Clarification of Faber series and related applications to complex variable methods in two-dimensional elasticity

Faber series are used extensively in the application of complex variable methods to two-dimensional elasticity theory, for example, mechanical analysis composite materials where representations potentials lead convenient expressions corresponding displacement and stress distributions. In many cases, use is combined with conformal mapping techniques which “transfer” a boundary value problem defined elastic body (physical plane) simpler posed an imaginary plane characterized by mapping. several instances literature, however, little attention has been paid domain definition leading often misunderstandings erroneous conclusions regarding concept feasibility series. this paper, we present thorough rigorous examination representation both physical (occupied material) (defined mapping) plane. addition, show that replacing truncated Taylor does not induce any additional errors numerical problem. We anticipate discussion paper will help clarify existing misinterpretations further extend their range problems mechanics.