Response Computation using Truncated Taylor Series

by Joseph E. Grant, (A.M.ASCE), Member of the Technical Staff; Sandia Labs., Livermore, CA,

Serial Information: Journal of the Engineering Mechanics Division, 1971, Vol. 97, Issue 2, Pg. 295-304

Document Type: Journal Paper


A numerical integration technique is presented that allows the user to integrate large systems of second-order differential equations with a truncated Taylor series. It is shown that by the addition of a fictitious damping term, the numerical instabilities that result when integrating the equation-of-motion directly are eliminated and the resulting integration is the dynamic response of the mechanical system. The stability criterion is derived and the accuracy of the method judged.

Subject Headings: Numerical methods | Computing in civil engineering | Integrated systems | Differential equations | Damping | Dynamic response | Mechanical systems

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