Thermoelectroelastic state of a multiply connected anisotropic plate

Abstract

Generalized complex potentials in a plane problem of thermoelectroelasticity are introduced. Expressions for the basic characteristics of the thermoelectroelastic state are derived. Boundary conditions for determining the complex potentials and the general form of these functions for a multiply connected plate are obtained. The potentials are used to solve a specific problem Keywords: thermoelectroelasticity, plane problem, generalized complex potentials, multiply connected plate Extensive studies have been carried out to determine the thermoelastic [2] and electroelastic [12] states of multiply connected anisotropic plates. However, thermoelectroelastic problems have not yet been analyzed. Note that the theory of electroelasticity [1] was used in [13,14] to study the stress-strain state and longitudinal vibrations of rectangular piezoceramic plates with sections polarized in two directions. In the present paper, to solve such problems in a new formulation, we introduce complex potentials and derive the governing equations of thermoelectroelasticity for multiply connected anisotropic plates. We will also solve a specific problem.

Problems of electromagnetoelasticity for a half-plane and a strip with holes and cracks

“…To satisfy the boundary conditions accurately, we varied the number of terms in series (9) and the number of points on the boundary of the hole and on the collocation segments of the straight-line boundaries. The collocation segment was selected so that its center was at the point of the straight-line boundary nearest to the hole.…”

“…The dependence of the EMES on the geometrical parameters of a strip with a circular hole or a crack is analyzed Introduction. In the recent decades, the electromagnetoelastic state (EMES) of piezomaterials in various electric and magnetic fields has been studied intensively [1,[9][10][11][12][13][14][15][16]. The fundamentals of electro-and magnetoelasticity and solutions of partial problems are discussed in [1, 10].…”

Plane problem of thermoelectromagnetoelasticity for multiply connected bodies

“…Efficient methods based on generalized complex potentials are proposed in [3,4,16], where either electric or magnetic properties were taken into account and thermal effects neglected. These methods were used in [6,7] to solve thermoelectroelastic and thermomagnetoelastic problems.…”

Thermoelastic bending of locally heated orthotropic shells

“…The effect of local mechanical loading on the stress distribution in anisotropic shells of revolution was examined in [14,19]. The localization of stresses in anisotropic plates due to inclusions was studied in [16,17]. Some general approaches to boundary-value problems of thermomechanics and thermoelasticity are addressed in [14,18].…”