关键词: 降维非线性有限元, 隐式迭代, 显式迭代, 无条件稳定

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