Application of a Collocation Method Based on Moving Least Squares Interpolation in Structural Dynamic Analysis

摘要

In this paper the weighted residuals method based on moving least squares interpolation was applied in structural dynamic analysis. The length of time was divided into an appropriate number of segments, and least squares point collocation method was used in each segments in order to obtain the coefficients in trial function. A step-by-step formula for calculating the coefficients in each segment was gained, and therefore the structural dynamic response can be obtained. The formula is unconditional stabilized and time-saving. Vibration systems of a mass point and a simply supported square plate were as two examples analyzed by this method, and the results were compared with theoretical results and Newmark's method, which had indicated that the weighted residuals method was very simple to use and also had a high accuracy when the time segment is less than a quarter of period of vibration.