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Date of Publication:2004-01-01

Journal:计算力学学报

Issue:4

Page Number:425-429

ISSN No.:1007-4708

Abstract: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 the problems subjected to symmetric essential boundary conditions. This paper uses Lagrange multiplier method to develop FE equation. Stiffness matrix for cyclic symmetric structure is block-circulate unless 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 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 substructure technique. For the block-diagonal property of the generalized stiffness matrix, the most computation can be carried out in a partitioning way. As a result, great efficiency can be gained, compared with basic FEM. The proposed algorithm can be easily applied to other analysis process for rotationally periodic structures, e.g. heat transfer problems, viscoelastic problems, etc. The contributions of this 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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