The exact solution is found to the three-dimensional electroelastic problem for a transversely isotropic piezoceramic body with a spheroidal cavity. The solutions of static electroelastic problems are represented in terms of harmonic functions. The case of stretching the piezoceramic medium at a right angle to the spheroid axis of symmetry is analyzed numerically. The dependence of the stress concentration factor on the geometry of the spheroid and the electromechanical characteristics of the material is studied.Piezoceramic materials are widely used in various industries. Structural members made of such materials may contain voids, inclusions, delaminations, and other defects, which are detrimental to mechanical and electric strength. This is the reason why the stress-strain state of piezoceramic bodies needs further analysis.The authors of [1-3, 7-11, etc.] studied the stress concentration near different types of heterogeneities. The papers [1, 7] set forth a method of solving three-dimensional electroelastic problems for a piezoceramic layer. There, boundary-value problems were reduced to systems of singular integro-differential equations solved using mechanical quadratures. The paper [6] studies the axisymmetric electroelastic field near a spheroidal cavity in a piezoceramic body and uses the general electroelastic solution expressed in terms of harmonic functions [5]. Nonaxisymmetric problems for such bodies have not yet been investigated because of severe mathematical difficulties.In the present paper, we will solve the general electroelastic problem for a piezoceramic body with a spheroidal cavity. The solution will be used to study the stress concentration near the cavity in the case where the piezoceramic medium is stretched at a right angle to the spheroid axis of symmetry.
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