References
- Al-Nageim, H., Mohammed, F., and Lesley, L. (1998), "Numerical results of the LR55 track system modelled as multilayer beams on elastic foundation," J. Constr. Steel Res., 46(1-3), 347-370. https://doi.org/10.1016/S0143-974X(98)00144-8
- Bechtold, J.E., and Riley, D.R. (1991), "Application of beams on elastic foundation and B-spline solution methodologies to parametric analysis of intramedullary implant systems," J. Biomech., 24(6), 441-448. https://doi.org/10.1016/0021-9290(91)90032-I
- Boyce, W.E., and DiPrima, R.C. (1997), Elementary Differential Equations and Boundary Value Problems, 6th edn., John Wiley & Sons, Inc., pp.436.
- Chen, C.N. (1998), "Solution of beam on elastic foundation by DQEM," J. Eng. Mech., ASCE, 124(12), 1381-4. https://doi.org/10.1061/(ASCE)0733-9399(1998)124:12(1381)
- Elser, M., Tschegg, E.K., and Stanzl-Tschegg, S.E. (1996), "Fracture behavior of polypropylene-fiber-reinforced concrete: Modelling and computer simulation," Comp. Sci. Tech., 56, 947-956. https://doi.org/10.1016/0266-3538(96)80017-0
- Filonenko-Borodich, M.M. (1940), "Some approximate theories of the elastic foundation", Uch. Zap. Mosk. Gos. Univ. Mekh., 46, 3-18 (in Russia).
- Filonenko-Borodich, M.M. (1945), "A very simple model of an elastic foundation capable of spreading the load", Sb. Tr. Mosk. Elektro. Inst. Inzh. Trans. No: 53 Transzheldorizdat (in Russian).
- Goldberg, D.E. (1989), Genetic Algorithms in Search, Optimization, and Machine Learning, Reading, Mass., US, Addison-Wesley Pub. Co.
- Hetenyi, M. (1946), Beams on Elastic Foundation, University of Michigan Press, Ann Arbor, Mich.
- Huk, D. (1988), "Postbuckling behavior of infinite beams on elastic foundations using Koiter's improved theory," Int. J. Non-linear Mech., 23(2), 113-123. https://doi.org/10.1016/0020-7462(88)90018-2
- Jain, L.K., and Wetherhold, R.C. (1992), "Effect of fiber orientation on the fracture toughness of brittle matrix composites," Acta Metall Mater., 40(6), 1135-1143. https://doi.org/10.1016/0956-7151(92)90412-8
- Karr, C.L., and Freeman, L.M. (1999), Industrial Application of Genetic Algorithms, CRC Press LLC.
- Kerr, A.D. (1964), "Elastic and viscoelastic foundation models," J. Appl. Mech., 31, 491-498. https://doi.org/10.1115/1.3629667
- Kerr, A.D. (1969), "Buckling of continuously supported beams," J. Eng. Mech. Div., ASCE, 95(EM1), 247-253.
- Kerr, A.D. (1984), "On the formal development of elastic foundation models," Ing.-Arc., 54, 455-464. https://doi.org/10.1007/BF00537376
- Kreyszig, E. (1993), Advanced Engineering Mathematics, 7th ed., John Wiley & sons, Inc., pp.128.
- Lentini, M. (1979), "Numerical solution of the beam equation with non-uniform foundation coefficient," J. Appl. Mech., 46, 901-904. https://doi.org/10.1115/1.3424675
- Leung, C.K.Y., and Li, V.C. (1992), "Effect of fiber inclination on crack bridging stress in brittle fiber reinforced brittle matrix composites," J. Mech. Phys. Solids, 40(6),1333-1362. https://doi.org/10.1016/0022-5096(92)90018-W
- Leung, C.K.Y., and Chi, J. (1995), "Crack-bridging force in random ductile fiber brittle matrix composites," J. Eng. Mech., ASCE, 121(12), 1315-1324. https://doi.org/10.1061/(ASCE)0733-9399(1995)121:12(1315)
- Li, V.C., Wang, Y., and Backer, S. (1991), "A micromechanical model of tension softening and bridging toughening of short random fiber reinforced brittle matrix composites," J. Mech. Physics of Solids, 39(5), 607-625. https://doi.org/10.1016/0022-5096(91)90043-N
- Li, V.C. (1992), "Postcrack scaling relations for fiber reinforced cementitious composites," ASCE J. Mater. Civ. Eng., 4(2), 41-57. https://doi.org/10.1061/(ASCE)0899-1561(1992)4:1(41)
- Liu, G.-S., and Lai, S.C. (1996), "Structural analysis model for mat foundations," J. Struct. Eng., ASCE, 122(9), 1114-1117. https://doi.org/10.1061/(ASCE)0733-9445(1996)122:9(1114)
- Mathews, J.H., and Fink, K.D. (1999), Numerical Methods Using MATLAB, 3rd., Prentice-Hall, Inc., 405-408.
- Michalewicz, Z. (1996), Genetic algorithms + data structures = evolution programs, 3rd ed., Berlin, New York, Springer-Verlag.
- Mourelatos, Z.P., and Parsons, M.G. (1987), "Finite element analysis of beams on elastic foundation including shear and axial effects," Comput. & Struct., 27(3), 323-331. https://doi.org/10.1016/0045-7949(87)90055-1
- Pasternak, P.L., (1954), "On a new method of analysis of an elastic foundation by means of two foundation constants," Gos. Izd. Lit. po Strait I Arkh, Moscow, the Soviet Union (in Russia).
- Press, W.H., Flannery, B.P., Teukolsky, S.A., and Vetterling, W.T. (1989), Numerical Recipes, Cambridge University Press, 289-293.
- Reissner, E. (1958), "A note on deflections of plates on a viscoelastic foundation," J. Appl. Mech., ASME, 25, 144-145.
- Selvadurai, A.P.S. (1979), Elastic Analysis of Soil-Foundation Interaction, Elsevier Sci. Publishing Co.
- Soh, C.K., and Yang, Y. (2000), "Genetic programming-based approach for structural optimization," J. Comput. Civ. Eng., ASCE, 14(1), 31-37. https://doi.org/10.1061/(ASCE)0887-3801(2000)14:1(31)
- Soldatos, K.P., and Selvadurai, A.P.S. (1985), "Flexure of beams on hyperbolic elastic foundation," Int. J. Solids Struct., 21(4), 373-388. https://doi.org/10.1016/0020-7683(85)90062-9
- Thambiratnam, D., and Zhuge, Y. (1996), "Free vibration analysis of beams on elastic foundation," Comput. & Struct., 60(6), 971-980. https://doi.org/10.1016/0045-7949(96)00053-3
- Timoshenko, S. (1956), Strength of Materials, Part II, 3rd ed., D. Van Nostrand Company, Inc.
- Ting, B.Y., and Mockry, E.F. (1984), "Beam on elastic foundation finite element," J. Struct. Eng., ASCE, 110, 2324-39. https://doi.org/10.1061/(ASCE)0733-9445(1984)110:10(2324)
- Vallabhan, C.V.G., and Das, Y.C. (1988), "Improved model for beams on elastic foundations," Elastic-Plastic Failure Modelling of Structures with Applications, Presented at the 1988 ASME Pressure Vessels and Piping Conf., Pittsburgh, PA, USA, v 141. Publ by ASME, New York, NY, USA, 107-113.
- Vallabhan, C.V.G., and Das, Y.C. (1991), "Modified Vlasov model for beams on elastic foundations," J. Geo. Eng., ASCE, 117(6), 956-966. https://doi.org/10.1061/(ASCE)0733-9410(1991)117:6(956)
- Vardy, A., Hu, X., and Brown, J. (1999), "Genetic algorithms for hydropower waterways," Dam Eng., 10(2), 69-98.
- Vlasov, V.Z., and Leontev, N.N. (1966), Beams, Plates and Shells on Elastic Foundations, Israel Program for Scientific Translations, Jerusalem, Isral.
- Waas, A.M. (1990), "Initial postbuckling behavior of beams on non-linear elastic foundations," Mech. Res. Commun., 17(4), 239-248. https://doi.org/10.1016/0093-6413(90)90084-P
- Wasti, S.T., and Senkaya, E. (1995), "Simple finite element for beams on elastic foundations," Strain, 31(4), 135-142. https://doi.org/10.1111/j.1475-1305.1995.tb00977.x
- Winkler, E. (1867), Theory of Elasticity and Strength, H. Dominicus, Prague, Czechoslovakia.