Matrix Method for Linear Response of Structures

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.