1,097 research outputs found
The behavior of symmetric Krylov subspace methods for solving Mx=(M−γI)v
No full textAbstractWe analyze the behavior of Krylov subspace methods for the solution of the symmetric system Mx=(M−γI)v when γ is close to some of the extreme eigenvalues of M. We show that a stagnation phase may occur if the structure of the right-hand side is not taken into account, and we analyze the occurrence and persistence of such stagnation. A natural alternative strategy is proposed and we show that the new approach provides a better approximation, with the same number of matrix–vector multiplications. Numerical experiments are also included
Study of high strain rate effect on sheet formability based on Nakazima test
No full textThe knowledge of the sheet metals formality is important for the success of the manufacturing processed based on plastic deformation. Even though many industrial processes take place at relatively high speeds, higher than the quasi-static regime ones, few studies are present in the literature on the evaluation of the formability at high speed. In this framework, the present paper aims at studying the effect of the high strain rate on the formability of AA6082 aluminium alloy, characterized by a thickness of 1 mm. An experimental equipment, based on the Nakazima test, mounted on a direct tension-compression Split Hopkinson Bar, has been developed in order to define the formability under dynamic loading conditions. The high strain rate behaviour of the alloy has been compared with the one obtained in quasi-static condition
Evaluation of Friction at High Strain Rate using the Split Hopkinson Bar
No full textThe present work aims at studying the influence of strain rate on the frictional behaviour of AA7075 aluminium alloy in the O-annealed temper state. To this purpose, ring compression tests were performed both under quasi-static and dynamic loading conditions. The high strain rate tests were carried out by means of the Split Hopkinson Tension-Compression Bar in the direct version. In both cases, hollow cylindrical samples, characterised by an initial outer diameter to inner diameter to height ratio of 6:3:2, were tested under dry condition and by lubricating with molybdenum disulphide grease. The different frictional behaviour exhibited by AA7075-O under quasi-static and dynamic loading conditions can be attributed to the strain rate effect both on the plastic flow behaviour of the deformed material, and on the thickness of the lubricant film
On the decay of the inverse of matrices that are sum of Kronecker products
No full textDecay patterns of matrix inverses have recently attracted considerable interest, due to their relevance in numerical analysis, and in applications requiring matrix function approximations. In this paper we analyze the decay pattern of the inverse of banded matrices in the form , where M is tridiagonal, symmetric and positive definite, In is the identity matrix, and stands for the Kronecker product. It is well known that the inverses of banded matrices exhibit an exponential decay pattern away from the main diagonal. However, the entries in show a non- monotonic decay, which is not caught by classical bounds. By using an alternative expression for , we derive computable upper bounds that closely capture the actual behavior of its entries. We also show that similar estimates can be obtained when M has a larger bandwidth, or when the sum of Kronecker products involves two different matrices. Numerical experiments illustrating the new bounds are also reporte
Numerical solution of a class of quasi-linear matrix equations
No full textGiven the matrix equation in the unknown matrix , we analyze existence and
uniqueness conditions, together with computational solution strategies for being a linear or nonlinear
function. We characterize different properties of the matrix equation and of
its solution, depending on the considered classes of functions . Our
analysis mainly concerns small dimensional problems, though several
considerations also apply to large scale matrix equations
High Strain Rate Behaviour of AA7075 Aluminum Alloy at Different Initial Temper States
No full textThe aim of this work is to study the mechanical properties of alloy AA7075 in both T6
and O temper states, in terms of visco-plastic and fracture behavior. Tension and compression tests
were carried out starting from the quasi-static loading condition 10-3 up to strain rates as high as 2 x
103 s-1. The high strain rate tests were performed using a Split Hopkinson Tension-Compression Bar
(SHTCB) apparatus. The tensile specimens were also subjected to micro-fractography analysis by
Scanning Electronic Microscope (SEM) to evaluate the characteristics of the fracture. The results
show a different behavior for the two temper states: AA7075-O showed a significant sensitivity to
strain rate, with a ductile behavior and a fracture morphology characterized by coalescence of
microvoids, whilst AA7075-T6 is generally characterized by a less ductile behaviour, both as
elongation at break and as fracture morphology. Brittle cleavage is accentuated with increasing
strain rate. The Johnson-Cook viscoplastic model wad also used to fit the experimental data with an
optimum matching
Democrazia e lealtà alle leggi: un problema educativo
No full textMARIA ZANICHELLI, Democrazia e lealtà alle leggi: un problema educativo, in AA.VV., La sostenibilità della democrazia nel XXI secolo, a cura di M. Cartabia e A. Simoncini, Bologna, Il Mulino, 2009, pp. 321-351.
ABSTRACT
Il saggio approfondisce il ruolo del senso del diritto e della lealtà alle leggi quali importanti fondamenti extra-politici della democrazia e garanzie della sua stessa ‘sostenibilità’. In quanto metodo politico la democrazia non è necessariamente capace di autofondarsi: la sua qualità e la sua tenuta dipendono da specifici contenuti valoriali, connessi ai comportamenti e alle convinzioni dei suoi attori. In effetti, prima che una modalità di decision making o di selezione della leadership, la democrazia è un ideale normativo, un ethos personale del cittadino e di chi governa, un modo di concepire sostanzialmente i rapporti individuo - autorità e la stessa convivenza umana (1). Non a caso diverse teorie contemporanee hanno posto in rilievo i profili preistituzionali della democrazia (O. Höffe, R. Dahl, E.-W. Böckenförde), configurando un catalogo di “virtù civiche” per i cittadini del XXI secolo (§ 2). Tra queste, occorre riconoscere un rilievo preminente alla lealtà, intesa come impegno a non tradire regole condivise (dal significato originario di fides, capacità di mantenere le promesse e rispettare la parola data). La sua declinazione civico-giuridica, la fedeltà alle leggi, possiede una peculiare valenza fondativa rispetto alla democrazia quale sistema politico basato sull’autolegislazione. La democrazia, infatti, necessita della lealtà dei consociati in modo più pregnante rispetto ad altre forme di governo. La sua pretesa di lealtà non è mera pretesa di obbedienza, poiché la forza vincolante delle norme e delle decisioni che essa produce poggia sul consenso, non sulla mera coercizione. Proprio per questo il rispetto delle leggi in democrazia diviene una forma di lealtà: non si tratta semplicemente di sottostare alle prescrizioni di un’autorità esterna, bensì di partecipare a un sistema che impegna tutti, poiché tutti, se non altro come elettori, ne hanno accettato i presupposti. In modo speculare, nel disprezzo delle leggi si annida una delle minacce più gravi al tessuto democratico di una società (§ 3). Cogliere un nesso fondante tra lealtà alle leggi e democrazia significa non solo riconoscere il ruolo specifico del diritto nel connotare la forma di governo democratica, ma anche ricondurre il significato della democrazia alle ragioni profonde che muovono l’agire dei soggetti, privati e pubblici, prima che ai meccanismi istituzionali che la qualificano politicamente. Il senso della legalità infatti è una qualità soggettiva dei consociati: presuppone una certa conoscenza del diritto, l’interiorizzazione di alcuni criteri di condotta, l’assunzione di un atteggiamento di lealtà verso le norme. Condizione essenziale per la sostenibilità della democrazia è dunque che cittadini e governanti condividano il senso del diritto e della legalità (§ 4).Ciò pone, d’altra parte, un problema eminentemente educativo. L’apprendimento e l’insegnamento della democrazia (G. Zagrebelsky), la possibilità di custodirne e alimentarne il significato, dipendono in larga misura dal ruolo della scuola, della famiglia e più in generale dal dialogo tra le generazioni e dalle diverse esperienze formative che coinvolgono l’individuo nel corso della sua esistenza. Da Platone a Montesquieu a Dewey a Maritain, il tema classico della paideia democratica si ripropone dunque anche oggi in tutta la sua pregnanza (§ 5)
Effect of process parameters on vertical forces and temperatures developed during friction stir welding of magnesium alloys
No full textThe effect of process parameters on vertical forces and temperatures developed during friction stir welding of AZ31 magnesium alloy sheets was widely investigated. To this end, FSW experiments were carried out with constant values of the rotational and welding speeds in the ranges from 1200 to 2500 rpm, and from 30 to 100 mm/min, respectively. The influence of the time between the end of the sinking stage and the beginning of the welding one was also studied using dwelling time values ranging from 0 to 120 s. Vertical forces occurring during all stages of friction stir welding were measured using a low-cost dynamometer developed by authors. Furthermore, temperatures in different positions of the welding line were monitored by means of K-type thermocouples. It was shown that during the dwelling stage the vertical force decreases until a steady state regime is reached. However, the dwelling time does not significantly affect the force value in the welding stage. The vertical force vs. time curve promptly reaches a steady state during the welding stage. The force value rises with increasing welding speed and decreasing rotational speed; such effect is consistent with the one showed by rotational and welding speeds on temperature measured in different positions during FSW. Finally, forces and temperatures have been related to the mechanical properties of the joints. It was shown that both the ultimate tensile strength and ultimate elongation exhibit the highest values under the process parameters leading to the lowest vertical force and highest welding temperature
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