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中文摘要：
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。
英文摘要：
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.
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