小周期复合材料弹性结构的混合有限元计算

Mixed Finite Element Method for Elastic Problems of Composite Materials with Small Period

摘要:

在多尺度渐近展开式的基础上，讨论小周期复合材料弹性结构均匀化方程的各向异性混合元，给出了关于位移向量的L2模和应变张量的H(div)模的误差估计.这种单元具有各向异性特征，解除了正则性条件的束缚，有较好的实用性.最后的数值结果验证了理论的正确性.

关键词:弹性结构; 均匀化方程; 各向异性; 混合有限元

Abstract:

Based on the multi-scale asymptotic expansion,a mixed finite element method is discussed on anisotropic meshes.The method involves homogenization theory in small periodic elastic structure of composite materials.The error estimates in L2norm for displacement vector and H(div)norm for strain tensor are derived. Relieving regularity assumption,this element is more practical.Finally,the numerical results validate the theoretical analysis.

Key words:elastic problems; homogenized equations; anisotropic; mixed finite element