摘要
为了提高结构刚度计算的精度,得到精确的梁转角函数和精度更高的挠度函数,利用链导法则,考虑所有的高阶微量,结合微量关系及几何特性,对梁的弯曲转角函数进行精确推导,揭示了传统近似方法误差的产生原因并利用精确转角函数得到精度更高的挠度函数。利用有限元模拟,进一步验证了精确函数的可靠性。结果表明,精确转角函数求出的转角值符合有限元模拟结果,基于精确转角函数推出的梁位移函数较传统近似挠曲线函数的误差较小。精确转角函数所推得的结果更符合梁的实际转角,更适用于实际工程,同时为进一步得到精确挠度函数提供理论依据;利用相关软件可以快速地得到精确转角函数的计算结果,可促进相关软件求解方法的更新,拥有广泛的应用前景。
In order to improve the accuracy of stiffness calculation and derive an accurate rotation angle function and a more accurate deflection function,bu using the chain rule,considering all the higher-order quantities,and combining the relations of higher-order quantities and geometric characteristics,the rotation angle function of the beam was accurately deduced,and the reason for the error of the traditional approximation method was revealed.Consequently a more accurate deflection function was obtained by using the precise rotation angle function.To further verify the reliability of the precise functions,simulation was performed by the method of finite elements.The results show that the value of the angle of rotation obtained by the precise rotation angle function satisfied the finite element simulation results.The accurate rotation angle function was more in line with the actual angle of the beam and was more suitable for practical engineering,which provides a theoretical basis for further approach of the precise deflection function.The calculation result of the accurate rotation angle function can be obtained quickly by related software,which could promote the update of the related software's solution method,and have a wide application prospect.
作者
张晓晴
刘晗
许银胜
李志强
ZHANG Xiaoqing;LIU Han;XU Yinsheng;LI Zhiqiang(School of Civil Engineering and Transportation,Guangzhou 510641,China;School of Mechanical and Automotive Engineering,South China University of Technology,Guangzhou 510641,China;College of Mechanical and Vehicle Engineering,Taiyuan University of Technology,Taiyuan 030024,China)
出处
《太原理工大学学报》
CAS
北大核心
2021年第3期473-477,共5页
Journal of Taiyuan University of Technology
基金
国家自然科学基金资助项目(11972163)。
关键词
挠曲线函数
梁转角函数
链导法则
有限元法
deflection function
angle of rotation function
the chain rule
the method of finite elements
