Steel shim stresses in multilayer bearings under compression and bending

Solutions are given for the tensile stresses in the steel reinforcing shims of elastomeric isolators. The method makes use of generalized plane stress and uses a stress function approach, treating the shim as a thin plate with body forces generated by surface shears on the top and bottom of the plate. It is shown that the pressure in the rubber acts as a potential for these body forces. The solutions are applicable to low and moderate shape factor bearings where it is acceptable to assume that the elastomer is incompressible, and also to the more common current situation when the shape factor is so large that the compressibility of the rubber must be included. The stress state in the steel reinforcing plates is calculated for both pure compression of the bearing and for when the bearing is loaded by a bending moment. These two cases, separately and in combination, are the typical situation in current practice. While a solution for the stress state in the shims of a circular isolator, assuming incompressibility and under pure compression, has been available using an analogy with the stresses in a rotating circular plate, the use of the stress function method is new and suggests a method to extend the solutions to other shapes of isolator other than circular. The solutions for pure compression, including compressibility of the rubber, and the solutions for bending, both incompressible and compressible, are entirely new. 1.