力学与实践 ›› 2020, Vol. 42 ›› Issue (6): 788-793.DOI: 10.6052/1000-0879-20-386

• 教育研究 • 上一篇    下一篇

复杂载荷作用下梁的弯曲变形微分求积法求解1)

葛仁余2), 吕良伟, 朱浩杰, 聂子龙, 张金轮   

  1. 安徽工程大学建筑工程学院,安徽芜湖 241000
  • 收稿日期:2020-09-09 修回日期:2020-10-07 出版日期:2020-12-20 发布日期:2020-12-20
  • 通讯作者: 2) 葛仁余,教授,从事计算固体力学教学、科研工作。E-mail: gerenyu@sina.com
  • 基金资助:
    1) 国家级大学生创新创业训练计划(201910363089),安徽省自然科学基金(1808085ME147),安徽工程大学校级本科教学质量提升计划 (2019jyxm16) 和安徽省教学质量工程研究项目(2017jyxm0319) 资助。

DIFFERENTIAL QUADR ATURE METHOD FOR SOLVING BENDING DEFOR MATION PROBLEMS OF BEAMS UNDER COMPLEX LOADS1)

GE Renyu2), LU Liangwei, ZHU Haojie, NIE Zilong, ZHANG Jinlun   

  1. School of Architecture and Civil Engineering, Anhui Polytechnic University, Wuhu 241000, Anhui, China
  • Received:2020-09-09 Revised:2020-10-07 Online:2020-12-20 Published:2020-12-20

摘要: 在课堂教学中,梁上作用较多复杂载荷时,需要分段建立载荷方程,耗费在积分运算和积分常数确定方面的工作量很大,尤其分布载荷为非线性表达式时,积分运算过程繁琐冗长。本文采用微分求积法求解梁的弯曲变形,并将求解过程程序化。首先,基于微分求积法基本原理,将梁的载荷方程转化为一组线性代数方程,再由高斯主元消去法求解该代数方程组,获得梁的挠度和转角正确解。论文通过3个教学实例,验证了微分求积法求解梁的弯曲变形的可行性和精确性。

关键词: 弯曲变形, 教学研究, 复杂载荷, 微分求积法, 编程计算

Abstract: In the classroom teaching, when there are complex loads acting on the beam, it is necessary to establish the load equation by sections, with a large amount of work in the integral calculation and the integral constant determination, especially when the distributed load is expressed in a nonlinear form, the integral operation becomes tedious. In this paper, the differential quadrature method is used to solve the bending deformation problems of beams, and the solving process is programmed. Firstly, based on the basic principle of the differential quadrature method, the load equation of the beam is transformed into a set of linear algebraic equations, and then the algebraic equations are solved by the Gaussian principal element elimination method to obtain the correct solutions of the deflection and the rotation angle of the beam. Through three teaching examples, the feasibility and the accuracy of the differential quadrature method for solving bending deformation problems of beam are verified.

Key words: bending deformation, teaching research, complex load, differential quadrature method, programming calculation

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