Elastic equilibrium of a medium containing a finite number of aligned spheroidal inclusions

strict solution in series is obtained of the elasticity theory problem for an unbounded domain containing some aligned spheroidal inhomogeneities under uniform far-field loads. The essence of the method used is the representation of the displacement field in a multiply-connected domain as a sum of general solutions for corresponding single-connected domains. Each term of this sum, in turn, is expanded into series on vectorial partial solutions of Lame’s equation in a local spheroidal basis. In order to satisfy exactly all interfacial boundary conditions, the re-expansion formulae (addition theorems) for external partial solutions are used. As a result, the primary boundary-value problem of elasticity theory is reduced to an infinite set of linear algebraic equations. The convergence rate of the proposed solution procedure is evaluated numerically. Some numerical results demonstrating the influence on stress distribution of material properties, spatial position of inclusions and external load are presented