板材轧制问题的快速有限元方法研究

在用刚塑性有限元法对轧制力进行计算的过程中,联合使用了基于下降思想寻求牛顿方向上阻尼因子的阻尼牛顿(DN)法和基于抛物线插值思想的一维布伦特(Brent)法,即阻尼牛顿和布伦特法(DN-Brent法).将DN-Brent法同传统牛顿(N-R)法进行对比分析,结果表明,两种算法得到的轧制力计算值都与实测值吻合较好,但DN-Brent法所需的迭代次数和CPU计算时间小于N-R法.验证了DN-Brent法在应用刚塑性有限元方法计算轧制力时的准确性和高效性.

Fast Finite Element Method for Flat Rolling Problems

The DN-Brent algorithm,a combination of damped Newton algorithm,which is based on the step-down idea for searching the damping factor in the Newtonian iterative direction,and one-dimensional Brent algorithm,which is based on the parabola interpolation idea,is employed in the rigid plastic finite element method to calculate rolling forces.Compared with the traditional Newton-Raphson(N-R) method,the computational results demonstrate that the rolling force values obtained by the two algorithms are both close to the practical measured values.However,the proposed algorithm needs less iteration numbers and CPU time,which verifies the accuracy and validity of the DN-Brent algorithm in the application of the rigid-plastic finite element method to the calculation of rolling forces.