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Spline approximations for direct integration of structural dynamics
Author(s) -
Liao ChingLung,
Wang HungChih
Publication year - 1988
Publication title -
earthquake engineering and structural dynamics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.218
H-Index - 127
eISSN - 1096-9845
pISSN - 0098-8847
DOI - 10.1002/eqe.4290160604
Subject(s) - spline (mechanical) , nodal , discretization , mathematics , cardinal point , thin plate spline , m spline , algorithm , mathematical analysis , spline interpolation , engineering , structural engineering , statistics , physics , medicine , optics , bilinear interpolation , anatomy
The application of spline functions in the analysis of structural dynamics is presented in this paper. The nodal points in time discretization for determining the spline curve can be separated into two classes: the p nodal points before the current time (including current time) and the q nodal points after the current time. On the p nodal points, the structural responses were calculated at previous time steps. The q nodal points represent the unknown structural response at future time steps which should meet the requirement of dynamic equilibrium. By a trial and error procedure, at least 16 families of spline curves with different locations of p and q nodal points can be found to meet the requirements of unconditional stability. The accuracy of each family is dependent on the order of the spline and the locations of the nodal points. The 16 families of spline curves supply a wide range of accuracy that can be selected easily. It can be shown that the well‐known Wilson‐method and the Houbolt method are special cases of the present spline approximations.