Aspects of the nonlinear analysis of elastomeric seismic isolators.

摘要

Isolation bearings consist of alternate layers of rubber bonded to thin metal plates and are used to effectively isolate structures from the damaging horizontal components of earthquakes. Their effectiveness is due to the low shear modulus of rubber compared to the extremely high value of the bulk modulus and to the energy dissipating internal mechanisms of the material.; Conventional analyses of isolation bearings are linear elastic and assume that the metal plates are rigid. They also rely on the assumption that within each rubber layer the deviatoric part of the normal stresses is negligible compared to the spherical part. In this work a solution is obtained by a displacement method, which involves no a-priori assumptions on the stresses and the "pressure" assumption is verified for thin layers. The approximate solution is formally obtained by using the Hellinger-Reissner variational principle.; The material properties of filled rubber are investigated and a three-dimensional finite strain constitutive model of rubber viscoelasticity is developed within the context of continuum mechanics and internal variables. The short time and cyclic behavior in the frequency range {dollar}10sp{lcub}-2{rcub}{dollar} to {dollar}10sp2{dollar} rad/s, typical of most earthquakes, is of particular interest. In this range the storage modulus and loss factor for vulcanized and unvulcanized natural rubbers vary only slightly with frequency. A fractional derivative model, which agrees well with experimental data in one-dimension, is employed to describe this type of behavior. The model is extended to the non-linear case through the use of a free energy function, consistent with the assumption of an additive stress decomposition motivated by the simple Kelvin model of linear viscoelasticity. A constitutive law for the inelastic part of the stress is provided. Deviatoric and volumetric response is considered and it is assumed that the volumetric response of the material is elastic. The elasticity of rubber is modeled following classical models (e.g. Rivlin, Ogden), extended to include compressibility. Due to the highly confined conditions of rubber in isolation bearings the effect of compressibility is important.; Numerical implementation is considered in a finite element context through a mixed three-field variational principle. Step-by-step integration of the constitutive law is performed and the effect of the number of history terms retained in the analysis is examined in connection with the fading memory property of the material. Simple shear experiments are used to assess the predictive capabilities of the model.