Bending response of a fiber-reinforced viscoelastic arched bridge model

Applied Mathematical Modelling

Volumn 27, Issue 3, 2003, Pages 233-248

  Allam, M N M ^a   Zenkour, A M ^b  

^a Mansoura University   (Egypt)

^b TANTA UNIVERSITY   (Egypt)

Author keywords

Bending response; Quadratic thickness variation; Reinforced viscoelastic beams; Small parameter and effective moduli

Indexed keywords

BEAMS AND GIRDERS; BENDING (DEFORMATION); BOUNDARY CONDITIONS; FIBER REINFORCED MATERIALS; MATHEMATICAL MODELS; STRUCTURAL LOADS; VISCOELASTICITY; VOLUME FRACTION;

QUASI-STATIC RESPONSE;

ARCH BRIDGES;

BENDING PROPERTY; BRIDGE; FIBER REINFORCED COMPOSITE; LOADING; TESTING; THICKNESS;

EID: 0037368076     PISSN: 0307904X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0307-904X(02)00123-3     Document Type: Article

References (26)

1. D. Abolinsh, Elasticity tensor for unidirectionally reinforced elastic material, Polym. Mech. 4 (1965) 25-59.
2. M.N.M. Allam, B.E. Pobedria, On solution of quasistatical problems anisotropic viscoelasticity, Izv. Acad. Nauk ArSSR, Mech. 31 (2) (1978) 19-27 (in Russian).
3. A.A. Illyoshin, B.E. Pobedria, Foundations of Mathematical Theory of Thermo-Visco-Elasticity, Nauka, Moscow, 1970 (in Russian).
4. D. Bland, The Linear Theory of Visco-Elasticity, Pergamon Press, New York, 1960.
5. C.J. Halpin, N.J. Pagano, Observations on linear anisotropic viscoelasicity, J. Compos. Mater. 2(1) (1968) 68-80.
6. M.N.M. Allam, Torsion of a composite, viscoelastic prismatic bar of triangular cross-section, Indian J. Pure Appl. Math. 13 (11) (1982) 1364-1368.
7. M.N.M. Allam, A.F. Ghaleb, Torsion of a composite, viscoelastic prismatic bar of rectangular cross-section, Appl. Math. Modelling 6 (1982) 197-201.
8. M.N.M. Allam, P.G. Appleby, On the plane deformation of fiber-reinforced viscoelastic plates, Appl. Math. Modelling 9 (1985) 341-346.
9. M.N.M. Allam, P.G. Appleby, On the stress concentrations around a circular hole in a fiber-reinforced viscoelastic plate, Res. Mech. 19 (1986) 113-126.
10. F. Essenburg, On the significance of the inclusion of the effect of transverse normal strain in problems involving beams with surface constraints, J. Appl. Mech. Trans. ASME, 97 Series E 42 (1) (1975) 127-132.
11. M. Levinson, A new rectangular beam theory, J. Sound Vib. 74 (1981) 82-87.
12. W.B. Bickford, A consistent higher-order beam theory, Dev. Theor. Appl. Mech. 11 (1982) 137-150.
13. A.A. Khdeir, J.N. Reddy, Free vibration of cross-ply laminated beams with arbitrary boundary conditions, Int. J. Eng. Sci. 32 (1994) 1971-1980.
14. A.M. Zenkour, Maupertuis-Lagrange mixed variational formula for laminated composite structures with a refined higher-order beam theory, Int. J. Non-Linear Mech. 32 (1997) 989-1001.
15. A.A. Khdeir, J.N. Reddy, An exact solution for the bending of thin and thick cross-ply laminated beams, Compos. Struct. 37 (1997) 195-203.
16. A.M. Zenkour, Transverse shear and normal deformation theory for bending analysis of laminated and sandwich elastic beams, Mech. Compos. Mater. Struct. 6 (1999) 267-283.
17. E. Ressiner, Remark on the theory of bending of plates of variable thickness, J. Math. Phys. 5 (1934) 363-366.
18. H.D. Conway, Closed form solutions for circular plates of variable thickness, J. Appl. Mech. 20 (1953) 564-569.
19. M. Ohga, T. Shigematsu, Bending analysis of plates with variable thickness by boundary element-transfer matrix method, Comput. Struct. 28 (1988) 635-641.
20. D.G. Fertis, M.M. Mijatov, Equivalent systems for variable thickness plates, J. Eng. Mech. ASCE 115 (1989).
21. D.G. Fertis, C.T. Lee, Elastic and inelastic analysis of variable thickness plates by using equivalent systems, Int. J. Mech. Struct. Mach. 21 (1993) 201-211.
22. D.G. Fertis, Nonlinear Mechanics, CRC Press, Boca Raton, 1993.
23. D.G. Fertis, Advanced Mechanics of Structures, Marcel Dekker, New York, 1996.
24. A.M. Zenkour, Elastic behaviour of an orthotropic beam/one-dimensional plate of uniform and variable thickness, J. Eng. Math. 44 (4) (2002) 331-344.
25. A.M. Zenkour, An exact solution for the bending of thin rectangular plates with uniform, linear, and quadratic thickness variations, Int. J. Mech., in press.
26. B.E. Pobedria, Structural anisotropy in viscoelasticity, Polym. Mech. 4 (1976) 557-561.