International Journal of Materials Engineering and Technology

The International Journal of Materials Engineering and Technology publishes peer-reviewed articles on various materials, their properties, processing, and applications in fields such as electronics, energy, and structural engineering. It also welcomes survey articles on advancements in material engineering.

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HAMILTONIAN SYMPLECTIC FORMALISM FOR STRUCTURAL SYSTEMS

Authors

  • Marcello Arici Pelermo University

Keywords:

Hamiltonian structural analysis, HSA, symplectic space, symplectic elasticity, bridge engineering

DOI:

https://doi.org/10.17654/0975044422001

Abstract

The Hamiltonian symplectic formalism is found to be very useful for structural mechanics, in the study of structural systems and for the analysis of civil engineering and bridge structures. The steps of the Hamiltonian Structural Analysis (HSA) procedure are briefly reported with reference to the study of a 3-D arbitrary shape, curved beam on elastic foundation.

References

K. R. Meyer and G. R. Hall, Introduction to Hamilton Dynamical Systems and N-body Problem, Springer, N.Y., 1992.

D. Morin, Introduction to Classical Mechanics: With Problems and Solutions, Cambridge University Press, 2007.

C. Lanczos, The variational principles of mechanics, Mathematical Expositions, No. 4, University of Toronto Press, 1964.

K. Hartnett, The fight to fix symplectic geometry, Quanta Magazine (2017). Org/20170209.

W. X. Zhong, Computational Structural Mechanics and Optimal Control, Dalian University of Technology Press, Dalian, 1993 (in Chinese).

W. X. Zhong, A New Systematic Methodology for Theory of Elasticity, Dalian University of Technology Press, Dalian, 1995 (in Chinese).

M. Arici, Forme Canoniche e principi variazionali in elastostatica ed in elastodinamica, XII Congresso AIMETA’95, Napoli 5 (1995a), 203-208 (in Italian).

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).

C. W. Lim and X. S. Xu, Symplectic elasticity: theory and applications, Appl. Mech. Rev. 63(5) (2011), 050802. DOI: 10.1115/1.400370.

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.

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.

W. X. Zhong, W. Yao and C. W. Lim, Symplectic Elasticity, World Scientific Publishing Co., Singapore, 2009, 292 pp.

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.

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.

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.

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.

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.

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.

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.

M. F. Granata, Analysis of non-uniform torsion in incrementally launched Bridges. Eng. Struct. 75 (2014), 374-387. doi.org/10.1016//i.

W. X. Zhong, On precise integration method, J. Comput. App.. Math. 163 (2004a), 59-78. doi:10.1016/j.com.2003.08.053.

W. X. Zhong, Duality System in Applied Mechanics and Optimal Control, Kluwer Academic Publishing, 2004b, 456 pp.

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Published

2022-05-20

Issue

Vol. 21 (2022)

Section

Articles

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How to Cite

HAMILTONIAN SYMPLECTIC FORMALISM FOR STRUCTURAL SYSTEMS. (2022). International Journal of Materials Engineering and Technology, 21(1), 1-10. https://doi.org/10.17654/0975044422001

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