锥形杆轴向拉伸的材料力学解答

SOLUTION FOR A CONICAL ROD SUBJECTED TO AXIAL TENSION IN MECHANICS OF MATERIALS

对于锥形杆受轴向均匀载荷拉伸的模型,本文基于横截面上轴向正应力均匀分布的假设,给出了其应力及截面变形的材料力学解答。结合ANSYS有限元分析结果及弹性力学精确解进行对比。发现锥角较小时,对于工程实际,材料力学解的误差可以接受。而锥角较大时,需要对轴向正应力公式作修正以使得材料力学解仍然适用。

For the model of a conical rod subjected to axial uniform tensile load in mechanics of materials,this paper presents the solution for stresses and section deformation by assuming that the axial normal stress is uniformly distributed over the cross section.The simulation results of ANSYS are compared with the exact solution from elasticity theory.It is found that the error in the solution from the material mechanics model is acceptable for engineering practice when the cone angle is small.When the cone angle is large,the axial normal stress expression should be modified so that the material mechanics solution is still applicable.