A hybrid finite element method for heterogeneous materials with randomly dispersed rigid inclusions
A hybrid finite element method for heterogeneous materials with randomly dispersed rigid inclusions
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DOI：
10.1002/nme.1620381004
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发表时间：
1995-05
影响因子：
2.9
通讯作者：
J. Zhang;N. Katsube
中科院分区：
文献类型：
--
作者：
J. Zhang;N. Katsube
本文提出了一种求解二维非均匀材料力学响应的杂交有限元方法。在传统的有限元方法中，必须用许多单元来表示一个夹杂。在这项工作中，每个夹杂物被嵌入一个多边形单元，只需要一个元素来代表一个夹杂物。在数值近似的应力和位移分布周围的夹杂物，经典的弹性解的多连通区域。一个修改后的混合功能被用作基础的元素制定的位移边界条件的元素被自动认为是在变分意义上。两个边值问题的计算结果表明了该方法的准确性和有效性。在一个例子中，结果表明，基于所提出的方法只有64个混合元素（450自由度）是几乎相同的那些基于传统的方法与2928个传统的元素（5526自由度）。
A hybrid finite element approach is proposed for the mechanical response of two-dimensional heterogeneous materials with linearly elastic matrix and randomly dispersed rigid circular inclusions of arbitrary sizes. In conventional finite element methods, many elements must be used to represent one inclusion. In this work, each inclusion is embedded inside a polygonal element and only one element is required to represent one inclusion. In numerically approximating stress and displacement distributions around the inclusion, classical elasticity solutions for a multiply-connected region are employed. A modified hybrid functional is used as the basis of the element formulation where the displacement boundary conditions of the element are automatically considered in a variational sense. The accuracy and efficiency of the proposed method are demonstrated by two boundary value problems. In one example, the results based on the proposed method with only 64 hybrid elements (450 degrees of freedom) are shown to be almost identical to those based on the traditional method with 2928 conventional elements (5526 degrees of freedom).