A unilateral boundary-value condition at the left end of a simply supported rod is considered. Variational and (equivalent) classical formulations are introduced and all solutions to the classical problem are calculated in an explicit form. Formulas for the energies corresponding to the solutions are also given. The problem is solved and energies of the solutions are compared in the pertubed as well as the unperturbed cases.
The elastoplastic rate problem is formulated as an unconstrained saddle point problem which, in turn, is obtained by the Lagrange multiplier method from a kinematic minimum principle. The finite element discretization and the enforcement of the min-max conditions for the Lagrangean function lead to a set of algebraic governing relations (equilibrium, compatibility and constitutive law). It is shown how important properties of the continuum problem (like, e.g., symmetry, convexity, normality) carry...
In this paper the contact problem for a cylindrical shell and a stiff punch is studied. The existence and uniqueness of a solution is verified. The finite element method is discussed.
Si risolve nella sua generalità il problema delle vibrazioni libere trasversali dei gusci sferici ortotropi ribassati, che in un precedente Lavoro era stato affrontato limitatamente al campo delle vibrazioni assialsimmetriche. L'integrazione delle equazioni del moto è conseguita per serie mediante particolari sviluppi, generabili grazie ad un'opportuna sostituzione di una delle variabili indipendenti.
In questo lavoro viene risolto il problema del contatto tra una membrana ed un suolo od ostacolo elastico con una approssimazione lineare a tratti della soluzione. Sono date alcune formulazioni equivalenti del problema discreto e se ne discutono le corrispondenti proprietà computazionali.
In order to describe a solid which deforms smoothly in some region, but non smoothly in some other region, many multiscale methods have recently been proposed. They aim at coupling an atomistic model (discrete mechanics) with a macroscopic model (continuum mechanics). We provide here a theoretical ground for such a coupling in a one-dimensional setting. We briefly study the general case of a convex energy, and next concentrate on a specific example of a nonconvex energy, the Lennard-Jones case....
In order to describe a solid which deforms smoothly in some region, but non smoothly in some other region, many multiscale methods have recently been proposed. They aim at coupling an atomistic model (discrete mechanics) with a macroscopic model (continuum mechanics). We provide here a theoretical ground for such a coupling in a one-dimensional setting. We briefly study the general case of a convex energy, and next concentrate on a specific example of a nonconvex energy, the Lennard-Jones case....
The authors study problems of existence and uniqueness of solutions of various variational formulations of the coupled problem of dynamical thermoelasticity and of the convergence of approximate solutions of these problems. First, the semidiscrete approximate solutions is defined, which is obtained by time discretization of the original variational problem by Euler’s backward formula. Under certain smoothness assumptions on the date authors prove existence and uniqueness of the solution and establish...
The present paper deals with numerical solution of the contact problem with given friction. By a suitable choice of multipliers the whole problem is transformed to that of finding a saddle-point of the Lagrangian function on a certain convex set . The approximation of this saddle-point is defined, the convergence is proved and the rate of convergence established. For the numerical realization Uzawa’s algorithm is used. Some examples are given in the conclusion.
The thermoelastic stresses created in a solid phase domain in the course of solidification of a molten ingot are investigated. A nonlinear behaviour of the solid phase is admitted, too. This problem, obtained from a real situation by many simplifications, contains a moving boundary between the solid and the liquid phase domains. To make the usage of standard numerical packages possible, we propose here a fixed-domain approximation by means of including the liquid phase domain into the problem (in...
It is proved that, as in three-dimensional elasticity, Betti's theorem represents a criterion for the existence of a stored-energy function for a Cosserat elastic shell.