【摘要】 在Lagrange有限元基础上,介绍了计算运动方程中节点力的不同积分方法.单点积分方法具有较高的计算效率,为了控制沙漏变形,必须引入抗沙漏节点力;采用2×2×2高斯积分可以避免沙漏变形,并有较高的计算精度,但导致计算量增大;而采用局部2×2×2高斯积分则同时具有两者的优点.三维侵彻的计算结果表明局部2×2×2高斯积分能够很好地控制沙漏变形,并有较高的计算效率;一维应变波的模拟计算结果也表明,2×2×2高斯积分比单点积分更加接近理论值.这说明所述方法和所建程序的合理性和有效性,它为侵彻贯穿过程的数值分析提供了一种实用和有效的手段.更多还原

【Abstract】 Based on the analysis of Lagrange finite element method,numerical integration methods to compute nodal force were briefly described.In order to control hourglass deformations,anti-hourglass nodal forces have to be used for single point quadrature,which has higher efficiency.The hourglass modes would be controlled and the numerical accuracy raised effectively if 2×2×2 Gaussian quadrature were adapted,but this would entail heavy computation.However,partial 2×2×2 Gaussian quadrature has the merits of two kinds of integration method.The numerical example of penetration indicated that partial 2×2×2 Gaussian quadrature could control hourglass deformations effectively and has higher efficiency.And the numerical simulations of one-dimensional strain wave also shown that 2×2×2 Gaussian quadrature is much better than single point quadrature.It is concluded that the method discussed and the program we developed are reasonable and effective,providing a useful method for the numerical study of penetration and perforation.更多还原