直接积分法与精细积分法结合求解结构动力方程

SOLVING STRUCTURAL DYNAMIC EQUATION USING COMBINATION OF THE PRECISE INTEGRATION METHOD AND DIRECT INTEGRATION METHOD

介绍精细积分法与单步Houbolt算法结合的方法,通过引入单步Houbolt算法的基本假设,将加速度分量从动力学方程中消去,动力学方程由二阶常微分方程组变为一阶常微分方程组,然后再用精细积分法进行逐步积分。该方法既利用了单步Houbolt算法的二阶精确和渐近消失的特点,也利用了精细积分高精度的优点,在简化运算量和数值稳定方面效果明显,表明了该方法在结构动力分析中的有效性。

It is presented a method that combines the precise integration method and single step Houbolt method.Introducing the basic assumptions of the single step Houbolt method,the acceleration vector is eliminated from the dynamic equation,and thus,transforming the second order ordinary differential equations to first order ordinary differential equations;then stepwise integration is done by the precise integration method.The method not only has the characteristic of single step Houbolt method,but also possesses of the advantage of high precision.The method is obvious in reducing the computation and numerical stability.The computational examples show the effectiveness of the method.