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171.
The influences of transverse and rotational symmetries on the strain-energy functions of elastic rods are discussed. Complete function bases are presented and, for some constrained theories, these bases are also proven to be irreducible. The treatment of symmetry is based on a reformulation of a recent work by Luo and O’Reilly. It is also shown how this work relates to existing treatments by Antman and Healey for a particular constrained rod theory. 相似文献
172.
In this paper we derive and mathematically justify models of micropolar rods and plates from the equations of linearized micropolar elasticity. Derivation is based on the asymptotic techniques with respect to the small parameter being the thickness of the elastic body we consider. Justification of the models is obtained through the convergence result for the displacement and microrotation fields when the thickness tends to zero. The limiting microrotation is then related to the macrorotation of the cross–section (transversal segment) and the model is rewritten in terms of macroscopic unknowns. The obtained models are recognized as being either the Reissner–Mindlin plate or the Timoshenko beam type. 相似文献
173.
We introduce a notion of solution to the wave equation on a suitable class of time-dependent domains and compare it with a previous definition. We prove an existence result for the solution of the Cauchy problem and present some additional conditions which imply uniqueness. 相似文献
174.
The hinged Kirchhoff plate model contains a fourth order elliptic differential equation complemented with a zeroeth and a second order boundary condition. On domains with boundaries having corners the strong setting is not well‐defined. We here allow boundaries consisting of piecewise C2, 1‐curves connecting at corners. For such domains different variational settings will be discussed and compared. As was observed in the so‐called Saponzhyan–Babushka paradox, domains with reentrant corners need special care. In that case, a variational setting that corresponds to a second order system needs an augmented solution space in order to find a solution in the appropriate Sobolev‐type space. 相似文献
175.
Michael Dokuchaev 《Journal of Pure and Applied Algebra》2007,208(1):77-87
In this article, among other results, we develop a Galois theory of commutative rings under partial actions of finite groups, extending the well-known results by S.U. Chase, D.K. Harrison and A. Rosenberg. 相似文献
176.
A model of a dynamic viscoelastic adhesive contact between a piezoelectric body and a deformable foundation is described. The model consists of a system of the hemivariational inequality of hyperbolic type for the displacement, the time dependent elliptic equation for the electric potential and the ordinary differential equation for the adhesion field. In the hemivariational inequality the friction forces are derived from a nonconvex superpotential through the generalized Clarke subdifferential. The existence of a weak solution is proved by embedding the problem into a class of second-order evolution inclusions and by applying a surjectivity result for multivalued operators. 相似文献
177.
M. Aassila M.M. Cavalcanti V.N. Domingos Cavalcanti 《Calculus of Variations and Partial Differential Equations》2002,15(2):155-180
We consider the nonlinear model of the wave equation
subject to the following nonlinear boundary conditions
We show existence of solutions by means of Faedo-Galerkin method and the uniform decay is obtained by using the multiplier
technique.
Received: 15 June 2000 / Accepted: 4 December 2000 / Published online: 29 April 2002 相似文献
178.
Summary. In this paper we consider a frictionless contact problem between an elastic–viscoplastic body and an obstacle. The process
is assumed to be quasistatic and the contact is modeled with normal compliance. We present a variational formulation of the
problem and prove the existence and uniqueness of the weak solution, using strongly monotone operators arguments and Banach's
fixed point theorem. We also study the numerical approach to the problem using spatially semi-discrete and fully discrete
finite elements schemes with implicit and explicit discretization in time. We show the existence of the unique solution for
each of the schemes and derive error estimates on the approximate solutions. Finally, we present some numerical results involving
examples in one, two and three dimensions.
Received May 20, 2000 / Revised version received January 8, 2001 / Published online June 7, 2001 相似文献
179.
S. Potapenko P. Schiavone A. Mioduchowski 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2005,56(3):516-528
In this paper, we solve fundamental boundary value problems in a theory of antiplane elasticity which includes the effects of material microstructure. Using the real boundary integral equation method, we reduce the fundamental problems to systems of singular integral equations and construct exact solutions in the form of integral potentials.Received: March 25, 2002 相似文献
180.
In this article we study the asymptotic behaviour as tends to 0 of the Neumann problem $-\Delta u_\epsilon+u_\epsilon=\epsilon$-periodic bounded open set of . The period cell of is equal to where is a regular open subset of the d-dimensional torus. We prove that if there exists a smallest integer such that the n-th non-zero eigenvalue of the spectral problem in satisfies , the limiting problem is a linear system of second order p.d.e.'s, of size n. By this spectral approach we extend in the periodic framework a result due to Khruslov without making strong geometrical
assumptions on the perforated domain .
Received: 20 December 2000 / Accepted: 11 May 2001 / Published online: 19 October 2001 相似文献