复合纤维的三角形截面梁组合扭转理论研究

Theoretical Study of Combined Torsion of FRP Beams with Triangular Cross Section

基于板梁理论,首先通过各板件的位移、应变、应力及FRP(增强复合纤维)材料的本构关系推导出悬臂梁在端部受集中扭矩情况下组合扭转的总应变能及总势能,接着基于能量变分法构建了FRP三角形梁组合扭转问题的能量变分模型与微分方程模型,最后通过边界条件求得最大扭转角的近似解析解,并与Ansys有限元软件模拟结果进行验证,验证结果表明理论计算得到的近似解与有限元模拟解基本吻合,证明了理论模型的正确性,可为工程设计提供参考。

Based on the plate beam theory,the total strain energy and total potential energy of the cantilever beam torsion in the case of concentrated torque at the end are deduced from the displacement,strain,stress and the intrinsic relationship of the FRP material of each plate,and then the energy variational model and the differential equation model of the combined torsion problem of FRP triangular beams are constructed based on the energy variational method.Finally,the approximate analytical solution of the maximum torsion angle is obtained by boundary conditions,and the results are verified with the simulation results of Ansys finite element software,which show that the approximate solution obtained by theoretical calculation basically agrees with the finite element simulation solution,proving the correctness of the theoretical model,which can provide reference for engineering design.