Matrix Method for Linear Response of Structures

by Gordon B. J. Mah,

Serial Information: Journal of the Engineering Mechanics Division, 1969, Vol. 95, Issue 5, Pg. 1101-1124

Document Type: Journal Paper


In solving the differential matrix equation which describes the motion of the structure, Taylor's series expansion is used to evaluate the solution step-by-step. In addition, two important techniques are developed to facilitate the calculation. The first one is the application of recurrence equations to save lots of computations. The second one is a scheme which can afford the step-by-step integration with large time-steps. In the existing numerical integration methods, the time-steps are necessary to be kept below certain limit to insure the stability of the solution. However, in the proposed method, the time-steps can be much larger than that limit and still produce a stable solution. The present method is also applicable to the evaluation of the dynamic response of elastic continuums with the accompaniment of the finite difference or the finite element methods.

Subject Headings: Finite element method | Linear functions | Structural response | Finite difference method | Matrix (mathematics) | Differential equations | Equations of motion | Computing in civil engineering

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