Keywords and phrases: Hamiltonian structural analysis, HSA, symplectic space, symplectic elasticity, bridge engineering.
Received: April 1, 2022; Accepted: May 5, 2022; Published: May 20, 2022
How to cite this article: Marcello Arici, Hamiltonian symplectic formalism for structural systems, International Journal of Materials Engineering and Technology 21 (2022), 1-10. http://dx.doi.org/10.17654/0975044422001
This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License
References:
[1] K. R. Meyer and G. R. Hall, Introduction to Hamilton Dynamical Systems and N-body Problem, Springer, N.Y., 1992. [2] D. Morin, Introduction to Classical Mechanics: With Problems and Solutions, Cambridge University Press, 2007. [3] C. Lanczos, The variational principles of mechanics, Mathematical Expositions, No. 4, University of Toronto Press, 1964. [4] K. Hartnett, The fight to fix symplectic geometry, Quanta Magazine (2017). Org/20170209. [5] W. X. Zhong, Computational Structural Mechanics and Optimal Control, Dalian University of Technology Press, Dalian, 1993 (in Chinese). [6] W. X. Zhong, A New Systematic Methodology for Theory of Elasticity, Dalian University of Technology Press, Dalian, 1995 (in Chinese). [7] M. Arici, Forme Canoniche e principi variazionali in elastostatica ed in elastodinamica, XII Congresso AIMETA’95, Napoli 5 (1995a), 203-208 (in Italian). [8] M. Arici, Ruolo della funzione Hamiltoniana in elastostatica e relazione con i principi variazionali dell’energia, IX Congresso It, di Meccanica Computazionale, AIMETA, Catania, 1995b, pp. 129-132 (in Italian). [9] C. W. Lim and X. S. Xu, Symplectic elasticity: theory and applications, Appl. Mech. Rev. 63(5) (2011), 050802. DOI: 10.1115/1.400370. [10] W. X. Zhong and X. X. Zhong, Computational structural mechanics, optimal control and semi-analytical method in PDE, Computers and Structures 37(6) (1990), 993-1004. [11] W. X. Zhong and F. W. Williams, Physical interpretation of the symplectic orthogonality of the eigen-solutions of a Hamiltonian or symplectic matrix, Computers and Structures 49(4) (1993), 749-750. [12] W. X. Zhong, W. Yao and C. W. Lim, Symplectic Elasticity, World Scientific Publishing Co., Singapore, 2009, 292 pp. [13] X. Li, F. Xu and Z. Zhang, Symplectic Eigenvalue analysis method for bending of beams resting on two-parameter elastic foundations, J. Eng. Mech. ASCE 143(9) (2017). DOI:10.1061/(ASCE)EM.1943-7889.0001315. [14] M. Huang, X. Zheng, C. Zhou and D. An, On the symplectic superposition method for new analytic bending, buckling, and free vibration solutions of rectangular nanoplates with all edges free, Acta Mechanica 232 (2021), 1-19. [15] M. Arici and M. F. Granata, A general method for non-linear analysis of bridge structures, Bridge Structures 1(3) (2005), 223-244. DOI: 10.1080/15732480500278236. [16] M. Arici and M. F. Granata, Generalized curved beam on elastic foundation solved by transfer matrix method, Structural Engineering and Mechanics 40(2) (2011), 279-295. [17] M. Arici, M. F. Granata and P. Margiotta, Hamiltonian structural analysis of curved beams with or without generalized two-parameter foundation, Archive of Applied Mechanics 83(12) (2013), 1695-1714. [18] M. Arici and M. F. Granata, Unified theory for analysis of curved thin-walled girders with open and closed cross-section through HSA method, Engineering Structures (2016). DOI: 10.1016/j.engstruct.2016.01.051. [19] M. Arici, M. F. Granata, G. Longo, Symplectic analysis of thin-walled curved box girders with torsion, distortion and shear lag warping effects, accepted for publication on Thin-Walled Structures (2022), TWST-D-21-01071R2. [20] M. F. Granata, Analysis of non-uniform torsion in incrementally launched Bridges. Eng. Struct. 75 (2014), 374-387. doi.org/10.1016//i. [21] W. X. Zhong, On precise integration method, J. Comput. App.. Math. 163 (2004a), 59-78. doi:10.1016/j.com.2003.08.053. [22] W. X. Zhong, Duality System in Applied Mechanics and Optimal Control, Kluwer Academic Publishing, 2004b, 456 pp.
|