Tilting Analysis of Rectangular Elastic Layers Bonded between Rigid Plates

A theoretical approach to determine the tilting stiffness of a rectangular elastic layer bonded between two rigid plates is presented. On the basis of two kinematics assumptions, the governing equation for the mean pressure is derived from the equilibrium equations. Using the approximate shear boundary condition, the mean pressure is solved and the tilting stiffness of the bonded rectangular layer is then established in an explicit single-series form. Whereas the finite element method can be applied to calculate the stiffness, the series solution provides a convenient way for parametric studies. Through the obtained pressure expressions, the horizontal displacements are derived from the corresponding equilibrium equations, from which the shear traction on the bonding surface can be found. The error of using the approximate shear boundary condition is negligible for the tilting stiffness, but becomes significant for the horizontal displacements and bonding shear stresses near the edges of the rectangular layers.