内压支撑下薄壁管弯曲变形力学分析

管件内压弯曲又称为管件充液弯曲,具有减小截面畸变,延缓薄壁管内侧失稳起皱,提高弯曲成形极限等优点。支撑内压在其中起到了关键性的作用,对于环向和轴向的应力应变分量具有重要影响。采用塑性理论,对内压和弯矩共同作用下的薄壁管弯曲变形进行理论分析。考虑内压对微元平衡方程的影响,建立一个新的理论分析模型,通过求解非线性方程组,得到薄壁管应力应变的分布规律,定量分析内压对薄壁管应力应变的影响趋势。同时通过将有限元分析得到的应力应变分量的信息,与理论解进行对比发现,理论预测和模拟结果相符合,验证所建立的理论分析模型的可靠性。结果表明,轴向和环向应力随内压升高均大大提高,环向应变随内压升高线性递增,而厚向应变线性减小。

Plastic Deformation Analysis of Thin-walled Tube Bending under Internal Pressure

The hydro-bending process of thin-walled tube provides several advantages:The section flattening is minimized by controlling the internal pressure,and the internal pressure delays the onset of wrinkling on the compression side and boosts the bending limit of the thin-walled tube.A new infinitesimal equilibrium equation for the hydro-bending process considering the effect of internal pressure is established.Then based on the plastic theory,the numerical solutions for the stress and strain components are obtained for a typical thin-walled tube.The finite element analysis is also conducted to verify the theoretical model.By comparing the theoretical result with the numerical results,it is found that the theoretical prediction and simulation results are in generally good agreement.The axial and circumferential stresses go up with the increasing of internal pressure.The circumferential strain increases linearly with pressure increasing,whereas the thickness strain decreases linearly as internal pressure increases.