Abstract: Aiming at the problem of making well balance between computation speed and precision in the traditional reduced nonlinear finite element method, a novel unconditionally stable explicit integration method is proposed. Based on the Taylor expansion analysis, the difference expressions of velocity and acceleration with third order accuracy are obtained to get new explicit integration equation, and its transfer matrix’s spectral radius is analyzed under the single degree of freedom system. Then the equation is modified to meet the requirements of the unconditional stability. Experimental results show that the equivalent damping ratio accuracy of improved explicit iteration algorithm is superior to that of the central difference method and implicit integration methods. Moreover, the computation time consuming is better than that of implicit integration method in reduced nonlinear finite element model, which improves the calculation speed. When the number of dimensions keeps in a high value, the model can still maintain good computing time consuming and frame rate to ensure the accuracy of the model.

Key words: reduced nonlinear finite element method, implicit integration, explicit integration, unconditionally stable

摘要： 针对传统降维非线性有限元计算速度与精确度难以兼顾的问题，提出了一种无条件稳定的显式迭代算法。基于泰勒展开式得到速度、加速度的三阶精度差分表达式从而获得新的有限元显式迭代方程，并分析其单自由度系统下的传递矩阵谱半径。改进迭代方程使谱半径始终小于1从而满足无条件稳定的要求。实验表明，改进后的显式迭代算法在等效阻尼比的精度上优于中心差分法和隐式迭代法；在降维非线性有限元模型计算中的计算耗时优于隐式迭代方法，提高了降维非线性有限元的迭代计算速度。模型在降维后维度数值较高时，仍能维持良好的计算耗时和帧率，保证了模型的精确度。

关键词: 降维非线性有限元, 隐式迭代, 显式迭代, 无条件稳定