复杂载荷下多层刚架的快速解析求解  

A FAST ANALYTICAL SOLUTION FOR MULTI-STORY FRAMES UNDER COMPLICATED LOADS

作　　者：李银山[1] 孙凯[1] 贾佩星 李彤[3] 

机构地区：[1]河北工业大学机械工程学院力学系,天津300130 [2]天津商业大学机械工程学院,天津300134 [3]华东理工大学承压系统与安全教育部重点实验室,上海200237

出　　处：《工程力学》2017年第B06期11-18,共8页Engineering Mechanics

基　　金：国家自然科学基金项目(10632040)

摘　　要：对于有复杂载荷的多层刚架,常用的方法无法求得解析解。提出了一种快速求解多层刚架解析解的连续分段独立一体化积分法。该方法首先将刚架进行连续分段,建立一种复杂载荷下刚架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、力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,实现了对复杂载荷多层刚架解析解的计算机求解。在多层刚架模型建立和求解推导过程中,不需进行载荷和刚架结构的简化,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,不仅适用于静定刚架,而且适用于超静定刚架。For multi-story frames under complicated loads, it is unable to obtain an analytical solution by common methods. A continuous subsection independent systematic integral method （CSISIM） is presented for fast determination of analytical solutions of multi-story frames. In CSISIM, a frame is separated into a series of segments firstly. The general mechanical model is established for solutions of frames under complicated loads. A forth-order differential deflection equation of any cross section is derived from the model. Then the general solutions of 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 enables analytical solution by computer for multi-story frames under complicated loads. It is not necessary to simplify loads or frames during establishing the model of multi-story frames and its process of derivation. Engineering examples show that CSISIM is suitable for computer programming and it can get systematic analytical solutions. It is not only suitable for statically determinate frames, but also suitable for statically indeterminate ones.

关 键 词：多层刚架 超静定 解析法 快速求解 一体化解法 

分 类 号：TU311.4[建筑科学—结构工程] TU311.1