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Emilio Turco Francesco dell’Isola Antonio Cazzani Nicola Luigi Rizzi 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2016,67(4):85
Hencky (Über die angenäherte Lösung von Stabilitätsproblemen im Raum mittels der elastischen Gelenkkette. Ph.D. thesis, Engelmann, 1921) proposed a discrete model for elasticae by introducing rigid bars and rotational springs. Hencky (Proc R Soc Lond A Math Phys Eng Sci 472(2185), 2016) approach has been introduced to heuristically motivate the need of second gradient continua. Here, we present a novel numerical code implementing directly the discrete Hencky-type model which is robust enough to solve the problem of the determination of equilibrium configurations in the large deformation and displacement regimes. We apply this model to study some potentially applicable problems, and we compare its performances with those of the second gradient continuum model. The numerical evidence presented supports the conjecture that Hencky-type converges to second gradient model. 相似文献
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Antonio Cazzani Flavio Stochino Emilio Turco 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2016,67(2):25
The problem of free vibrations of the Timoshenko beam model has been addressed in the first part of this paper. A careful analysis of the governing equations has shown that the vibration spectrum consists of two parts, separated by a transition frequency, which, depending on the applied boundary conditions, might be itself part of the spectrum. Here, as an extension, the case of a doubly clamped beam is considered. For both parts of the spectrum, the values of natural frequencies are computed and the expressions of eigenmodes are provided: this allows to acknowledge that the nature of vibration modes changes when moving across the transition frequency. This case is a meaningful example of more general ones, where the wave-numbers equation cannot be written in a factorized form and hence must be solved by general root-finding methods for nonlinear transcendental equations. These theoretical results can be used as further benchmarks for assessing the correctness of the numerical values provided by several numerical techniques, e.g. finite element models. 相似文献
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Cazzani Antonio Serra Mauro Stochino Flavio Turco Emilio 《Continuum Mechanics and Thermodynamics》2020,32(3):665-692
Continuum Mechanics and Thermodynamics - This work discusses some alternate models of a mixed assumed strain finite element which has been developed for laminated plates. After a brief theoretical... 相似文献
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Antonio Cazzani Flavio Stochino Emilio Turco 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2016,67(2):24
The problem of free vibrations of the Timoshenko beam model is here addressed. A careful analysis of the governing equations allows identifying that the vibration spectrum consists of two parts, separated by a transition frequency, which, depending on the applied boundary conditions, might be itself part of the spectrum. For both parts of the spectrum, the values of natural frequencies are computed and the expressions of eigenmodes are provided. This allows to acknowledge that the nature of vibration modes changes when moving across the transition frequency. Among all possible combination of end constraints which can be applied to single-span beams, the case of a simply supported beam is considered. These theoretical results can be used as benchmarks for assessing the correctness of the numerical values provided by several numerical techniques, e.g. traditional Lagrangian-based finite element models or the newly developed isogeometric approach. 相似文献
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Maria Grazia Cazzani Nieri 《Annali di Matematica Pura ed Applicata》1994,167(1):351-387