Based on the fact that the development of nonlinear solid mechanics has been closely integrated with the material microstructure, it derived the vertical stress satisfying the harmonic function at any point from the super-elastic constitutive equation of the rubber; further, the uniaxial equivalent elastic modulus
E_\rm c
and the pure bending equivalent bending stiffness
E_\rm cI_\rm s
of the single-layer rubber were obtained from the vertical stress integration. The seismic isolation rubber bearing was equivalent to a homogeneous body conforming to
E_\rm c and
E_\rm cI_\rm s, and the partial differential equilibrium equation macroscopically reflecting the degree of shear and bending deformation of the rubber bearing was established in the simultaneous action of two external load, and its general solution was obtained. The difficulties of the geometrical non-uniformity of large shear deformation of rubber support were solved in the vertical and horizontal loads. On this basis, a full-scale seismic isolation test of rubber bearing for compression and shear experiment was carried out. According to the experimental shear modulus
G
and horizontal shear strain
\gamma
curves, the experimental curves of the horizontal thrust
F_\rm H
and
\gamma 
of the bearing were obtained. It was almost completely overlapped with the theoretical curve. Therefore by introducing the material nonlinearity into the above differential equilibrium equation, the double nonlinear problem of large shear deformation of the superelastic rubber bearing was solved. Through the above answers, the internal force distribution law of the rubber bearing was obtained, which has a clear guiding significance for judging the weak part of the bearing. Subsequently, the comparative analysis of two more important characteristics (shear strain correlation and axial pressure correlation) of the rubber bearing was carried out, the results showed that as the axial force increased, the
P-
Δ effect of the rubber bearing was not obvious, but the change of internal stress in the rubber couldn't be ignored, Concurrently, the greater the shear strain was, the stronger the pressure dependence was. The horizontal thrust and displacement of the support can be obtained through the sensor monitoring the internal stress of the support, achieving the health monitoring of the isolated building during the earthquake.
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