In order to achieve highly accurate and efficient numerical calculations of structural dynamics, time collocation method is presented. For a given time interval, the numerical solution of the method is approximated by...In order to achieve highly accurate and efficient numerical calculations of structural dynamics, time collocation method is presented. For a given time interval, the numerical solution of the method is approximated by a polynomial. The polynomial coefficients are evaluated by solving algebraic equation. Once the polynomial coefficients are evaluated, the numerical solutions at any time in the interval can be easily calculated. New formulae are derived for the polynomial coefficients,which are more practical and succinct than those previously given. Two structural dynamic equations are calculated by the proposed method. The numerical solutions are compared with the traditional fourth-order Runge-Kutta method. The results show that the method proposed is highly accurate and computationally efficient. In addition, an important advantage of the method is the simplicity in software programming.展开更多
基金Supported by Liu Hui Applied Mathematics Center of Nankai University-Tianjin University( No. H10124).
文摘In order to achieve highly accurate and efficient numerical calculations of structural dynamics, time collocation method is presented. For a given time interval, the numerical solution of the method is approximated by a polynomial. The polynomial coefficients are evaluated by solving algebraic equation. Once the polynomial coefficients are evaluated, the numerical solutions at any time in the interval can be easily calculated. New formulae are derived for the polynomial coefficients,which are more practical and succinct than those previously given. Two structural dynamic equations are calculated by the proposed method. The numerical solutions are compared with the traditional fourth-order Runge-Kutta method. The results show that the method proposed is highly accurate and computationally efficient. In addition, an important advantage of the method is the simplicity in software programming.
