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Please use this identifier to cite or link to this item: http://ntour.ntou.edu.tw:8080/ir/handle/987654321/24492

Title: A Reliable Three-Node Triangular Plate Element Satisfying Rigid Body Rule and Incremental Force Equilibrium Condition
Authors: Shyh-Rong Kuo;Chih-Chang Chi;Weichung Yeih;Jiang-Ren Chang
Contributors: NTOU:Department of Systems Engineering and Naval Architecture
Keywords: Geometric nonlinear;Finite element method;Geometric stiffness matrix;Rigid body rule;Incremental force and moment equilibrium condition
Date: 2006-07
Issue Date: 2011-10-20T08:12:30Z
Publisher: Journal of the Chinese Institute of Engineers
Abstract: Abstract:This paper proposes a simple method for deriving the geometric stiffness matrix (GSM) of a three-node triangular plate element (TPE). It is found that when the GSM of the element is combined into the global one of the structure, this structural stiffness matrix becomes symmetric and satisfies both the rigid body rule and incremental force and moment equilibrium (IFE) conditions, which are basically two fundamental conditions for analysis of mechanics. The former condition has been widely used in the community of mechanics; while the latter one, to our best knowledge, has never been considered. Advantages with the GSM derived are that derivations only need simple matrix operations without cumbersome non-linear virtual strain energy derivations and tedious numerical integrations and more appealingly, this derived GSM can be explicitly given for applications. In addition, based on IFE and the rigid body rule conditions, a reasonable GSM for the three-node TPE must be asymmetric; however, an asymmetric matrix usually gives rise to tedious numerical calculation especially in geometrically nonlinear problems and further, greatly influences computation efficiency. Fortunately, the skew-symmetric parts of the derived GSM can be canceled out once they are merged into the global stiffness matrix of the structure. In this regard, this structural stiffness matrix becomes a symmetric one and thus enhances its effectiveness. Finally, several examples are provided for validating the robustness of the derived GSM.
Relation: 29(4), pp.619-632
URI: http://ntour.ntou.edu.tw/handle/987654321/24492
Appears in Collections:[系統工程暨造船學系] 期刊論文
[河海工程學系] 期刊論文

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