Uniform asymptotic formulae for Green's tensors inelastic singularly perturbed domains with multiple inclusions
Michael J. Nieves, V. G. Maz, A. B. Movchan · 2006
We present uniform asymptotic approximations of Green’s kernels for boundary value problems of elasticity in singularly perturbed domains containing small holes. We consider the case of an isotropic Lam e operator with the Dirichlet boundary conditions for two and three dimensions, in addition we shall also study the situation of anti-plane shear. The main feature of the asymptotic approximations mentioned is their uniformity with respect to the independent spatial variables. We also oer examples, where results of asymptotic approximations are compared with independent accurate numerical simulations, and demonstrate the superior features of the asymptotic method. The motivation for the talk, came from the asymptotic formulae derived