Precise Integration Method For Dynamic Time History Analysis Of Building Structure With Base Isolation

Earthquake disaster is a serious threat to life property and safety of human. The strength and elasticity of structure member has been used in traditional elastoplastic seismic design method of plastic deformation. This can ensure the personal safety but fail to meet actual project needs. Therefore, the applications of grid beam emerged for this requirement. Isolation layer is used to set isolation layer in the top and bottom of the base structure into two divided parts, which are the upper structure and the foundation. For recent years, the application of grid beam system has been analyzed and calculated by the scholars all over the world. It is shows that the acceleration response in seismic structure will be greatly reduced, even to a slight level under appropriate stiffness and damping during the design process of the structure. Because of its simplicity, low cost and good damping effect, isolation structure has become the new trend of building structure seismic development in the new century. So it’s significantly necessary to do the dynamic analysis to the structure of base seismic isolation system. In this paper, we deploy dynamic time history analysis method to study the changing process of applicated laminated rubber frame structure and shear wall structure under the action of frequent earthquake based on the Hamiltonian theory. We use shear model to calculate the layer anti push rigidity, then derive the stiffness matrix of the whole structure according to the motion equation of relationship between middle floor and its up-down floors in the process of the earthquake.We use parallel Timoshenko beam model to analyze frame shear wall structure. Adding up the shear deformation and bending deformation under the action of earthquake, the stiffness matrix of the layer unit is derived according to Hamiltonian system and the precise integration method.The application of finite element method deduces super structure integral stiffness matrix.The motion equation between vibrating up-down parts and isolation layer according the D’Alembert’s principle. Then we use the numerical method of substitution to merge these two equations into one. Finally, for one single engineering example, we deploy the precise integration method and MATLAB programming to do dynamic time history analysis and obtain high precision seismic responses value. It is showed that, structure displacement, velocity and acceleration of the base isolated structure are significantly reduced compared with the traditional node and the damping function is very effective. In a word, this research has practical significance to the aseismic engineering.