„Engineering” error evaluation in approximate structural analysis

Summary It is observed that pure mathematical estimates of errors involved by the introduction of approximate procedures in structural analysis may be insufficient to judge the effectiveness of the method and the adequacy of the results. This circumstance can be explained by the simultaneous presence of many other uncertainties that, making necessary the application of one or more safety coefficients, tend to adsorb, at least partially, the influence of wrong calculations on structure reliability.To take this effect into account, a definition of «error» is proposed, that is strictly related to the concept of «failure probability» (in the wide sense) of the structure. Next, an attempt is made to evaluate the «error on safety», in the context of the Reliability Theory. Finally, possible applications are investigated, and the results are discussed.

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Sommario Si considerano gli errori introdotti nel calcolo delle strutture dall'uso di metodi approssimati. Si osserva che stime di errore puramente matematiche possono essere insufficienti a giudicare l'efficienza del metodo adottato e l'applicabilità dei risultati. Questa circostanza può derivare dalla presenza di molti altri fattori di incertezza che, comportando l'applicazione di uno o più coefficienti di sicurezza, tendono a riassorbire, almeno parzialmente, l'influenza degli errori di calcolo sull'affidabilità delle strutture.Per tenere conto di questo effetto, si propone una definizione di errore strettamente legata alla nozione di «Probabilità di collasso» (in senso lato) della struttura. Si tenta pertanto di valutare l'«errore in sicurezza» nel contesto della teoria della affidabilità. Infine si esplorano alcune possibili applicazioni e si discutono i risultati ottenuti.

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This work was supported by the Consiglio Nazionale delle Ricerche (C.N.R.), Italy.     

Use of Kirkwood–Buff Integrals for Extracting Distinct Diffusion Coefficients in Macromolecule–Solvent Mixtures

The possibility to extract velocity correlation quantities from fluctuation thermodynamic properties is explored in the case of macromolecule–solvent mixtures. Indeed, Kirkwood–Buff integrals, G_ij, together with self‐diffusion and viscosity data can provide an approximation for distinct diffusion coefficients (DDCs), D^d_ij. Herein, D^d_ij for binary polyethyleneglycol (PEG)(i)–water(0) systems is calculated. These systems show positive values of D^d_ii coefficients, indicating strong PEG–PEG interaction, and providing marker of water mediated PEG–PEG networks. The efficiency of several standard DDCs present in literature for D^d_ij analysis is compared, summarizing the usefulness of each one, depending on the nonideality degree.

     

Enhanced nonlinear effects in pulse propagation through epsilon‐near‐zero media

In recent years, unconventional metamaterial properties have triggered a revolution of electromagnetic research which has unveiled novel scenarios of wave‐matter interaction. A very small dielectric permittivity is a leading example of such unusual features, since it produces an exotic static‐like regime where the electromagnetic field is spatially slowly‐varying over a physically large region. The so‐called epsilon‐near‐zero metamaterials thus offer an ideal platform where to manipulate the inner details of the “stretched” field. Here we theoretically prove that a standard nonlinearity is able to operate such a manipulation to the point that even a thin slab produces a dramatic nonlinear pulse transformation, if the dielectric permittivity is very small within the field bandwidth. The predicted non‐resonant releasing of full nonlinear coupling produced by the epsilon‐near‐zero condition does not resort to any field enhancement mechanism and opens novel routes to exploiting matter nonlinearity for steering the radiation by means of ultra‐compact structures.

     

Vibration reduction in a flexible-link mechanism through synthesis of an optimal controller

In this paper, reduction of vibration of a flexible planar mechanism is achieved through synthesis of an optimal controller. A finite element model, based on the equivalent rigid-link system theory, is used to accurately describe the dynamic behavior of the system. The model, which accounts for geometric and inertial nonlinearities of the mechanism, has been fully validated through experimental tests. In order to be able to employ the classical optimal control theory, a suitable linear model has been derived from the original one by means of a suitable linearization procedure. Vibration reduction can then be obtained by first defining an adequate performance index, which accounts for vibration amplitude, then by solving Riccati’s equation in order to find the controller that minimizes the performance index, i.e. the optimal controller. The results of several tests that have been carried out are also reported, to show the effectiveness of the synthesized control system.