| 刘岭,杨海天.基于拉格朗日乘子法和群论的具有任意位移边界条件的旋转周期对称结构有限元分析[J].计算力学学报,2004,21(4):425~429 |
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| 基于拉格朗日乘子法和群论的具有任意位移边界条件的旋转周期对称结构有限元分析 |
| FE analysis based on Lagrange multipliers method and group theory for structures of cyclic symmetry under arbitrary displacement boundary conditions |
| 修订日期：2002-11-21 |
| DOI：10.7511/jslx20044075 |
| 中文关键词: 旋转周期对称 有限元 群 拉格朗日乘子 |
| 英文关键词:cyclic symmetry,FEM,group,lagrange multiplier |
| 基金项目:国家自然科学基金(10102024)，重点基金项目(10032030)，973项目(G1999032805)，教育部重点基金[99149]，教育部骨干教师资助计划[2000-65]资助项目. |
| 刘岭 杨海天 |
| [1]大连理工大学工程力学系,辽宁大连116024 [2]大连理工大学工业装备结构分析国家重点实验室,辽宁大连116024 |
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| 全文下载次数: 9 |
| 中文摘要: |
| 对任意位移边界条件下的旋转周期对称结构，由拉格朗日乘子法建立有限元方程。在对称适应的坐标系下，由结构刚度矩阵的块循环性质，利用群变换给出一种新的求解方法。数值验证给出令人满意的结果。 |
| 英文摘要: |
| Cyclic symmetry can be found in many engineering structures. When analyze behaviors of these structures, computing efficiency can be greatly improved if structural symmetry is fully exploited. However, it seems that most of the existing algorithms utilizing symmetry only relate to problems subjected to symmetric essential boundary conditions. The present paper uses Lagrange multiplier method to develop FE equation. Stiffness matrix for cyclic symmetric structure is block-circulate so long as a kind of symmetry-adapted reference coordinate system is adopted. By a group transformation, structure is then analyzed in a group space. Base vector of this space used in this paper is orthogonal with respect to group representation matrix. As a consequence, generalized stiffness matrix is block-diagonal. A matrix transformation is then proposed to make the generalized stiffness matrix nonsingular. Solve the whole equation system by a method similar to substructuring technique. For the block-diagonal property of the generalized stiffness matrix, most computation can be carried out in a partitioning way. As a result, great efficiency can be gained, compared to basic FEM. The proposed algorithm can be easily applied into other analysis process for rotationally periodic structures, e.g. heat transfer problems, viscoelastic problems, etc. The contributions of the present paper are twofold. Firstly, a matrix transformation combined with group theory and numerical methods is proposed to analyze structures of cyclic symmetry subjected to arbitrary boundary conditions. Secondly, the computational convenience and efficiency are fully discussed and demonstrated by means of three numerical examples. |
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