End effects in anti-plane shear for an inhomogeneous isotropic linearly elastic semi-infinite strip
The equation \(\text{div}(A\nabla u)=0\) is studied under zero Dirichlet boundary conditions in the strip \(0<x_2 <h,\) \(x_1 >0\), where \(u\) is the shear displacement in the direction \(x_1\) of an inhomogeneous elastic body. It is assumed that \(A_{12}= A_{21}=0\), and \(A_{11} = A_{22}=\mu\). By setting \(w=\mu ^{1/2}u,\) the equation is reduced to the form \(\Delta w + Fw=0\), and the estimate \(|w|\leq k_1 \text{exp}(-k_2 x_1)\) is derived. Optimality of this estimate is discussed.
scientific article; zbMATH DE number 1330600