Analysis On Isolation Performance Of Single-layer Spherical Reticulated Domes Using Three Dimensional Isolation With Vertical Variable Stiffness

The single-layer spherical reticulated shell is one of the main forms of spatial structures and has been widely used in sports stadiums and exhibition centers.The existing earthquake hazard shows that the reticulated domes will have different degrees of damage under the earthquake,which seriously threatens the safety of people's lives and property.The isolation technology is nowadays mainly used for horizontal isolation which cannot meet the need of isolation for single-layer spherical reticulated shells that have long span and basic period.The strut models for this kind of structures cannot take computational accuracy into account while improving the computational efficiency.Accurate calculation of the response of the structure before and after isolation is the basis of analyzing the isolation performance of the three-dimensional isolated singlelayer spherical reticulated shell.Therefor,It is necessary to further study the three dimensional isolation and hysteretic model of members for a single layer spherical reticulated shell.Based on the research results of three-dimensional isolation system,this paper conducts a series of research on new three-dimensional isolation device,calculated model of isolation device and members of structures and dynamic response of three-dimensional isolation systems.The main research work and conclusions are as follows:(1)A three-dimensional seismic isolation device with variable vertical stiffness for single-layer spherical reticulated shells is developed.The formulas for calculating the stiffness and displacement of the combined hydraulic cylinders in different phase are derived,and the mechanical properties,hysteretic properties and isolation effects of the combined hydraulic cylinders are studied by sinusoidal dynamic test and shaking table test.The results show that the longer vertical isolation period and variable vertical stiffness characteristics can be achieved by changing the type and number of hydraulic cylinders working in different phase.The maximum errors of stiffness at each stage,control threshold and isolation displacement are no more than 4.9%.Under sinusoidal excitation,the vertical hysteretic curve of the device is in good agreement with the design curve.The device has a good isolation effect on the acceleration in the shaking table test for a SDOF system with the average reduction ratio of 41.2%.(2)Numerical model of the three-dimensional seismic isolation system of singlelayer spherical reticulated domes with variable vertical stiffness is established based on beam elements and connector elements.Based on the results of sinusoidal dynamic test and shaking table test,the hysteretic model of combined hydraulic cylinder is established.The theory hysteretic model considering member buckling and global buckling is derived.Empirical parameters are introduced to consider the local buckling and the attenuation of the critical bearing capacity.A highly effective hysteretic model of members is established and verifyed by the test.Based on the Vumat subroutine,the numerical model of three-dimensional isolation system of single-layer spherical reticulated domes with highly efficiency is established.The results show that the hysteretic model can accurately simulate the response of the combined hydraulic cylinder under different working conditions.The errors in simulating the device stiffness,control threshold and support reaction force under sinusoidal tests of different frequencies are not more than 8.3%;the error in simulating the peak acceleration under seismic excitation is not more than 6.9%.The hysteretic model of members can accurately simulate the hysteretic behavior of members with different slenderness ratio,section and the boundary condition.The simulation results of critical forces is less than 3.9%.(3)The isolation performance of three-dimensional isolation single-layer spherical reticulated shells with vertical variable stiffness is analyzed.Single-layer spherical reticulated domes with different form,span and rise to span ratio are established and the responses of superstructures with no isolation,traditional isolation and vertical variable stiffness isolation are calculated.The influence of structure parameters and isolation device parameters on the isolation performance of threedimensional isolation device with vertical variable stiffness is analyzed.Compared with the no variable stiffness three-dimensional isolation device,the vertical variable stiffness three-dimensional isolation device can improve the isolation effects of acceleration internal force less than 5%,but can more effectively limit the vertical isolation displacement and overturning displacement,with an average reduction rate of 35.2% and 40.5%,respectively.Three-dimensional isolation device has good isolation effect for different types of single-layer spherical reticulated shells,and the difference of isolation effects between the maximum acceleration and internal force of different types of single-layer spherical reticulated shells is no more than 14.6%.The influence of span and span ratio on isolation effects of acceleration and internal force is lower than 8% and 32%,respectively.The vertical isolation displacement and overturning displacement increase with the increase of span,the maximum change rate is close to 50%.The influence of the ratio of rise to span on the vertical isolation displacement is less than 21%.The vertical isolation displacement and overturning displacement can be reduced by changing the stiffness ratio and control threshold of the isolation device without significantly changing the isolation effects(less than 7%).(4)The calculation method of maximum vertical isolation displacement considering the influence of horizontal earthquake is established.The coefficient of the overturning moment produced by the horizontal earthquake on the vertical isolation displacement is derived.Based on the nonlinear Newmark method and kinematic equation of the single degree freedom system,the calculation method of maximum vertical isolation displacement considering the influence of horizontal earthquake is established which is validated by the results of whole model with different forms.The influence of span and rise to span ratio on the results are also analysised.The results show that the time history curve of vertical isolation displacement calculated by the single-degree-of-freedom model under vertical earthquake action is consistent with the calculation results by the finite element model.The maximum error is not more than 6.8%.The calculated results of the maximum vertical isolation displacement of superstructures with different form,span and rise to span ratio are safer than those of overall finite element model,and the maximum average error is 15.6%.The influence of span and rise to span ratio on results is small and the average error of the results of the maximum vertical isolation displacement of single-layer spherical reticulated shells with different span and rise to span ratio varis within 12%.