BULETINUL INSTITUTULUI POLITEHNIC DIN IAŞI

BULETINUL INSTITUTULUI POLITEHNIC DIN IAŞI
Publicat de
Universitatea Tehnică „Gheorghe Asachi” din Iaşi
Tomul LVIII (LXII), Fasc. 3, 2012
Secţia
MATEMATICĂ. MECANICĂ TEORETICĂ. FIZICĂ
ON SOME AXIAL-SYMMETRIC PROBLEMS OF THE
MICROPOLAR ELASTICITY THEORY
BY
ION CRĂCIUN ∗
“Gheorghe Asachi” Technical University of Iaşi,
Department of Mathematics and Informatics
Received: May 28, 2012
Accepted for publication: July 20, 2012
Abstract. The steady vibrations of the linear theory of micropolar elasticity
of an isotropic, homogeneous, and centrosymmetric elastic body occupying the
three dimensional region B are considered. A generalized Galerkin representation
of a regular solution of basic differential equations in B of this theory is given. In
the case of cylindrical coordinates (, r θ, z)
under the assumption of axially
symmetry (causes and effects do not depend of the variable θ), from governing
equations in the amplitudes of displacement and rotation vectors we obtain two
independently systems, each one containing three partial differential equations.
The unknowns of the second system are the second component of the amplitude
of displacement vector u, and the first and the third components of the amplitude
of rotation vector φ , all depending only of variables r and z in B, for each θ.
The aim of this paper is the study of such obtained system. Thus, the Galerkin
representation of a regular solution by stress functions is obtained, the actions
both of body and couple-body loadings are analysed, and the action of a
concentrated couple-body is considered.
Key words: micropolar elasticity; axially-symmetric problems; stress
functions; concentrated loadings.
1. Introduction
The classical theory of elasticity is inadequate to represent the behaviour
of certain materials such as polycrystalline materials, granular bodies, bodies
∗ e-mail: ialcraciun@yahoo.com