文献类型：期刊文献

中文题名：求解变截面梁变形的快速解析法

英文题名：A FAST ANALYTICAL METHOD FOR THE DEFORMATION OF BEAMS WITH VARYING CROSS-SECTIONS

作者：李银山[1];官云龙[1];李彤[2];李欣业[1]

机构：[1]河北工业大学力学系,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

年份：2015

卷号：32

期号：S1

起止页码：116

中文期刊名：工程力学

外文期刊名：Engineering Mechanics

收录：CSTPCD;;EI(收录号：20153001050686);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：复杂载荷;变刚度梁;快速解析法;分段独立积分;程序化求解

外文关键词：complex load;;variable stiffness beam;;fast analytical method;;subsection independently;;computerized solution

摘要：对于有复杂载荷的变刚度梁,常用的方法无法求得解析解。该文提出了一种快速求解变截面梁变形解析解的连续分段独立一体化积分法。该法首先将梁进行连续分段,建立一种复杂载荷下变刚度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曲线微分方程。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。在连续曲线形变截面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,直接用符号运算软件编制对梁变形求解解析解的程序,实现了对复杂载荷变刚度梁解析解的计算机求解。该文采用连续分段独立一体化积分法求得了阶梯形变截面梁、等高变宽变截面梁和等宽变高变截面梁等三个工程实例的解析解。工程实例表明,该方法建立数学模型简单,计算编程程式化,可以快速求得解析解。
For beams with varying stiffness and complex loads, the common method is unable to obtain analytic solutions. A continuous subsection independently systematic integral method(CSISIM for short) is presented for fast determination of analytical solutions of the deformation of beams with varying sections. In CSISIM, the beam is first separated into segments. A general mechanical model is established for solution of beams with varying stiffness under complex 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 four-fold integration.Integral constants are determined from the boundary conditions and continuity conditions. It is not necessary to simplify loading and beam structure when establishing a model of continuous curved variable cross-section beam and processing the derivation. The beam deformation analytical solution procedure is programed directly by using symbolic computation software. It realizes an analytic solution by computer for beams with varying stiffness under complex loads. In this paper, there are three engineering examples-a stepped beam, a uniform depth variable width cross-section beam, and a uniform width variable height cross-section beam. Their analytical solutions are obtained by CSISIM. The engineering examples show that it is simple to establish mathematical models using this method. Calculation programming is systematic. Analytical solution can be quickly obtained.