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For a class of operator matrices appearing in elasticity, the eigen-vector expansion theorem is considered. It is shown that the eigen-vectors possess the symplectic orthogonality. And a necessary and sufficient condition for the completeness of the eigen-vector system is further given. As concrete applications, the obtained results are tested for the plate bending equation and the buckling deflection problem of rectangular thin plates.
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Keywords:
- operator matrix /
- eigen-vector expansion theorem /
- elasticity
[1] Zhong W X 1991 Computational Structural Mechanics and Applications 8 229 (in Chinese) [钟万勰 1991 计算机结构力学及其应用 8 229]
[2] Zhong W X 2004 Duality System in Applied Mechanics and Optimal Control (Dordrecht: Kluwer Academic Publishers)
[3] Zhong W X 1995 A New Systematic Methodology for Theory of Elasticity (Dalian: Dalian University of Technology Press) (in Chinese) [钟万勰 1995 弹性力学求解新体系 (大连: 大连理工大学出版)]
[4] Stephen N G 2004 Int. J. Mech. Sci. 46 1327
[5] Yao W A, Sui Y F 2004 Appl. Mathemat. Mech. 25 178
[6] Leung A Y T, Xu X S, Gu Q, Leung C T O, Zheng J J 2007 Int. J. Numer. Methods Eng. 69 2381
[7] Xu X S, Chu H J, Lim C W 2008 Int. J. Struct. Stabil. Dynam. 8 487
[8] Yao Z, Zhang H W, Wang J B, Zhong W X 2008 Chinese J. Solid Mech. 29 13 (in Chinese) [姚征, 张洪武, 王晋宝, 钟万勰 2008 固体力学学报 29 13]
[9] Zhang W 2009 Arch. Appl. Mech. 79 793
[10] Zhao L, Chen W Q 2009 Mech. Mater. 41 1330
[11] Zhao L, Chen W Q 2010 Comp. Struct. 92 1753
[12] Tretter C 2008 Spectral Theory of Block Operator Matrices and Applications (London: Imperial College Press)
[13] Wang H, Alatancang, Huang J J 2011 Chin. Phys. B 20 010209
[14] Huang J J, Alatangcang, Wang H 2010 Chin. Phys. B 19 120201
[15] Gohberg I C, Krein M G 1969 Introduction to the Theory of Linear Nonselfajoint Operators in Hilbert Space (Providence RI: Amer. Math. Soc.)
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[1] Zhong W X 1991 Computational Structural Mechanics and Applications 8 229 (in Chinese) [钟万勰 1991 计算机结构力学及其应用 8 229]
[2] Zhong W X 2004 Duality System in Applied Mechanics and Optimal Control (Dordrecht: Kluwer Academic Publishers)
[3] Zhong W X 1995 A New Systematic Methodology for Theory of Elasticity (Dalian: Dalian University of Technology Press) (in Chinese) [钟万勰 1995 弹性力学求解新体系 (大连: 大连理工大学出版)]
[4] Stephen N G 2004 Int. J. Mech. Sci. 46 1327
[5] Yao W A, Sui Y F 2004 Appl. Mathemat. Mech. 25 178
[6] Leung A Y T, Xu X S, Gu Q, Leung C T O, Zheng J J 2007 Int. J. Numer. Methods Eng. 69 2381
[7] Xu X S, Chu H J, Lim C W 2008 Int. J. Struct. Stabil. Dynam. 8 487
[8] Yao Z, Zhang H W, Wang J B, Zhong W X 2008 Chinese J. Solid Mech. 29 13 (in Chinese) [姚征, 张洪武, 王晋宝, 钟万勰 2008 固体力学学报 29 13]
[9] Zhang W 2009 Arch. Appl. Mech. 79 793
[10] Zhao L, Chen W Q 2009 Mech. Mater. 41 1330
[11] Zhao L, Chen W Q 2010 Comp. Struct. 92 1753
[12] Tretter C 2008 Spectral Theory of Block Operator Matrices and Applications (London: Imperial College Press)
[13] Wang H, Alatancang, Huang J J 2011 Chin. Phys. B 20 010209
[14] Huang J J, Alatangcang, Wang H 2010 Chin. Phys. B 19 120201
[15] Gohberg I C, Krein M G 1969 Introduction to the Theory of Linear Nonselfajoint Operators in Hilbert Space (Providence RI: Amer. Math. Soc.)
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