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中文摘要：
在计算移动荷载过桥问题中广泛使用的Newmark方法必须在每一时间步内限制荷载的大小和作用位置都不能改变。精细积分法虽然允许荷载的大小在每一时间步长内发生变化，但是仍假定其作用位置是不变的，未能采取措施以描述荷载沿着桥面的连续移动性。本文提出三种精细积分格式，在每一时间步内不但允许移动荷载的大小按简谐规律连续变化，而且模拟了简谐荷载在空间域的连续移动。通过与Newmark方法和简单问题的解析解进行数值比较，表明用本文提出的方法可以用较粗的结构单元和较大的时闻步长而获得很高的计算精度。在精度相同的前提下，计算效率比Newmark方法可提高1～2个数量级。
英文摘要：
Precise integration method has been widely used and proved quite effective. So far, however, the loads have been assumed to exert on fix points within each time step. That can not reflect the moving property of moving loads within each time step. For the well known Newmark method, not only such moving property can not be reflected, but also the applied forces must be regarded as constants. These assumptions have restricted the precision and efficiency of these methods in dealing with problems of moving variable loads passing through bridges, particularly for high frequency load components. In the present paper, the precise integration method is developed so that the above assumptions have both been removed. Numerical results show that the proposed method is very efficient. Typically, for high frequency moving loads, only a few percentages of computational efforts are required in comparison with that when Newmark method is used.
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