Simplified stiffness formulae for elastic layers bonded between rigid plates

An elastic layer bonded between two rigid plates has higher compressive stiffness and tilting stiffness than those of an unbonded layer. This effect has been adopted in the design of reinforced elastomeric bearings. Although compressive stiffness and tilting stiffness of bonded layers can be theoretically derived, some of the theoretical solutions are cumbersome in practical application. In this paper, simplified formulae for compressive stiffness and tilting stiffness of bonded elastic layers of circular, square and infinite-strip shapes are developed from theoretical solutions. Every set of simplified formulae consists of three approximated equations in which each equation has its applicable range of shape factor and bulk modulus. The divisions between the applicable ranges of different approximated equations are also established so that errors of the simplified formulae can be minimized.