圆柱壳纯弯曲时塑性失稳临界曲率半径模型

薄壁管材在等曲率矫直生产中，塑性失稳临界曲率半径作为重要的工艺参数，直接决定了设备结构和产品质量。而目前现场仍沿用经验图表结合人工经验和反复试矫对其进行估定，亟待建立针对性的临界曲率半径数学模型以指导生产。在力学建模和分析时，就是确定具有初始曲率的圆柱壳体在纯弯曲条件下塑性失稳的临界曲率半径，为此从旋转壳体一般几何方程出发，基于J2形变理论和能量理论，运用里茨法建立了圆柱壳体在纯弯曲条件下塑性失稳时的临界弯矩，以此确定了临界曲率半径模型，并给出了数值解法。应用ANSYS/LS-DYNA进行了有限元动态仿真试验，证明了模型是近似正确的，并通过仿真对比分析证明了轴向起皱先于截面畸变是圆柱壳体在纯弯曲条件下塑性失稳的主要模态。

The Plastic Buckling Critical Radius Model of The Cylindrical Shell Subject to Pure Bending

The critical curvature-radius as the main straightening technical parameter, decides the structure of equipment and the quality of products for straightening thin-walled tubes with equal curvature, however, it is usually carried out based on the experiential data and chart by skilled labourers, whose art is based on long experience and experiments, the special mathematical model of the critical radius is immediately necessary. But during mechanical modeling and analyzing, it is the critical curvature-radius that the cylindrical shell with the initial curvature under pure bending occurs plastic buckling, therefore, applying the general strain-displacement relations of the shell of revolution, the plastic buckling critical bending-moment model of the cylindrical shell under pure bending is presented by the Ritz method, based on the J2 deformation theory and energy method, then the critical radius is subsequently obtained and it is also shown how to solve synchronously. In order to certify whether it is correct, we have done some dynamic simulations by ANSYS/LS-DYNA, the results have shown that the model is approximate correct, by the comparison of the results of the simulations it is shown that wrinkling on the compression side of the cylindrical shell occurs before buckling due to ovalisation when the cylindrical shell occurs plastic buckling subject to pure bending.