文献类型：期刊文献

中文题名：复杂载荷下变刚度超静定梁快速解析求解

英文题名：A FAST ANALYTICAL SOLUTION FOR STATICALLY INDETERMINATE BEAM OF VARIABLE STIFFNESS UNDER COMPLICATED LOAD

作者：李银山[1];韦炳威[1];李彤[2];贾佩星[3]

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

年份：2016

卷号：33

期号：B06

起止页码：33

中文期刊名：工程力学

外文期刊名：Engineering Mechanics

收录：CSTPCD;;EI(收录号：20162702564101);Scopus;北大核心:【北大核心2014】；CSCD:【CSCD2015_2016】；

基金：国家自然科学基金项目(10632040)

语种：中文

中文关键词：变刚度;超静定;解析法;快速求解;一体化解法

外文关键词：variable stiffness; statically indeterminate; analytical solution; fast determination; systematic method

摘要：采用连续分段独立一体化积分法求解了复杂载荷下变刚度超静定梁的弯曲变形问题。该方法首先将梁进行连续分段,建立复杂载荷下变刚度梁的通用力学模型,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;编写了相应数学模型的求解解析解程序。在连续曲线形变刚度超静定梁模型建立和求解推导过程中,不需进行载荷和梁结构的简化。采用该方法求解了阶梯截面超静定梁,惯性矩按坐标平方规律变化超静定梁和惯性矩按坐标四次方规律变化超静定梁等三个工程实例的解析解。结果表明,连续分段独立一体化积分法编程程式化,与有限元法相比,其优越性是可以快速得到一体化的弯曲变形解析解。
For statically indeterminate beams of variable stiffness under complicated load, a continuous subsection independently systematic integral method （CSISIM） is presented for fast determination of the analytical solutions of deformation. In CSISIM, the beam is first separated into segments series. The general mechanical model is established for variable stiffness beams under complicated load. The forth-order differential deflection equation of any cross section is derived from the model. Then the general solutions of beam deflection are obtained independently by forth-fold integration. Integral constants are determined by boundary conditions and continuity conditions. The solution procedure is developed for the corresponding mathematical model. It does not need to simplify loads and beam structure during establishing the model of the continuous curve shaped variable stiffness beam and its process of derivation. This method is used to give the analytic solutions of three engineering examples of statically indeterminate beams including beams of stepped cross sections, beams of inertia moment varied quadratically and beams of inertia moment varied by the fourth power. The results show that the CSISIM is suitable for computer programming. Compared with the finite element method, the advantage of the method is that it can quickly get the analytical solution of bending deformation.