Abstract :
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
