A new formulation for the analysis of elastic layers bonded to rigid surfaces

Elastic layers bonded to rigid surfaces have widely been used in many engineering applications. It is commonly accepted that while the bonded surfaces slightly influence the shear behavior of the layer, they can cause drastic changes on its compressive and bending behavior. Most of the earlier studies on this subject have been based on assumed displacement fields with assumed stress distributions, which usually lead to ‘‘average’’ solutions. These assumptions have somehow hindered the comprehensive study of stress/displacement distributions over the entire layer. In addition, the effects of geometric and material properties on the layer behavior could not be investigated thoroughly. In this study, a new formulation based on a modified Galerkin method developed by Mengi [Mengi, Y., 1980. A new approach for developing dynamic theories for structural elements. Part 1: Application to thermoelastic plates. International Journal of Solids and Structures 16, 1155–1168] is presented for the analysis of bonded elastic layers under their three basic deformation modes; namely, uniform compression, pure bending and apparent shear. For each mode, reduced governing equations are derived for a layer of arbitrary shape. The applications of the formulation are then exemplified by solving the governing equations for an infinite-strip-shaped layer. Closed form expressions are obtained for displacement/ stress distributions and effective compression, bending and apparent shear moduli. The effects of shape factor and Poisson s ratio on the layer behavior are also investigated.