State space elastostatics of prismatic structures

International Journal of Mechanical Sciences

Volumn 46, Issue 9, 2004, Pages 1327-1347

  Stephen, N G ^a  

^a UNIVERSITY OF SOUTHAMPTON   (United Kingdom)

Author keywords

Degenerate modes; Hamiltonian; Linear elasticity; Saint Venant; State space

Indexed keywords

DIFFERENTIAL EQUATIONS; HAMILTONIANS; LINEAR SYSTEMS; MATHEMATICAL TRANSFORMATIONS; MATRIX ALGEBRA; STRESS ANALYSIS;

DEGENERATE MODES; LINEAR ELASTICITY; SAINT-VENANT; STATE SPACE;

ELASTICITY;

EID: 5744221761     PISSN: 00207403     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ijmecsci.2004.07.008     Document Type: Article

References (26)

1. Zhong WX, Ouyang HJ. Hamiltonian system and simplectic geometry in mechanics of composite materials. (I)-Fundamental theory. Applied Mathematics and Mechanics (English Edition) 1992; 13:1017-22.
2. Zhong WX. Plane elasticity in sectorial domain and the Hamiltonian system. Applied Mathematics and Mechanics (English Edition) 1994; 15:1113-23.
3. Wang ZG, Tang LM. Hamiltonian systems in elasticity and their variational principles, Applied Mathematics and Mechanics (English Edition) 1995;16:125-31.
4. Zhong WX, Xu XS. Direct solutions of the Saint Venant problems. In: Lin YK, Su TC, editors, Proceedings of the 11th Conference, Engineering Mechanics, Fort Lauderdale, May 1996. p. 1151-4.
5. Timoshenko SP, Goodier JN. Theory of Elasticity, 3rd ed. New York: McGraw-Hill; 1970.
6. Yao WA, Xu C. A restudy of the paradox of an elastic wedge based on the Hamiltonian system. ASME Journal of Applied Mechanics 2001;68:678-81.
7. Stephen NG, Wang PJ. Saint-Venant's principle and the plane elastic wedge. International Journal of Solids and Structures 1999;36:345-61.
8. Xu XS, Zhong WX, Zhang HW. The Saint-Venant problem and principle in elasticity. International Journal of Solids and Structures 1997;34:2815-27.
9. Stephen NG, Wang MZ. Decay rates for the hollow circular cylinder. ASME Journal of Applied Mechanics 1992;59:747-53.
10. Bahar LY. A state space approach to elasticity. Journal of the Franklin Institute 1975;299:33-41.
11. Vlasov VZ. Method of initial functions in problems of theory of thick plates and shells. Proceedings of the 9th International Congress of Applied Mechanics Brussels, vol. 6. 1957. p. 321-30.
12. Sosa HA, Bahar LY. Transition from Airy stress function to state space formulation of elasticity. Journal of the Franklin Institute 1992;329:817-28.
13. Johnson Jr MW, Little RW. The semi-infinite elastic strip. Quarterly Journal of Applied Mathematics 1965;22:335-44.
14. Druz AN, Ustinov YA. Green's tensor for an elastic cylinder and its applications in the development of Saint-Venant theory. PMM Journal of Applied Mathematics and Mechanics 1996;60:97-104.
15. Druz AN, Polyakov NA, Ustinov YA. Homogeneous solutions and Saint-Venant problems for a naturally twisted rod. PMM Journal of Applied Mathematics and Mechanics 1996;60:657-64.
16. Kargin DP, Kurbatova NV, Ustinov YA. Homogeneous solutions and Saint-Venant problems for a helical spring. PMM Journal of Applied Mathematics and Mechanics 1998;62:641-8.
17. Ustinov YA. Solutions of the Saint-Venant problem for a cylinder with helical anisotropy. PMM Journal of Applied Mathematics and Mechanics 2003;67:89-98.
18. Stephen NG, Wang PJ. On Saint-Venant's principle in pin-jointed frameworks. International Journal of Solids and Structures 1996;33:79-97.
19. Synge JL. The problem of Saint-Venant for a cylinder with free sides. Quarterly of Applied Mathematics 1945;2:307-17.
20. Dougall J. An analytical theory of the equilibrium of an isotropic elastic rod of circular cross section. Transactions of the Royal Society of Edinburgh 1913;49:895-978.
21. Getman IP, Ustinov YA. On the energy flux on resonances in semi-infinite bodies. Soviet Physics Doklady 1990;35:93-5.
22. Getman IP, Ustinov YA. Wave propagation in an elastic longitudinally inhomogeneous cylinder. PMM Journal of Applied Mathematics and Mechanics 1990;54:83-7.
23. Zhong WX, Williams FW. Physical interpretation of the symplectic orthogonality of a Hamiltonian or symplectic matrix. Computers and Structures 1993;49:749-50.
24. Moler C, Van Loan C. Nineteen dubious ways to compute the exponential of a matrix. SIAM Review 1978;18:801-36.
25. Massonnet C. Two-dimensional problems. In: Flugge W editor. Handbook of Engineering Mechanics. New York: McGraw-Hill; 1962 [Chapter 37].
26. Zhong WX. A new systematic methodology for theory of elasticity. Dalian University of Technology Press, 1995 [In Chinese].