大刚度法在结构动力分析中的应用、误差分析与改进

ERROR ANALYSIS AND IMPROVEMENTS OF LARGE SPRING/STIFFNESS METHOD FOR STRUCTURAL DYNAMIC RESPONSE ANALYSIS

为检验大刚度法(LSM)的计算精度,以2自由度有限元模型为例,采用瑞利阻尼假设,分别基于一致激励和多点激励情形,输入4组地震动位移,分析了结构的地震反应并与传统理论方法结果做了对比。从理论上分析了LSM误差产生的原因,指出了它的适用条件,分别提出了适用于一致激励和多点激励的改进方法——基于地震动位移阻尼项修正的改进LSM,验证了它们的计算精度。并分析了阻尼系数对LSM和改进LSM的影响。结果表明:采用瑞利阻尼时,理论上LSM不适用于结构地震反应分析;一致激励分析时,LSM的误差与瑞利阻尼的质量相关系数α及刚度相关系数β都有关系,而多点激励分析时误差只与刚度相关系数β密切相关;阻尼系数越大,LSM误差越大,而改进LSM误差很小且表现稳定;改进的LSM可较大幅度提高计算精度,与传统理论方法结果符合精度高。

To verify the practical applicability and accuracy of the large spring/stiffness method （LSM）, the dynamic responses of a two-degree-freedom （2DOF） finite element model using the Rayleigh damping assumption are performed respectively according to the LSM and traditional theoretical methods under four groups of seismic ground motion excitations. The origin of errors and the applicability of the LSM are discussed. Then the improved LSM application to a uniform excitation and a non-uniform excitation are respectively presented herein, based on the modification of ground displacements considering the influences of Rayleigh damping. It indicates that the LSM is inapplicable to the structural seismic response analysis in the case of Rayleigh damping theoretically. And the errors depend on the damping coefficients a and β in the ease of the uniform seismic excitation and on the coefficient β in the case of the non-uniform seismic excitation respectively. The errors increase monotonously with the aggrandizement of the damping coefficient β. It is also validated that the improved LSM is able to yield results that are identical to those of traditional theoretical methods.