On the Poincaré—steklov Operator for an Incompressible Elastic Strip

For an incompressible stratified elastic strip, we consider the Poincaré—Steklov operator that maps normal stresses into normal displacements on a part of the boundary. To construct the transfer function (TF) of this operator, a variational formulation of the boundary value problem for displacement transforms is used. A definition is given and the existence and uniqueness are proved for a generalized solution of the variational problem. This problem is approximated by the finite element method. The leading term of the asymptotic expansion of the TF for small and the three-term asymptotic expansion of the TF for large values of the Fourier transform parameter are obtained. Padé approximations of the obtained asymptotic series are constructed. To reduce computational costs a combined approach to calculating the TF has been developed using its asymptotic expansions and Padé approximations.