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中文核心期刊

用于板料成形反向模拟的特殊应力更新算法

A noval stress integration algorithm in inverse analysis method of sheet metal stamping

  • 摘要: 提出了一种改进的反向模拟法,以最终构型为研究对象,采用Euler坐标系,基于虚功原理获得有限元列式. 改进的反向模拟法采用了一种基于塑性流动理论的本构方程,可以充分考虑应变历史对塑性变形的影响. 为了避免流动理论应力更新算法过程中关于未知量\Delta\lambda 的非线性方程的求解,引入等效应力思想,无需Newton-Raphson迭代直接计算未知量\Delta \lambda . 盒形件的拉深实例中,传统的基于塑性形变本构方程的反向模拟法和改进的基于塑性流动本构方程的反向模拟法计算结果,分别与基于增量有限元法的正向数值模拟求解器LS-DYNA计算结果进行对比. 通过获得的坯料轮廓、成形极限图、等效应变分布、计算效率等的比较,验证了所提出的基于塑性流动理论本构模型的应力更新算法的有效性.

     

    Abstract: An improved inverse analysis method is proposed for sheetmetal stamping based on the final workpiece in Euler coordinate system. Theprinciple of the virtual work is firstly adopted to obtain the equivalentequations. The constitutive equation in the present method is based on flowtheory of plasticity to consider the loading history, while deformationtheory of plasticity in the classical inverse analysis method. The plasticmultiplier \Delta \lambda is directly obtained with the concept ofthe equivalent stress in order to avoid numerous iterations inNewton-Raphson scheme \Delta \lambda. The numerical resultsobtained from the classical and improved inverse analysis methods arecompared with those from the incremental forward finite element solverLS-DYNA. It shows that the proposed constitutive equation is effective andreliable with the comparisons of blank configurations, Forming LimitedDiagram (FLD), the effective strain distribution and computationalefficiency.

     

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