Analytical solution for compression stiffness of bonded rectangular layers

Abstract

It is well known that the compression stiffness of bonded layers increases due to the restricted lateral expansion if Poisson's ratio is near 0.5. While analytical solutions have previously been obtained for circular, infinite-strip and square shapes, this paper presents the first analytical attempt for bonded rectangular layers. On the basis of two kinematic assumptions and by means of variable transformation, the governing equations are derived. The double series approach provides a direct means of computation with second-order convergence. The solutions agree well with the published results for special cases of square layers and infinite strips, and with finite element results for rectangular layers. Besides illustrating the importance of including the compressibility effect, the numerical study shows that the effect of length-to-width ratio is significant on the effective compression modulus of rectangular pads.