References

Alampalli, S. and Kunin, 1. (2002) Rehabilitation and field testing of an FRPbridge deck on a truss bridge. Compo site Structures, 57(1-4),373-375

Ambartsumyan, S.A. (1970) Theory of Anisotropic Plates. TechnomicPublications, Stanford Co.

Anwer , M.N. and Sherief, H.H. (1988) State space approach to generalizedthermalelasticity. Journal ofThermal Stresses , 11,353-365.

Auricchio, F. and Sacco , E. (1999) A mixed-enhanced Finite-Element for theanalysis of laminated composite plates. lntemational Journal of NumericalMethods in Engineering, 44,1481-1504.

Babich , Y. (1972) Equilibrium stability of three-dimensional orthotropic bodiesunder small deformation. Prikladnaya Mekanika , 8(2), 16-24.

Bahar, L.Y. (1972) Transfer matrix approach to layered system. Journal ofEngineering Mechanics , 9(5), 1159-1172.

Bahar, L.Y. and Hetnarski, R.B. (1978) State space approach to thermoelasticity.Journal ofThermal Stresses, I, 135-145.

Bahar , L.Y. and Hetnarski, R.B. ( 1980) Coupled thermo-elasticity of a layeredmedium. Journal ofThermal Stresses, 3,141-152.

Beakou , A. and Touratier, M. (1993) A rectangular finite element for analysingcomposite multi-layered shallow shells in statics , vibration and buckling.International Journal ofNumerical Methods in Engineering, 36,627-653.

Becker, W. (1993) Closed-form solution for the free-edge effect in cross-plylaminates. Composite Structures, 26, 39-45.

Berthelot, J. (1999) Composite Materials: Mechanical Behaviour and StructuralAnalysis, Springer-Verlag, New York.

Bhirnaraddi, A. (1991) Free vibration analysis of doubly-curved shallow shells onrectangular planform using three-dimensional elasticity theory. lnternationalJournal ofSolids and Structures, 27(7), 897-913 .

Bhirnaraddi, A. and Chandrashekhara, K. (1992) Three-dimensional elasticitysolution for static response of simply supported orthotropic cylindrical shells .Composite Structures, 20, 227-235.

258 References

Boresi, AP., Schmidt, RJ. and Sidebottom, a .M. (1993) Advanced Mechanics ofMaterials , 5lh edn, John Wiley & Sons, Inc.

Brebbia, C.A, Telles, J.c.F. and Wrobel, t.c. (1984) Boundary ElementTechniques: Theory and Applications in Engineering. Springer-Verlag, Berlin andHeidelberg.

Butler, H. (1971) Theory of elasticity of a multilayered medium. Journal ofElasticity, I, 125-143.

Celep, Z. (1980) Free vibration of some circular plates of arbitrary thicknes s.Journal ofSound and Vibration. 70(3), 379-388 .

Chamis , C.C. and Sendeckyj, G.P. (1968) Critique on theories predictingthermoelastic properties of fibrous composites . Journal of Composite Materials,July, 332-358.

Chandrashekhara, K and Gopalakrishnan, P. (1982) Elasticity solution for amultilayered transversely isotropic circular cylindrical shell. Journal of AppliedMechanics . 48, 108-114.

Chandrashekhara, K and Rao, KS.N. (1998) Method of initial functions for theanalysis of laminated circular cylindrical shells under axisymmetric loading.Mechanics of Composite Materials and Structures , 5, 187-201.

Chen , W.Q., Ding, HJ. and XU, R.Q. (2001) Three-dimensional static analysis ofmulti-layered piezoelectric hollow spheres via the state space method.International Journal ofSolids and Structures , 38,4921-4936.

Chern, Y.c. and Chao, C.c. (2000) Comparison of natural frequencie s of laminatesby 3-D theory. Journal ofSound and Vibration, 230(5), 1009-1030.

Cheung, Y.K . and Wu, C.L (1972) Free vibrations of thick layered cylindershaving finite length with various boundary conditions. Journal of Sound andVibration, 24(2), 189-200.

Chree, C. (1889) The equation of an isotropic elastic solid in polar and cylindricalco-ordinates, their solution and application. Transaction s of CambridgePhilosophical Society, 14,250-369.

Chou, F.H. and Achenbach, J.D. (1972). Three-dimensional vibrations oforthotropic cylinders , Journal ofEngineering Mechanics , 98, 813-822 .

Christensen, R.M. (1979) Mechanics of Composite Materials. John Wiley andSons , New York.

Copson , E.T. (1975) Partial Differential Equations. Cambridge University Press ,Cambridge.

DeRusso , P.M., Roy, RJ., Close, C.M. and Desrochers , AA (1998). StateVariables for Engineers. John Wiley & Sons, Inc.

Ding, HJ. and XU, R.Q. (2000) Free axisymmetric vibration of laminatedtransversely isotropic annular plates. Journal of Sound and Vibration, 230(5),1031-1044.

References 259

Dong, S.B. (2000) Buckling analysis of angle-ply multi-laminated long hollowcylinders, Discussion. Journal ofEngineering Mechanics, 126(8),887.

Dong, S.B. and Goetschel , D.B. (1982) Edge effects in laminated composite plates .Journal ofApplied Mechani cs, 49,129-135.

Eason, G., (\962) On the vibration of anisotropic cylinders and spheres . AppliedScience Research, 12, 81-85.

Elgerd, O.L. (1967) Control System The01)'. McGraw-Hili, Kogakusha, Inc.

Eringen , A.C. and Maugin, G.A. (1991) Electrodynamics of Continua. Springer,Berlin.

Fan, J.R. (\ 996) Exact Theory ofLaminated Thick Plates and Shells . Science Press ,Beijing.

Fan, J.R. and Ding, KW. (\ 993a) Analytical solution for thick closed laminatedcylindrical shells. International Journal ofMechanical Sciences, 35(8), 657-668 .

Fan, J.R. and Ding, KW. (l993b) Exact solution for thick laminated closedcylindrical shells with two clamped edges. Applied Mathematical Modelling, 17,632-641.

Fan, J.R. and Ding , KW. (\ 995) Exact solution for laminated thick cantilevercylinders. Applied Mathematics and Mechanics, 16(2), 133-147.

Fan, J.R. and Sheng, H.Y. (\ 992) Exact solution for thick laminates with clampededges. Acta Mechanica Sinica , 24, 574-583 .

Fan, J.R. and Sheng, H.Y. (1997) Exact solution for laminated continuous opencylindrical shells. Applied Mathematics and Mechanic s, 18(II), 1073-1086.

Fan, J.R. and Sheng, H.Y. (2002) Personal correspondences.

Fan, J.R. and Ye, J.Q. (1990a) A series solution of the exact equation for thickorthotropic plates. International Journal ofSolids and Structures, 26(7) , 773-778.

Fan, J.R. and Ye, J.Q. (1990b) An exact solution for the statics and dynamics oflaminated thick plates with orthotropic layers . International Journal of Solids andStructures, 26(5/6), 655-662.

Fan, J.R. and Ye, J.Q. (\ 99Oc) Exact solutions for axisymmetric vibration oflaminated circular plate. Journal ofEngineering Mechanics, 116(4),920-927.

Fan, J.R. and Ye, J.Q. (\ 993) Exact solutions of buckling for simply supportedthick laminates. Composite Structures, 24, 23-28 .

Fan, J.R. and Zhang, J. (\992a) Analytical solutions for thick doubly curvedlaminated shells. Journal ofEngineering Mechanics, 118(7), 1338-1356 .

Fan, J.R. and Zhang, J. (1992b) Exact solutions for thick laminated shells, Sciencein China, 35(11) , 1343-1355 .

Faraji, S. and Archer, R.R. (1985) Method of initial functions for thick shells .International Journal ofSolids and Structures, 21, 851-863 .

260 References

Faraji, S. and Archer, R.R. (1989) Method of initial functions for thick transverselyisotropic shells.lngenieur Archive, 60, 1-9.

Fliigge, W. and Kelkar, V.S. (1968) The problem of an elastic circular cylinder.

International Journal ofSolids and Structures, 4, 397-420.

Folkes, M.J. and Arridge, R.G.e. (1975) The measurement of shear modulus inhighly anisotropic materials: The validity of St. Venanat 's Principle. Journal ofPhysics D: Applied Physics, 8, 1053-1064.

Forsberg, K. (1964). Influence of boundary conditions on the modal characteristicsof thin cylindrical shells. American Institute ofAeronautics and Astronautics, 2-12,2150-2157

Garg, S.K., Svalbonas, V. and Gurtman, G.A (1973) Analysis of StructuralComposite Material. M. Dekker, New York.

Ghosh, AK. and Agrawal, M.K., (1994) Radial vibration of spheres. Journal ofSound and Vibration, 171,315-322.

Goetschel, D.B. and Hu, T.H. (1985) Quantification of Saint-Venant's principle fora general prismatic member. Computers and Structures, 21, 869-874.

Grigorenko, Y.M., Vasilenko, AT. and Parkratova, N.D. (1974) Computation ofthe stressed state of thick-walled inhomogeneous anisotropic shells. PrikladnayaMekhanika, 10(5), 86-93.

Halpin, J.e. and Tsai, S.W. (1969) Effects of environmental factors on compositematerials. AFML-TR 67-243 (june)

Hashin, Z. (1965) On elastic behavior of fibre reinforced materials of arbitrarytransverse plane geometry . Journal ofMechanics and Physics ofSolids , 13, 119.

Hashin, Z. and Rosen, B.W. (1964) The elastic moduli of fiber-reinforcedmaterials. Journal ofApplied Mechanics, June, 223-232.

Hawkes, T.D. and Soldatos, K.P. (1992) Three-dimensional axisymmetricvibrations of orthotropic and cross-ply laminated hollow cylinders. AIM Journal,30, 1089-1098.

Hermans, U. (1967) The elastic properties of fibre reinforced materials when thefibers are aligned. Proceedings Koninklijke Nederlandse Akademie vanWetenschappen, Series B,70(1), 1-9.

Heylinger, P.R. (1991), Axisymetric free vibrations of finite anisotropic cylinders.Journal ofSound and Vibartion, 148,507-520.

Hidebrand, EB. (1952) Methods of Applied Mathematics , Prentice-Hall,Englewood Cliffs, NJ.

Hill, R. (1964) Theory of mechanical properties of fibre-strengthened materials: I.Elastic behaviour. Journal ofMechanics and Physics ofSolids , 12, 199.

Hohn, F. (1973) Element Matrix Algebra 3rd edn, The Macmillan Company, NewYork.

References 261

HolIaway, L.C . and Leeming, M.B. (1999) Strengthening of Reinforced ConcreteStructures: Using Externally Bonded FRP Composites in Structural and CivilEngineering . CRC Press .

Horgan, C.O . and Knowles, J.K (1983) Recent developments concerning Saint­Venant's principal. Advances in Applied Mechanics, Vo1.23, J.W . Hutchinson, ed.,Academic Press, New York, pp. I79-269 .

Horgan, C.O. (1989) Recent developments concerning Saint-Venant's principle:An update . Applied Mechanics Review, 42,295-303.

Hu, H.C. (1981) Variational Principles and Their Applications in Mechanics ofElasticity . Science Press, Beijin .

Huang , KH. and Dasgupta, A. (1995) A layer-wise analysis of free vibrations ofthick composite cylindrical shelIs. Journal ofSound and Vibration, 186,207-222.

Huang , N.N. (1995) Exact analysis for three-dimensional free vibrations of cross­ply cylindrical and doubly-curved laminates. Acta Mechanica, 108,23-34.

Huang , N.N. and Tauchert, T.R. (1991) Thermoelastic solution for cross-plycylindrical panels. Journal ofThermal Stresses, 14,227-237.

Iyengar, KT.S.R. Chandrashekhara, K. and Sebastian (1975) Thick circularcylindrical shelIs under axisymmetric loading . Acta Mechanica, 23, 137-144.

Iyengar, KT.S.R. and Raman , P.V . (1980) , Axisymmetric free vibration of thickannular plates . Journal ofthe Acoustical Society ofAmerica, 68, 1748-1749.

Iyengar, KT.S.R. and Pandya, S.K. (1986), Application of the method of initialfunctions for the analysis of composite laminated plates. Ingenieur Archive, 56,407-4H'.

Jeffreys, H. (1957) Cartesian Tensors. Cambridge University Press , London.

Jones, R.M. (1975) Mechanics of Composite Materials. Hemisphere Publishing,New York.

Jiang , L.Z. and Lee, J.S. (1994) Plane orthotropic layered by transfer matrix-splineboundary element. Journal ofEngineering Mechanics, 120(5), 1026-1041.

Kalamkarov, A.L. (1992) Composite and Reinforced Elements of Construction.Wiley & Sons Ltd, Chichester.

Kaprielian, P.V . (1985) The Effects of Holes and Free Edges on the Stresses inLaminated Plates . PhD thesis, University of Nottingham, England.

Kaprielian, P.V., Rogers, T.G . and Spencer, AJ.M. (1988) Exact theory for thestretching and bending of laminated plates by edge loading,. I: Isotropic plates .Phil. Trans. R. Soc. Lond. A234, 565-594.

Kardomateas, G.A. (2000) Effect of normal strains in buckling of thick orthotropicshelIs. Journal ofAerospace Engineering, 13(3),85-91.

262 References

Kennett, B.L.N. (1983) Seismic Wave Propagation in Stratified Media. CambridgeUniversity Press.

Khdeir, AA, Reddy, J.N. and Frederic , D. U989) A study of bending, vibrationand buckling of cross-ply circular cylindrical shells with various shell theories.International Journal ofEngineering Sciences, 27, 1337-1351.

Khdeir, A.A. and Reddy, J.N. (1990) Influence of edge conditions on the modalcharacteristics of cross-ply laminated shells . Computers and Structures , 34, 817­826.

Klemm, J.L. and Little, R.W. (1970) The semi-infinite elastic cylinder under self­equilibrated end loading. SIAM Journal ofApplied Mechanics , 19, 712-729 .

Knowles, J.K (1966) On Saint-Venant's Principal in the two dimensional lineartheory of elasticity. Archive for Rational Mechanics and Analysis, 21, 1-22

Lee, J.S. and Jiang, L.Z. (1996) Exact electroelastic analysis of piezoelectriclaminae via state space approach. International Journal of Solids and Structures,13(7), 977-990.

Lekhnitsk ii, S.G. (1963) Theory of Elasticity of an Anisotropic Elastic Body.Holden-Day, Inc, San Francisco .

u , S, Wang, R., Luo, Z. and Hua, X. (1985) Analytical solution for interlaminarstresses in a fiber-reinforced double-layer cylindrical shell. Acta Mechanica Sinica ,2,159-170.

Librescu, L., Khdeir, A.A. and Frederick , D. (1989) A shear deformable theory oflaminated composite shallow shell type panels and their response analysis, l-freevibration and buckling . Acta Mechanica , 76, 1-33.

Lur'e; AI., Mcvean, D.B. and Radok, J.R. (1964) Three-dimensional Problems ofthe Theory ofElasticity. Interscience Publishers .

McLachlan , N.W. (1955) Bessel Functions for Engineers , 2nd edn. OxfordUniversity Press, London .

Miller, KL. and Horgan, C.O. (1995) End effects for plane deformations of anelastic anisotropic semi-infinite strip. Journal ofElasticity , 38,261 -316.

Mirsky, I. (1966) Three dimensional and shell theory analysis for axisymmetricvibrations of orthotropic shells . Journal ofAcoustics Society of America, 39, 549­554.

Moore, I.D. (1990) Three-dimensional response of elastic tubes. InternationalJournal ofSolids and Structures, 26, 391-400 .

Noor, AK and Burton, W. S. (1989). Assessment of shear deformation theoriesfor multilayered composite plates. Applied Mechanics Review, 42, 1-13.

Noor, A.K and Burton, W. S. (I 990a). Assessment of computational models for ofmulti-layered composite shells. Applied Mechanics Review, 43,67-97.

References 263

Noor, A.K. and Burton, W. S. (I 990b). Three-dimensional solutions forantisymmetrically laminated anisotropic plates. Journal ofApplied Mechanics, 57,182-188.

Noor, A.K. and Peters, J. M. (1989) Stress, vibration, and buckling of multilayeredcylinders. Journal ofStructural Engineering, 115,69-88.

Nosier, A. and Reddy, J.N. (1992) Vibration and stability analyses of cross-plylaminated circular cylindrical panels. Journal of Sound and Vibration, 157, 139­159.

Nye, J.F. (1976) Physical Properties of Crystal and Their Representation byTensors and Matrices. Oxford University Press, Oxford.

Pagano , N.J. (1969) Exact solutions for composite laminates in cylindricalbending. Journal ofComposite Materials, 3, 398-41 I.

Pagano, N.J. (1970) Exact solutions for rectangular bi-directional compositeaminates in cylindrical bending. Journal ofComposite Materials, 4(1), 21-34.

Poltorak, K. and Nagaya, K. (1985). A method for solving free vibration problemsof three-layered plates with arbitrary shapes. Journal of Acoustics Society ofAmerica, 78(6), 2042-2048 .

Rayleigh, L. (1877) Theory ofSound. Cambridge University Press.

Reddy, IN. (1993). An evaluation of equivalent-single-layer and layerwisetheories of composite laminates . Composite Structures, 25, 21-35.

Reissner, E. (1945) The effect of transverse shear deformation on the bending ofelastic plates. Journal ofApplied Mechanics. 12, 69-77.

Reissner, E. (1950) On a variational theorem in elasticity, Journal of Mathematicsand Physics . 29(2), 90-95

Ren, J.G. (1989) Analysis of simply supported laminated circular cylindrical shellroofs . Composite Structures , 11,277-292.

Robbins, D.H. and Reddy, IN. (1993) . Modelling of thick composites using alayer-wise laminated theory. International Journal of Numerical Methods inEngineering, 36, 655-677 .

Robbins, D.H. and Reddy, J.N. (1996). Variable kinematic modeling of laminatedcomposites plates, International Journal ofNumerical Methods in Engineering, 39,2283-2317.

Rogers, T.G., Watson, P. and Spencer, A.lM. (1992) An exact three-dimensionalsolution for normal loading of inhomogeneous and laminated anisotropic elasticplates of moderate thickness . Proceedings of Royal Society. London, A437, 199­213.

Rogers, T.G., Watson, P. and Spencer, A.J.M. (1995) Exact three-dimensionalelasticity solutions for bending of thick inhomogeneous and laminated strips undernormal pressure. International Journal of Solids and Structures, 32(12), 1659­1673.

264 References

Ruddock, GJ. and Spencer, AJ.M. (1997) A new approach to stress analysis ofanisotropic laminated elastic cylinders. Proceedings of Royal Society, London, A,453, 1067-1082.

Shah, A.H., Ramkrishnan, V.V. and Datta, S.K, (1969a), Three-dimensional andshell theory analysis of elastic waves in a hollow sphere Part I: Analyticfoundation. Journal ofApplied Mechanics. 36, 431-439 .

Shah, A.H., Ramkrishnan , V.V. and Datta, S.K, 1969b, Three-dimen sional andshell theory analysis of elastic waves in a hollow sphere Part 2: Numerical results,Journal ofApplied Mechanics, 36,440-444.

Sheng . H,Y. (1999). Axisymmetric bending of laminated circular plate witharbitrary thickness. Journal of Hefei University of Technology, 22(4), 61-65 .

Sheng . H,Y. (2000a). Thick laminated circular plates on elastic foundationsubjected to a concentrated load. Structural Engineering and Mechanics, 10(5),441-449

Sheng. H,Y. (2000b). Analytical solution of bending problem for thick laminatedcircular plates on elastic foundation with free edges. Chinese Journal ofGeotechnical Engineerin g, 22(3), 323-326.

Sheng, RY. and Fan, lR. (2000). Variational solutions for static and dynamicanalyses of thick laminated open cylindrical shells. Journal of VibrationEngineering , 13(4),552-558.

Sheng, H.Y., Fan, lR. and Liu, H.X. (1997). A variational solution for vibrationanalysis of laminated plates with arbitrary thickness. Journal ofHef ei University ofTechnology, 20(6), 22-27.

Sheng, RY., Fan, l .R. and Liu, H'x. (1998). A variational solution for laminatedclosed cylindrical shells with arbitrary thickness. Journal of Anhui Institute ofArchitecture, 6(1), 15-21.

Sheng, RY. and Ye, lQ. (2002a) A semi-analytical finite element for laminatedcomposite plates. Composite Structures, 57(1-4), 117-123.

Sheng, H.Y. and Ye, lQ. (2002b) A state space finite element for laminatedcomposite plates. Computer Methods in Applied Mechanics and Engineering,191(37-38) ,4295-4276.

Soldatos, K.P. (1994) Review of three dimensional dynamic analyses of circularcylinders and cylindrical shells. Applied Mechanics Review, 47(10), 501-516.

Soldatos, KP. and Hadjigeorgiou , V.P. (1990) Three-dimen sional solution of thefree vibration problem of homogeneou s isotropic cylindrical shells and panels.Journal ofSound and Vibration, 137, 369-384.

Soldatos, K.P. and Hawkes, T.D. (1991) An iterative three-dimensional solution·ofthe free vibration problem of homogeneous orthotropic hollow cylinders.Structural Dynamics 2 (eds Kratzig et at.), Balkema, Rotterdam, pp.883-889.

References 265

Soldatos, KP. and Ye, I.Q . (1994). Wave propagation in anisotropic laminatedhollow cylinders of infinite extent. Journal ofAcoustics Society ofAmerica, 96(5) ,Part I, 3744-3752 .

Soldatos. K.P. and Ye, J.Q. (1995a) Axisymmetric static and dynamic analysis oflaminated hollow cylinders composed of monoclinic elastic layers. Journal ofSound and Vibration, 184(2),245-259.

Soldatos, KP. and Ye, I.Q . (1995b). Stationary thermoelastic analysis ofhomogeneous orthotropic and cross-ply laminated cylinders and cylindrical panels.Acta Mechanica, 110(1-4), 1-18.

Spencer, AJ.M., Rogers, T.G. and Watson, P. (1993a) Transfer matrix methodapplied to anisotropic inhomogeneous, non-circular elastic cylinders, in Anisotropyand inhomogeneity inelasticity and Plasticity, AMD 158, ASME, 7-11.

Spencer, A.I.M., Watson, P. and Rogers, T.G. (I 993b) Exact theory ofheterogeneous anisotropic elastic plates. Material Science Forum, 123-125, 235­244.

Spencer, AJ.M., Watson, P. and Rogers, T.G. (1990) Stress analysis of anisotropiclaminated circular cylindrical shells, in Recent Developments in Compositematerials Structures (Hui, D and Sun, C.T., eds) AD 19 and AMD 1l3, ASME,New York, 57-60.

Spencer, A.I .M., Watson, P. and Rogers, T.G. (1995) Stress and deformation inmoderately anisotropic inhomogeneous elastic plates. Zeilschrift fur AngewandteMathematik und Physik, 46, 5225-5244.

Spilker, R.L. (1982). Hybrid-stress eight element for thin and thick multilayeredlaminated plates. International Journal of Numerical Methods in Engineering, 18,801-828.

Srinivas, S. (1974) Analysis of laminated, composite, circular cylindrical shellswith general boundary conditions . NASA TR R-4/2 (April).

Srinivas, S. and Rao, A.K (1970) Bending, vibration and buckling of simplysupported thick orthotropic rectangular plates and laminates. International JournalofSolids and Structures, 6, 1463-1481.

Stephen, N.G. and Wang, M.Z. (1992) Decay rates for hollow circular cylinder.Journal ofApplied Mechanics, 59, 747-753.

Stephen, N.G. and Wang, P.I. (1996) Saint Venant decay-rates-A procedure for theprism of general cross-section . Computers and Structures, 58, 1059-1066.

Tarn, I.Q . and Wang, YM. (2001) Laminated composite tubes under extension,torsion, bending, shearing and pressuring: a state space approach. InternationalJournal ofSolids and Structures, 38, 9053-9075.

Timarci, T. and Soldatos , KP. (1994) Comparative dynamic study for symmetriccross-ply circular cylindrical shells on the basis of a unified shear deformable shelltheory. Journal ofSound and Vibration, 187(4), 609-624.

266 References

Tsai, S.W. (1966) Mechanics of composite material, Part II, Theoretical aspects,Air Force Materials Laboratory Tech Rept, AFML-TR-149.

Toupin, R.A., (1965) Saint-Venant's principle. Archive for Rational Mechanic s andAnalysis, 18, 83-96.

Tullini, N. Savoia, M. and Horgan, e.O. (1997) End effects in multilayeredorthotropic strips with imperfect bonding. Mechanics ofMaterials, 26, 23-34.

Varadan, T.K. and Bhaskar, K. (1991) Bending of laminated orthotropic cylindricalshells-an elasticity approach, Composite Structures, 17, 141-156.

Vinson, J.R. and Sierakowski, R.L. (1987) The Behavior of Structures ComposedofComposite Materials. Martinus Nijhoff Publishers .

Vlasov, V.Z. (1957) The method of initial functions in problems of theory of thickplates and shells, in Proc. Ninth Int. Congress Appl. Mech. , Brussels, 321-330 .

Wang, SJ. (1987) Introduction to the Mechanics of Composite Materials .Chongqin University Press, China .

Wang, X. (1994). An elastodynamic solution for an anisotropic hollow sphere .International Journal ofSolids and Structures, 31, 903-911.

Wang, Y.M. Tarn, J.Q. and Hsu, C.K. (2000) State space approach for stress decayin laminates. International Journal ofSolids and structures , 37, 3535-3553.

Washizu, K. (1975) Variational Methods in Elasticity and Plasticity . 2nd edn,Pergamon Press, Oxford.

Watson, P. (1991) The Stress and Deformation of Laminated Elastic Plates andShells. PhD thesis, University of Nottingham.

Whitney, J.M. (1967) Elastic moduli of unidirectional composites with anisotropicfilaments. Journal ofComposite Materials, April, 188-193.

Whitney, J.M. (1987) Structural Analysis of Laminated Anisotropic Plates .Technomic Publishing Corp.

Whitney, lM. and Riley, M.B. (1964) Elastic stress-strain proerties of fibre­reinforced composite materials. AFML-TR-65-238, December.

Wijeyewickrema, A.e., Horgan, c.o. and Dundurs, J. (1996) Further analysis ofend effects for plane deformations of Sandwich strips. International Journal ofSolids and Structures , 33,4327-4336.

Wu, ZJ. and Wardenier, J. (1998). Further investigation on the exact elasticitysolution for anisotropic thick rectangular plates. International Journal of Solidsand Structures, 35 (7-8), 747-758.

Wynn, P. (1956) On a procrustean technique for the numerical transformation ofslowly convergent sequences and series. Proceeding of Cambridge PhilosophicalSociety, 52, 663-671.

References 267

Xu, K, Noor, A.K and Tang, Y.Y. (1995) Three-dimensional solutions forcoupled thermoelectroelastic response of multilayered plates. Computer Methods inApplied Mechanics and Engineering, 126, 355-371.

Xu, K, Noor, A.K and Tang, Y.Y. (1997) Three-dimens ional solutions for freevibrations of initial stressed thermoelectroelastic multilayered plates. ComputerMethods in Applied Mechanics and Engineering , 141, 125-139.

Yao, J.e. (1969) Long cylindrical tube subjected to two diametrically oppositeloads. The Aeronautical Quarterly, 20, 365-381.

Ye, J.Q. (1995a) Axisymmetric buckling of homogeneous and laminated circularplates. Journal ofStructural Engineering, 121(8), 1221-1224.

Ye, J.Q. (1995b) Axisymmetric buckling analysis of homogeneous and laminatedannular plates. International Journal of Pressured Vessels and Piping, 62, 153­159.

Ye, J.Q. (1997a) Axisymmetric vibration analysis of laminated hollow cylinderswith ring stiffeners. Composite Structures, 38(1-4), 151-156.

Ye, J.Q. (1997b) A three-dimensional free vibration analysis of cross-ply laminatedrectangular plates with clamped edges. Computer Methods in Applied Mechanicsand Engineering, 140,383-392.

Ye, J.Q. (1997c) Axisymmetric vibration of laminated annular plates composed oftransversely isotropic layers. Journal ofSound and Vibration, 205(2), 250-256.

Ye, J.Q. (1999) Buckling analysis of angle-ply multi-laminated long hollowcylinders' , Journal ofEngineering Mechanics, 125(8),964-969.

Ye, J.Q. (2000a), Vibration Analysis of laminated composite panels with clampededges. Proceedings 5th Conf. Engineering System Design and Analysis, July 10-13,2000, Montreux, Switzland .

Ye, J.Q. (2000b) Discussion on 'Buckling analysis of angle-ply multi-laminatedlong hollow cylinders', Closure. Journal ofEngineering Mechanics, 125(8).

Ye, J.Q. (2001a) Decay rate of edge effects in cross-ply-laminated hollowcylinders . International Journal ofMechanical Sciences, 43, 455-470.

Ye, J.Q. (2001b) Edge effects in angle-ply laminated hollow cylinders . CompositeStructures, 52, 247-253.

Ye, J.Q. and Soldatos, KP. (1994a), Three-dimensional stress analysis orthotropicand cross-ply laminated hollow cylinders and cylindrical panels. ComputerMethods in Applied Mechan ics and Engineering, 117, 331-351.

Ye, J.Q. and Soldatos, KP. (1994b), Three-dimensional vibration of laminatedcylinders and cylindrical panels with symmetric or antisymmetric cross-ply lay-up.Composites Engineering, 4(4), 429-444.

Ye, J.Q. and Soldatos, KP. (1995) Three-dimensional buckling analysis oflaminated composite hollow cylinders and cylindrical panels. International JournalofSolids and Structures, 32(13), 1949-1962.

268 References

Ye, J.Q. and Soldatos, K.P. (1996), Three-dimensional vibrations of laminatedcomposite plates and cylindrical panels with arbitrarily located lateral surfacespoint supports. International Journal ofMechanical Sciences, 38,271-281.

Ye, J.Q. and Soldatos, K.P. (1997), Three-dimensional vibrations of cross-plylaminated hol1ow cylinders with clamped edge boundaries . Journal of Vibrationand Acoustics, 119,317-323.

Young, P.G. and Dickinson, S.M. (1994) Free vibration of a class of solids withcavities . International Journal ofMechanical Sciences , 36, 1099-1107.

Zhong, W.x. and Williams, F.W. (1994) A precise time step integration method.Proceedings of Institution of Mechanical Engineers , Part C: Journal ofMechanical Engineering Sciences, 208,427-430

Index

A

14,22,28178-180168-175

217143-151

9177838678

204

cross -ply laminatesaxisymmetric plates

Buckling of shellsangle-ply laminatescross-ply laminatespre-buckling state

continuous platescross-ply laminatesplates with clamped edgesplates with free edgessimply supported plates

Bending of cylindrical shells175-186

anisotropic inhomogeneous,non-circular cylindersshells with simply supportededges 175shells with clamped edges 181shells with free edges 183

Bending of spheres 199Bessel functions 102Boundary element method 250-253Boundary integral equation 252Buckling of laminated plates 76-77,

114-11976

114159-175

168159159

Angle-ply laminatebending,bucklingstress decayvibration,

Anisotropic materialsdefinition of 22stress-strain relations 21

Asymptotic solution 97Axisymmetric bending of laminates

circular plates 119-123hollow cylinders 178-180plates on foundations 123-126

Axisymmetric buckling of laminatesannular plates 117-119circular plates 115-117

Axisymmetric vibration of laminatesannular plates 108-114circular plates 102-108laminated sphere 191-199stiffened cylinders 158

Azimuthal displacement 191

B cBending of laminated plates

axisymmetric plates 119 Cayley-Hamilton method 46

270 Index

139167

D

41-43

50-52

213 ,216207,226216,222

205213214

208217224

84,181,18415-18,201

208,216,2243637483622

7-9253

2415161718

20233

exponentiallengthmodesratetorsionaltorsion less

Decay of stressesin a cross-ply cylinderin an angle-ply cylinderin a rectangular strip

Dirac functionDifferential arc lengthDifferential equation

first order 31time-invariant 32time-varying 52

Direction cosines 229Doubly -curved laminated shells 200

vibration of 200-204Dynamic stiffness equation 153

Eigen-expansionEigenvalues

distinctrepeated

EigenvectorsElastic constantsElasticity approach to moduliElliptic cavityEngineering constantsEquilibrium equations

rectangular systemcylindrical systemspherical systemdoubly-curved

Exponential matricescalculated by seriesexpansionscalculated by matrixtransformation 43-46calculated by Caley-Hamiltommethod 46-50calculated by time stepintegration method

E

142,178175-186159-175208-223

205159158186

128-159

77,175,181 ,18376,159-167

91208186

59-76141

Characteristic equation 36Characteristic value (see eigenvalue)Characteristic vector (see

eigenvector)Circular plate 102,115,119,123Composite material s 1-12

charaterisation of 4-9classification of 1-4definition of 13D modelling of 9-12

Constrained stiffness matrix 74,157Constraint equations 71,72,157Continuity conditions at interfaces

65,105,135146,165,197

212,24129

Decay 207damped sinusoidal 213,216,221

Continuous systemCoupling

bending and extensionbending and torsionlongitudinal and torsionaldeformations 144,151torsion and tension 222

Cross-ply laminatesbendingbucklingpiezoelectricstress decaythermoelasticityvibrationforced vibration

Cylindrical shellsaxisymmetricbendingbucklingdecay of stresseseccentric ellipticalpre-bucklingstiffenedthermoelasticityvibration

Index 271

F L

constructiondefinition ofplatesshellssymmetric

Lagrangian multiplier method 69,73154

Laminatesanti-symmetric 141,149,155,167

177,178,214,21533

58,99127,191,207

94,140,149,155,173174,176,177

6195,200

7

Law of mixturesLegendra polynomialLongitudinal modulus

G

Fibre composites 2Finite difference method 248-250Finite element method 228-247Fourier series 63,78,80,84,87,88

133,151,162,181Fourier inverse transfer 252Fourier transfer 251Free edges 86,109,126,183Fundamental matrix 33Fundamental solution 252

Galerkin methodweighted Galerkin form

Green's theorem

254255

231,233M

H

Hankel transform 112Homogeneous system 32,53Homogenisation 4Hooke's law 21

moniclinic 22orthotropic 23transversely isotropic 23isotropic 24

I

Interface stresses distributions 8195,124-125,176-179

,204,217,222223,225,243

Inhomogeneous system 249Isotropic material

definition of 24stress-strain relations 24

Interior point supports 156

Matrix (material)Matrix (mathematics)

constrained stiffness 74,157charateristic equation of 36diagonalisation of 39eigenvalues of 35exponential 33fundamental 33modal 39polynomial of 46similarity transformation of 40stiffness 70,153system 31,205transfer 33transition 33

Mechanical properties of fibres 2Mechanics of material approach

to moduli 5-7Meridianal displacement 192Metric coefficients 15

rectangular co-ordinates 16cylindrical co-ordinates 17spherical co-ordinates 18doubly-curved co-ordinates 201

Micromechanics 5,9Mixed variational equations 237

272 Index

Monoclinic materialsHooke's lawvibration of cylinder

22143

Q

Qusi-cylindrical co-ordinates 205

NR

Node functiondisplacementstress

Non-circular cylindersNon-homogeneous system

234234204

31,34,54

Reciprocal relations 25Betti 's theorem 252

Recursi ve formulation 137,I48165, I 97,212,24 I

Representative volume element 4-6

o s

3

256,8

230232

36195,200

46191919

19131325230

227250248228254

94,96234

246,8

73,154187186

185,20030

Self-equilibrated stresses 209,2 I3214,223

Semi-analytical methodstate equationboundary elementfinite differencefinite elementvariational

Sensitivity coefficientsShape functionShear modulus

longitudinalShells (see laminates)Spheroidal vibrationState equation

time-invarianttime-varying

State spaceState variables

judicious arrangmentState vectorStationary

energytemperaturethermo-elastic bending

Strainsdirectshear

Strain-displacement relations

Particle compositesPiezoelectric materials

bending of plates 9 I-97bending of hollow spheres 199electric displacements 92,200electric potential 93,200

Piezothermoelastic layer 93Plane strain 185Plates (see laminates)Poisson's ratios

LongitudinalPolynomials

characteristicLegendrematrix

Principlesvirtual displacementsvirtual forces

p

Orthotropic materialscompliances for 235definition of 23engineering constants 25Hooke's law 23material axes of 26stress-strain relations 23

Index 273

T

202021

202235

73207,208

2071414

95,18614212122232324

31,205

Unidirectionally reinforcedlaminate s

Unit impulse

Wave propagationWeighted Galerkin methodWeighted formWinkler's foundation

128254,255224,254

123

6-86-8

2,4-6,2383,181

230-233254-256

99-114128-159200-204191-200

19259-76

185,191230232230

224,230-233232

4

y

v

u

Young 's moduluslongitudinaltranverse

Variational method

w

Vibration of laminatesaxisymmetric platescylindrical shellsdoubly-curved shellshollow spheresradialrectangular platestorsional

Virtual displacemetVirtual forceVirtual strainVirtual work

ComplementaryVolume fraction·

rectagular systemcylindrical systemspherical systemdoubly-curved

Strain-stress relationsStrain energy

decay ofupper bound estimate

Stressshearthermaltensor

Stress-strain relationsgeneral anisotropicmonoclinicorthotropictransversely isotropicisotropic

System matrixSuccesssive approximation

method 53,127 ,136-138

Tensordielectric 92piezoelectric 92stress 14thermo-conductivity 187thermo-elasticity 187

Thermo-elasticity 186,94-96coefficients of expansion 188

Time-invariant system 32Time-varing system 52Time step integration method 50Torsion 185Transformation of stiffness 27Transverse modulus 8Transverse stresses (see interface

stresses)Transversely isotropic materials 23

Hooke's law 23plate 99-126spherical shell 191-199