Symplectic elasticity

Symplectic Elasticity

Volumn , Issue , 2009, Pages 1-292

  Yao, Weian ^a   Zhong, Wanxie ^a   Lim, Chee Wah ^b  

^a DALIAN UNIVERSITY OF TECHNOLOGY   (China)

^b CITY UNIVERSITY OF HONG KONG   (Hong Kong)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84967444033     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1142/6656     Document Type: Book

References (70)

1. Rongchang Shi, Matrix Analysis, Beijing: Beijing Institute of Technology Press, 1996 (in Chinese).
2. Yizhong Lan and Chunlai Zhao, Theory of Linear Algebra, Beijing: Peking University Press, 1998 (in Chinese).
3. Department of Mathematical Mechanics of Peking University, Advanced Algebra, Beijing: People’s Education Press, 1978 (in Chinese).
4. J. Koszul and Yiming Zou, Theory of Symplectic Geometry, Beijing: Science Press, 1986 (in Chinese).
5. MengZhao Qin, Symplectic geometry and computing Hamiltonian mechanics, Mechanics and Practice, 1990, 12(6): 1-20 (in Chinese).
6. Yanbai Zhou, Lectures on Theoretical Mechanics, Beijing: People’s Education Press, 1979 (in Chinese).
7. Lingxi Qian, Statically Indeterminate Structural Analysis, Shanghai: Shanghai Scientific and Technical Publishers, 1951 (in Chinese).
8. S.P. Timoshenko and J.N. Goodier, Theory of Elasticity, 3rd edn., New York: McGraw-Hill, 1970.
9. Haichang Hu, Variational Principle of Elasticity and Its Application, Beijing: Science Press, 1981 (in Chinese).
10. Longfu Wang, Theory of Elasticity, Beijing: Science Press, 1984 (in Chinese).
11. Zudao Luo and Sijian Li, Mechanics of Anisotropic Materials, Shanghai: Shanghai Jiaotong University Press, 1994 (in Chinese).
12. Qinghua Du, Zhuhua Xiong and Xuewen Tao, Fundamentals of Applied Solid Mechanics, Vol. 2, Beijing: Higher Education Press, 1996 (in Chinese).
13. Jialong Wu, Elasticity, Shanghai: Tongji University Press, 1993 (in Chinese).
14. L.H. Tsien, Principle of Complementary Energy, Scientia Sinica, 1950, 1: 449-456 (in Chinese).
15. Xueren Zhao, Xusheng Zhao and Zhaoxiong Cheng, Solid Mechanics, Beijing: Chinese Scientific and Technical Publishers, 1993 (in Chinese).
16. Wanxie Zhong and Weian Yao, New solution system for plate bending and its application, ACTA Mechanica Sinica, 1999, 31(2): 173-184 (in Chinese).
17. Wanxie Zhong and Weian Yao, Multi-variable variational principle for three dimensional elasticity, ACTA Mechanica Solida Sinica, 2000, 21(SI): 126-129 (in Chinese).
18. S. Timoshenko, Strength of Materials, 3rd edn., New York: Van Nostrand, 1955-1956.
19. Haichang Hu, Variational Principle of Elasticity and Its Application, Beijing: Science Press, 1981 (in Chinese).
20. Zudao Luo and Sijian Li, Mechanics of Anisotropic Materials, Shanghai: Shanghai Jiaotong University Press, 1994 (in Chinese).
21. Wanxie Zhong and Xiangxiang Zhong, On the transverse eigenvector solution of the elliptic partial differential equation in the prismatic domain, Journal on Numerical Methods and Computer Applications, 1992, 13(2): 107-118 (in Chinese).
22. Wanxie Zhong and Zaishi Yang, Partial differential equations and Hamiltonian system, in: F.Y. Cheng and Zizhi Fu, eds., Computational Mechanics in Structural Engineering, London: Elsevier, 1992: 32-48.
23. Wanxie Zhong and F.W. Williams, On the localization of the vibration mode of sub-structural chain-type structure, Proceedings of the Institution of Mechanical Engineers, Part C, 1991, 205(C4): 281-288.
24. Wanxie Zhong, Huajiang Ouyang and Zicheng Deng, Computational Structural Mechanics and Optimal Control, Dalian: Dalian University of Technology Press, 1993 (in Chinese).
25. Wanxie Zhong, A New Systematic Methodology for Theory of Elasticity, Dalian University of Technology Press, 1995 (in Chinese).
26. E.T. Whittaker, A Treatise on the Analytical Dynamics, 4th edn., Combridge: Cambridge University Press, 1960.
27. V.I. Arnold, Mathemaical Methods of Classical Mechanics, New York: Springer-Verlag, 1978.
28. Kang Feng and Mengzhao Qin, Hamilton Methodology for Hamiltonian Dynamical Systems, Progress in Natural Science, 1991, 1(2): 102-112 (in Chinese).
29. Wanxie Zhong, On the reciprocal theorem and adjoint symplectic orthogonal relation, ACTA Mechanica Sinica, 1992, 24(4): 432-437 (in Chinese).
30. Wanxie Zhong, Plane elasticity problem in strip domain and Hamiltonian system, Journal of Dalian University of Technology, 1991, 31(4): 373-384 (in Chinese).
31. Wanxie Zhong and F.W. Williams, On the direct solution of wave propagation for repetitive structures, Journal of Sound and Vibration, 1995, 181(3): 485-501.
32. K.F. Graff, Wave motion in elastic solids, Oxford: Clarendon Press, 1975.
33. J.D. Achenbach, Wave Propagation in Elastic Solids, New York: North-Holland, 1973.
34. Zhilun Xu, Elasticity, Beijing: Higher Education Press, 1990 (in Chinese).
35. Changjun Cheng, Elasticity, Lanzhou: Lanzhou University Press, 1995 (in Chinese).
36. S.P. Timoshenko and J.N. Goodier, Theory of Elasticity, 3rd edn., New York: McGraw-Hill, 1970.
37. N.I. Muschelishvili, Some Basic Problems of the Mathematical Theory of Elasticity, Groningen, Netherlands: Noordholf, 1953.
38. Wanxie Zhong, Plane elasticity problem in strip domain and Hamiltonian system, Journal of Dalian University of Technology, 1991, 31(4): 373-384 (in Chinese).
39. Wanxie Zhong, Method of separation of variables and Hamiltonian system, Computational Structural Mechanics and Applications, 1991, 8(3): 229-240 (in Chinese).
40. Wanxie Zhong, A New Systematic Methodology for Theory of Elasticity, Dalian University of Technology Press, 1995 (in Chinese).
41. Weian Yao, Hamiltonian system for plane anisotropic elasticity and analytical solutions of Saint-Venant problem, Journal of Dalian University of Technology, 1999, 39(5): 612-615 (in Chinese).
42. S.G. Lekhnitskii, Theory of Elasticity of an Anisotropic Body, [s.l.] Mir Publisher, 1981.
43. Zudao Luo and Sijian Li, Mechanics of Anisotropic Materials, Shanghai: Shanghai Jiaotong University Press, 1994 (in Chinese).
44. Wanxie Zhong, A New Systematic Methodology for Theory of Elasticity, Dalian University of Technology Press, 1995 (in Chinese).
45. Wanxie Zhong and Weian Yao, Analytical solutions on Saint-Venant problem of layered plates, Acta Mechanica Sinica, 1997, 29(5): 617-626 (in Chinese).
46. Wanxie Zhong and Weian Yao, The Saint-Venant solutions of multi-layered composite plates, Advances in Structural Engineering, 1997, 1(2): 127-133.
47. Zudao Luo and Sijian Li, Mechanics of Anisotropic Materials, Shanghai: Shanghai Jiaotong University Press, 1994 (in Chinese).
48. Longfu Wang, Theory of Elasticity, Beijing: Science Press, 1984 (in Chinese).
49. Jialong Wu, Elasticity, Shanghai: Tongji University Press, 1993 (in Chinese).
50. Hongqing Zhang and Alatancang, Completeness of symplectic orthogonal system, Journal of Dalian University of Technology, 1995, 35(6): 754-758 (in Chinese).
51. E. Sternberg and W.T. Koiter, The wedge under a concentrated couple: a paradox in the two-dimensional theory of elasticity, Journal of Applied Mechanics, 1958, 25(3), 575-581.
52. J.P. Dempsey, The wedge subjected to tractions: a paradox resolved, Journal of Elasticity, 1981, 11(1): 1-10.
53. Weian Yao, Jordan solutions for polar coordinate Hamiltonian system and solutions of paradoxes in elastic wedge, Acta Mechanica Sinica, 2001, 33(1): 79-86 (in Chinese).
54. W.X. Zhong, X.S. Xu and H.W. Zhang, On a direct method for the problem of elastic curved beams, Engineering Mechanics, 1996, 13(4): 1-8 (in Chinese).
55. S.P. Timoshenko and S. Woinowsky-Krieger, Theory of Plates and Shells, New York: McGraw-Hill, 1959.
56. Zhilun Xu, Elasticity, Beijing: Higher Education Press, 1990 (in Chinese).
57. Jialong Wu, Elasticity, Shanghai: Tongji University Press, 1993 (in Chinese).
58. Longfu Wang, Theory of Elasticity, Beijing: Science Press, 1984 (in Chinese).
59. S.P. Timoshenko and J.N. Goodier, Theory of Elasticity, 3rd edn., New York: McGraw-Hill, 1970.
60. N.I. Muschelishvili, Some Basic Problems of the Mathematical Theory of Elasticity, Groningen, Netherlands: Noordholf, 1953.
61. Haichang Hu, Variational Principle of Elasticity and Its Application, Beijing: Science Press, 1981 (in Chinese).
62. R.V. Southwell, On the analogues relating flexure and extension of flat plate, Quarterly Journal of Mechanics and Mathematics, 1950, 3: 257.
63. Wanxie Zhong and Weian Yao, New solution system for plate bending and its application, Acta Mechanics Sinica 1999, 31(2): 173-184 (in Chinese).
64. Wanxie Zhong and Weian Yao, Similarity between finite elements in plane elasticity and plate bending, Chinese Journal of Computational Mechanics 1998, 15(1): 1-13 (in Chinese).
65. B. Fraeijs De Veubeke and O.C. Zienkiewicz, Strain-energy bounds of finiteelement analysis by slab analogy, J Strai Analysis, 1967, 2: 265-271.
66. B. Fraeijs De Veubeke and G. Sander, An equilibrium model for plate bending, I J Solids and Structures, 1968, 4(4): 447-468.
67. Wanxie Zhong and Weian Yao, Multi-variable variational principles for plate bending and plane elasticity, Acta Mechanica Sinica 1999, 31(6): 717-723 (in Chinese).
68. Wanxie Zhong and Weian Yao, New solution system for plate bending -force method Hamiltonian system and its application, in: C.J. Cheng, S.Q. Dai and Y.L. Liu, eds., Modern Maths and Mechanics (MMM-VII), Shanghai: Shanghai University Press, 1997, 121-129.
69. Weian Yao, Wanxie Zhong and Bin Su, New solution system for circular sector plate bending and its application, Acta Mechanica Solida Sinica, 1999, 12(4): 307-315.
70. Bin Su, Application of Hamiltonian System in Anisotropy Plate Bending, Master Dissertation of Dalian University of Technology, 2000 (in Chinese).