Elastic/piezoelectric solids with electro-mechanical singular surfaces

摘要

When a tensor-valued function $varvec{sigma (x)}$ is continuous in regions Σ0 and Σ1, but has a finite jump across the interface Γ01 between Σ0 and Σ1, then Γ01 is referred to as singular surface relative to the field $varvec{sigma (x)}$ . In this paper, it is intended to give a general treatment of three-dimensional static and free vibration analysis of bodies composed of multi-phase elastic and/or piezoelectric bodies with electro-mechanical singular surfaces. The geometry of the medium, boundary conditions, and the geometry of the singular surfaces may be arbitrary. The displacement field and the electric potential in each region are expressed in terms of functions composed of 3-D series and special 3-D functions. The composite functions are selected in such a way that they satisfy exactly: (1) the continuity of the displacement and the electric potential across the singular surfaces; and (2) the homogeneous and inhomogeneous kinematical boundary conditions. This methodology leads to remarkable accuracies in computation of the field quantities, including the quantities, which are discontinuous across the singular surfaces. Taking advantage of any symmetry that may be present in the problem, will substantially increase the convergence rate. For illustrations several examples are examined. Comparisons with the exact solutions, whenever available, established the remarkable accuracy and robustness of the present methodology.