Exact analysis of curved beams and arches with arbitrary end conditions: A Hamiltonian state space approach

Journal of Elasticity

Volumn 107, Issue 1, 2012, Pages 39-63

  Tarn, Jiann Quo ^a   Tseng, Wei Der ^a,b  

^a NATIONAL CHENG KUNG UNIVERSITY   (Taiwan)

^b NAN JEON INSTITUTE OF TECHNOLOGY   (Taiwan)

Author keywords

Curved beams; Cylindrical orthotropy; Eigenfunction; Hamiltonian; State space; Symplectic orthogonality

Indexed keywords

CURVED BEAMS; EIGEN FUNCTION; ORTHOTROPY; STATE SPACE; SYMPLECTIC;

ARCHES; CURVED BEAMS AND GIRDERS; EIGENVALUES AND EIGENFUNCTIONS; ELASTICITY;

HAMILTONIANS;

EID: 84855433792     PISSN: 03743535     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10659-011-9335-4     Document Type: Article

References (14)

1. Oden, J.T., Ripperger, E.A.: Mechanics of Elastic Structures, 2nd edn. McGraw-Hill, New York (1981)
2. Barber, J.R.: Intermediate Mechanics of Materials. McGraw-Hill, New York (2001)
3. Massonnet, C.: Two-dimensional problems. In: Flügge, W. (ed.) Handbook of Engineering Mechanics. McGraw-Hill, New York (1962). Chap. 37
4. Timoshenko, S.P., Goodier, J.N.: Theory of Elasticity, 3rd edn. McGraw-Hill, New York (1970)
5. J.Q. Tarn 2002 A state space formalism for anisotropic elasticity. Part I: rectilinear anisotropy Int. J. Solids Struct. 39 5143 5155 10.1016/S0020-7683(02)00411-0 1044.74006 1993198 (Pubitemid 35219009)
6. J.Q. Tarn 2002 A state space formalism for anisotropic elasticity. Part II: cylindrical anisotropy Int. J. Solids Struct. 39 5157 5172 10.1016/S0020-7683(02)00412-2 1087.74509 1993198 (Pubitemid 35219010)
7. J.Q. Tarn H.H. Chang W.D. Tseng 2009 Axisymmetric deformation of a transversely isotropic cylindrical body: a Hamiltonian state-space approach J. Elast. 97 131 154 10.1007/s10659-009-9213-5 1188.74006 2563155
8. J.Q. Tarn H.H. Chang W.D. Tseng 2010 A Hamiltonian state space approach for 3D analysis of circular cantilevers J. Elast. 101 207 237 10.1007/s10659-010-9256-7 05953004 2671638
9. Goldstein, H.: Classical Mechanics. Addison-Wesley, Reading (1965)
10. Arnold, V.I.: Mathematical Methods of Classical Mechanics. Springer, Berlin (1978)
11. Pease, M.C.: Methods of Matrix Algebra. Academic Press, New York (1965)
12. Kantorovich, L.V., Krylov, V.I.: Approximate Methods of Higher Analysis. Noordhoff, Groninger (1964)
13. Hildebrand, F.B.: Methods of Applied Mathematics, 2nd edn. Prentice-Hall, Englewood Cliffs (1965)
14. Sokolnikoff, I.S.: Mathematical Theory of Elasticity. McGraw-Hill, New York (1956)