate unitalerally constrained between two elastic half-spaces and loaded by axial forces. For this problem we discuss the existence of the lowest positive and greatest negative critical load multiplier and provide a characterization of these multipliers by means of the minimal properties of a suitable functional.

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Sommario In questo lavoro viene mostrato come sia possibile estendere le ben note proprietà variazionali dei carichi critici di una struttura elastica dal caso dei vincoli bilaterali a quello dei vincoli unilaterali. In particolare viene esaminato il problema di svergolamento di una piastra rettangolare elastica, sollecitata da forze assiali agenti nelle due direzioni e vincolata unilateralmente tra due semispazi elastici. Per tale problema si discute l'esistenza del più piccolo moltiplicatore positivo dei carichi e del più grande negativo per cui si ha instabilità. Inoltre viene fornita una caratterizzazione variazionale di tali moltiplicatori mediante le proprietà di minimo di un opportuno funzionale.