【作者】 李银山； 霍树浩； 韩旭； 李欣业；

【Author】 LI Yin-shan;HUO Shu-hao;HAN Xu;LI Yin-ye;Department of Mechanics,School of Mechanical Engineering,Hebei University of Technology;

【机构】 河北工业大学机械工程学院力学系；

【摘要】 对于多跨超静定梁影响线,常用的方法无法求得解析解。提出了一种快速求解多跨超静定梁解析解的连续分段独立一体化积分法。该方法首先将梁进行连续分段,建立一种移动载荷下梁求解的通用力学模型,从该模型推导出任一截面的具有四阶导数的挠度微分方程。然后独立积分四次,得到挠度的通解。再根据边界条件和连续性条件确定积分常数。用Maple语言开发出相应的求解解析解程序,实现了对移动载荷下多跨超静定梁影响线解析解的计算机求解。在多跨超静定梁模型建立和求解推导过程中,不需进行梁结构的简化,工程实例表明,连续分段独立一体化积分法编程程式化,可以得到一体化解析解,不仅适用于静定梁影响线,而且适用于超静定梁影响线。更多还原

【Abstract】 For an influence line of a multi-span statically indeterminate beam, it is unable to obtain the analytical solution by the common methods. A continuous subsection independently systematic integral method(CSISIM for short) is presented for fast determination influence lines of analytical solution of multi-span statically indeterminate beams. In CSISIM, the framework is separated into segments series firstly. The general mechanical model is established for solution of beams under moving loads. The forth-order differential deflection equation of any cross section is derived from the model. Then the general solutions of the deflection are obtained independently by forth-fold integration. Integral constants are determined by boundary conditions, force conditions and continuity conditions. The solution procedure is developed with Maple language to determine the corresponding analytical solution. It realizes analytical solution by computer for influence lines of multi-span statically indeterminate beams. It does not need to simplify loads and framework during establishing model of the multi-span statically indeterminate beams and its process of derivation.The engineering example shows that, CSISIM is suitable for computer programming and it can get systematic analytic solution. The way to solve influence line is not only suitable for statically determinate framework, but also suitable for statically indeterminate ones.更多还原