1,720,995 research outputs found
Sul calcolo dell'interazione elastica terreno struttura per i telai fondati su suolo a due parametri
No full text
On the Linearization of Stress in Constrained Elasticity
No full textThe linearization of stress in an elastic body subject to internal constraints is discussed. It is shown that, as in the nonlinear case, the stress resulting from the linearization process is composed of a reactive part that does no work in each admissible motion, and an active part that lies in the complement of the reaction space.
Una formulazione variazionale esatta del problema di equilibrio di una capsula sferica soggetta a trazioni uniformi al contorno
No full text
Sulla teoria non lineare dei gusci elastici sottili
No full textLa teoria non lineare dei gusci elastici sottili, formati da materiali del tipo di St. Venant-Kirhhoff, è esaminata secondo un nuovo punto di vista che attribuisce natura costitutiva alle classiche ipotesi di Kirchhoff-Love. Queste sono riguardate come restrizioni sulle possibili deformazioni, da valere in ogni moto ammissibile, ossia come un vincolo interno per il materiale che costituisce il guscio; la conseguente decomposizione dello sforzo in parti attiva e reattiva consente di risolvere le contraddizioni implicite nelle formulazioni usuali della teoria dei gusci.
Si determina la forma delle funzioni di risposta compatibili con il vincolo interno assunto; quindi, per integrazione sullo spessore delle condizioni di stazionarietà del funzionale tridimensionale dell'energia, si ottengono le equazioni bidimensionali di equilibrio (espresse nella configurazione di riferimento) e le condizioni al contorno associate
On the geometry of constraint manifolds
No full textThe paper examines the properties that constraint manifolds possess as Riemannian submanifolds of the Euclidean space of all second-order tensors and have implications on the description of mechanical behavior of internally constrained bodies. It is shown that constraint manifolds corresponding to some usual internal constraints have non-zero curvature and, hence, possess a non-Euclidean structure that has to be taken into account when the active and reactive parts of the Piola-Kirchhoff stress are differentiated with respect to deformation gradient.
On the stability of elastic annular rods
No full textThe stability of equilibrium of non-linearly elastic rods, whose deformations obey the classical Kirchhoff''s equations, is considered. A variational formulation of the equilibrium problem is given, and the equilibrium equations for infinitesimal deformations superimposed to a finite transformation of a rod are deduced. The stability of annular rings, in which the twisting strain is non-null, is investigated by study of the second variation of the energy functional.
On nonlinear deformations of nonlocal elastic rods
No full textThe nonlinear theory of Kirchhoff and Clebsch is extended to rods made of nonlocal materials; the motion equations are written and the balance of energy is proved.
In view of application to the study of equilibrium configurations, by means of the usual assumptions of nonlocal elasticity the integro-differential equations of the theory are transformed into differential equations.
Deformations of pure bending about a principal direction of inertia of rods subject to forces and couples applied at their ends are studied: equilibrium equations are integrated by means of elliptic functions, and solutions for rods made of nonlocal and classic elastic materials are compared.
The curves formed in equilibrium by the axes of rods made of nonlocal materials are distinguished in inflexional and non-inflexional elastica.
The equilibrium of cantilevers subject to a force applied at their free end is also examined:
the results for rods of classic and nonlocal materials are discussed by regarding the deformed axial curve of a cantilever as a segment of an inflexional elastica
On the dynamics of shells in the theory of Kirchhoff and Love
No full textThe non-linear theory of thin shells is examined from a new point of view that regards the classical Kirchhoff-Love hypotheses as constitutive assumptions reflecting the presence of internal constraints in the material of which the body is formed; the consequent splitting of the stress into an active and a reactive part together with the choice of a response mapping compatible with the assumed internal constraints make the Kirchhoff-Love theory fully consistent with the three-dimensional theory. The restrictions on the constitutive relations due to the presence of the internal constraints are discussed and the materials compatible with the considered constraints are determined. A derivation of the displacement field corresponding to the Kirchhoff-Love assumptions is given and the two-dimensional equations of motion, with the accompanying boundary conditions, are obtained by integrating over the thickness the conditions for a stationary value of the three-dimensional Hamiltonian functional associated with the motion of the shell.
- …
