基于“板-梁理论”单轴对称FGM工字形梁组合扭转  

Uniaxial symmetric FGM I-beam combination torsion based on the"plate beam theory"

作　　者：张文福[1] 周宇 ZHANG Wenfu;ZHOU Yu(School of Civil Engineering and Architecture,Nanjing Institute of Technology,Nanjing 211167,China;School of Mechanical Engineering,Nanjing Institute of Technology,Nanjing 211167,China)

机构地区：[1]南京工程学院建筑工程学院,江苏南京211167 [2]南京工程学院机械工程学院,江苏南京211167

出　　处：《安徽科技学院学报》2025年第1期91-101,共11页Journal of Anhui Science and Technology University

基　　金：国家自然科学基金面上项目(51578120,51178087,52178143)。

摘　　要：针对目前功能梯度材料(Functionally Graded Materials,FGM)工字形截面梁为研究对象的研究较少,本研究以“板-梁理论”为基础,以上翼缘为矩形实体单轴对称的工字形截面梁为对象,展开组合扭转理论研究。基于“板-梁理论”,推导总应变能方程,得到梁的翘曲刚度和自由扭转刚度,然后通过外力势能公式和总应变能公式逐步推导得出总势能表达式。在此基础上,利用能量变分模型和微分方程模型,结合边界条件,推导出梁端部最大扭转角计算公式,将求出的最大扭转角与ANSYS建立的有限元模型结果进行对比。误差最小为0.01%,误差最大为1.85%。本文推导了FGM沿宽度变化上翼缘为矩形实体单轴对称工字形梁的组合扭转总应变能表达式,给出了一端固定、一端自由边界条件下扭转角及最大扭转角的表达式,从而进一步验证“板-梁理论”的正确性。At present,there is relatively little research on functional gradient materials(FGM)I-section beams as the research object.Based on Professor ZHANG Wenfu's"plate beam theory",this paper focuses on the composite torsion theory of I-section beams with rectangular solid and uniaxial symmetry as the object.Based on the"plate beam theory",the total strain energy equation was derived to obtain the flexural stiffness and free torsional stiffness of the beam.Then,the total potential energy expression was gradually derived through the external force potential energy formula and the total strain energy formula.On this basis,using the energy variational model and differential equation model,combined with boundary conditions,the calculation formula for the maximum torsion angle at the end of the beam was derived.The calculated maximum torsion angle was then compared with the finite element model results established by ANSYS.The minimum error was 0.01%and the maximum error was 1.85%.The expression for the combined torsional total strain energy of a rectangular solid single axis symmetric I-beam with a wing edge along the width variation of FGM was derived.The expressions for the torsional angle and maximum torsional angle under one end fixed and one end free boundary conditions were given,further verifying the correctness of the"plate beam theory".

关 键 词：功能梯度材料 组合扭转 板-梁理论 有限元分析 

分 类 号：S852.3[农业科学—基础兽医学]