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本文在对轴向力、内压、扭矩组合载荷作用下的弹塑性范围内的圆管,利用弹塑性理论,推导出了解本问题的虚功原理公式,采用等参二次线单元对该虚功原理公式离散化,再借助普兰特—雷斯(Prandtl—Reuss)方程导出了弹塑性有限元方程式。运用折线负荷法和比例负荷法对圆管进行了各种变形动态解析,求出了两种负荷路径下的稳定界限应力,指出了不同负荷路径对圆管不稳定界限的影响,为设计、加工、使用弹塑性管材提供了参考依据。
Based on the elasto-plastic theory, the formulas of virtual work principle of this problem are deduced by using the elastic-plastic theory under the combined axial and internal pressure and torque loads. The work theory formula is discretized, and then the elasto-plastic finite element equation is derived by the Prandtl-Reuss equation. The dynamic analysis of the circular pipe under different loads is carried out by means of the line load method and the proportional load method. The steady limit stress under two load paths is obtained. The influence of different load paths on the instability of the circular pipe is pointed out. The design, processing , The use of elastoplastic pipe provides a reference.