Numerical Method for Structural Shock Response

by G. J. O'Hara,
P. F. Cuniff,


Serial Information: Journal of the Engineering Mechanics Division, 1964, Vol. 90, Issue 2, Pg. 51-82


Document Type: Journal Paper

Abstract: Numerical integration equations are derived for determining the response of nonlinear structures subjected to transient loads. The numerical method consists of approximating the nonlinear variables and the forcing functions in the differential equation of motion over a short interval of time by their mean value, by a straight line, or by a segment of a parabola. This allows for Duhamel integral-type solutions for the nonlinear terms. A step solution follows that uses an iteration method during each increment of the solution. The sufficient condition for the convergance of the iteration method is presented for the case of a finite number of numerical equations. Example problems of a one-degree-of-freedom system and a two-degree-of-freedom system are solved by the numerical integration equation, and the solutions are compared with response curves obtained from analog computers at the U. S. Naval Research Laboratory.

Subject Headings: Numerical methods | Structural response | Transient loads | Equations of motion | Degrees of freedom | Nonlinear response | Load factors | Nonlinear analysis

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