AN UNCONDITIONALLY STABLE CALCULATION SCHEME FOR THE DYNAMIC RESPONSE OF STRUCTURES BY THE METHOD OF SPLINE COLLOCATION

作     者：Lin Wenjing Xu Cida, Department of Engineering Mechanics, Tongji University, Shanghai 

作者机构：Department of Engineering Mechanics Tongji University Shanghai 

出 版 物：《Acta Mechanica Sinica》 (力学学报(英文版))

年 卷 期：1988年第4卷第2期

页      面：156-164页

主　　题：dynamic response spline function calculation scheme 

摘      要：In this paper, by the method of collocation, using the cubic B-spline function as the trialfunction in the time domain and putting zero residuals of the differential equation of motion of thestructure at two points of time, the authors obtain an unconditionally stable calculation scheme for thedynamic response of the structure. When a parameter θ in the scheme is within the interval 0.15 θ 0.5 the scheme is absolutely stable. It is shown that the accuracy of the scheme, as may be measuredby AD (the decay of the amplitudes), PE (the elongation of periods) and the algorithmic dampingratio, is better than that of traditional methods——the Wilson-θ’s method, the Newmark’s methodand the Houbolt’s method. A numerical example is given in which a certain dynamic response problemis solved by the method of this paper and results are compared with that of the traditional methods andthe analytic method showing that the accuracy of the method by this paper is superior to the otherones. The computational scheme for the dynamic response of structures by this paper may be regardedas an effective, convenient and accurate method for dynamic response of structures.