偶应力问题的杂交/混合元分析
Hybrid/mixed finite element analysis of couple-stress problems
查看参考文献18篇
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文摘
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将弹性力学中Hellinger-Reissner变分原理推广到偶应力理论中，并以罚函数的形式引入其的束条件，提出了一种有效的杂交/混合单元。文中分别分析了带中心小孔平板在轴向均匀加载时的应力集中情况，以及含中间裂纹的无限平板单轴拉伸时的位移场和应力场。算例表明，该单元计算效率高，精度好，即使在材料本征长度很小时，仍然能够得到相当理想的结果。 |
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其他语种文摘
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In this paper the Hellinger-Reissner variational principle in classical elasticity is extended to couple-stress theory. Based on the generalized variational principle?a new effective hybrid/mixed finite element method for couple-stress theory is put forward and its constraint is introduced by a penalty function technique. In addition, the single element stability conditions and its patch stability test are discussed. Farther the verification for the element eigenvalues makes sure that the present mothod is reliable. Two numerical examples are given: the stress concentration around a central circular hole in a uniformly axially loaded field,and the displacement and stress fields around a crack in an infinite plate of uni-axial tension. The numerical results show that the present method has high efficiency and good accuracy. The considerably satisfying results can be obtained, even if the characteristic length is very small. |
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来源
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计算力学学报
,2003,20(4):427-433 【核心库】
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关键词
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偶应力理论
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杂交/混合元
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罚函数
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稳定性条件
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地址
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中国科学院力学研究所, 非线性力学国家重点实验室, 北京, 100080
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语种
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中文 |
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文献类型
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研究性论文 |
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ISSN
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1007-4708 |
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学科
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数学 |
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基金
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国家自然科学基金
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文献收藏号
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CSCD:1167287
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18
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