An Inclusion Of Arbitrary Shape In An Infinite Or Semi-infinite Isotropic Multilayered Plate - Wang, Xu (2016)
This paper proposes a simple method based on analytical continuation and conformal mapping to obtain an analytic solution for a two-dimensional arbitrarily shaped Eshelby inclusion with uniform main plane eigenstrains and eigencurvatures in an infinite or semi-infinite isotropic laminated plate. The main plane of the plate is chosen in such a way that the in-plane displacements and out-of-plane deflection on the main plane are decoupled in the equilibrium equations. Consequently, the complex potential formalism for the isotropic laminate can be readily and elegantly established. One remarkable feature of the present method is that simple elementary expressions can be obtained for the internal elastic field within the inclusion of any shape in an infinite laminated plate. Several examples are presented to illustrate the general method.