Variational principle of hybrid energy and the fundamentals of 3-D laminate theory - A new approach for the analysis of interlaminar stresses in composite laminates. (English) Zbl 0729.73280
Summary: This paper discusses the discontinuity of stresses and strains at interlaminar surfaces of the composite laminate and presents a three- dimensional laminate theory for composite materials. This paper also presents a new type of elastic energy based on the globally continuous variables in laminates, different from the traditional potential energy and complementary energy. Then a variational principle corresponding to the three-dimensional laminate theory is developed. The theory and the principle could be a basis of verifying the two-dimensional laminate theory and determining the interlaminar stresses near the free edges.
MSC:
| 74S30 | Other numerical methods in solid mechanics (MSC2010) |
| 74P10 | Optimization of other properties in solid mechanics |
| 74E30 | Composite and mixture properties |
| 74G70 | Stress concentrations, singularities in solid mechanics |
References:
| [1] | Lekhnitskii, S.G.,Theory of Elasticity of an Anisotropic Body, Gostekhizdat, Moscow (1950). (in Russian). Transl., Holden-Day, San Francisco (1963). Second Edition, Nauka, Moscow, (1977), (in Russian). Transl., Mir Publishers, Moscow (1981). |
| [2] | Pipes, R.B.,J. Compos. Mater.,4, Oct (1970), 538–548. |
| [3] | Altus, E., A. Rotem, and M. Shmueli,J. Compos. Mater.,14 (1980), 21–30. |
| [4] | Engblom, J.J. and O.O. Ochoa,Int. J. Numer. Methods Eng.,21, 10. Oct. (1985), 1759–1776. · Zbl 0588.73128 · doi:10.1002/nme.1620211003 |
| [5] | Heppler, G.R. and J.S. Hansen,Adv. in Compos. Mater.,1 Aug. (1980), 666–692. |
| [6] | Yeh, J.R. and I.G. Tabjbakhsh,J. Compos. Mater.,20, 4. Jul. (1986), 347–364. · doi:10.1177/002199838602000403 |
| [7] | Natarajan, R., S.V. Hoa, and T.S. Sankar,Int. Numer. Methods Eng.,23, 4. Apr. (1986). 623–633. · Zbl 0585.73138 · doi:10.1002/nme.1620230408 |
| [8] | Lucking, W.M., S.V. Hoa and T.S. Sankar,J. Compos. Mater.,18, 2. Mar. (1984), 188–198. · doi:10.1177/002199838401800207 |
| [9] | Rybicki, E.F.,J. Compos. Mater.,5 (1971), 354–360. · doi:10.1177/002199837100500305 |
| [10] | Khalil, S.A., C.T. Sun and W.C. Hwang,Int. J. Fract.,31, 1. May (1986), 37–51. · doi:10.1007/BF00033928 |
| [11] | Moriya, K.,Nippon Kikai Gakkai Ronbunshu a Hen,52, 478, Jun. (1986), 1600–1607. |
| [12] | Spilker, R.L. and D.M. Jakobs,Int. Numer. Methods Eng.,23, 4. Apr. (1986), 555–578. · Zbl 0584.73100 · doi:10.1002/nme.1620230404 |
| [13] | Wang, S.S. and F.G. Yuan,J. Appl. Mech.,50 (1983), 835–844. · Zbl 0526.73080 · doi:10.1115/1.3167154 |
| [14] | Hsu, P.W. and C.T. Herakovich,J. Compos. Mater.,11 (1977), 422–427. · doi:10.1177/002199837701100405 |
| [15] | Tang, S.,J. Compos. Mater.,10, 1, Jan. (1976), 69–78. · doi:10.1177/002199837601000106 |
| [16] | Bar-Yoseph, P. and T.H.H. Pian,J. Compos. Mater.,15, 3, May (1981), 225–239. · doi:10.1177/002199838101500303 |
| [17] | Bar-Yoseph, P. and T.H.H. Pian,Comput. Methods Appl. Mech. Eng.,36, 3, Mar (1983), 309–329. · doi:10.1016/0045-7825(83)90127-5 |
| [18] | Pagano, N.J.,Int. J. Solids Structures,14 (1978), 385–400. · Zbl 0377.73079 · doi:10.1016/0020-7683(78)90020-3 |
| [19] | Wang, J.T.S. and J.N. Dickson,J. Compos. Mater.,12 (1978), 390–401. · doi:10.1177/002199837801200404 |
| [20] | Oery, H., H. Reimerdes and S. Dieker,Z. Flugwiss Weltraumforsch,8, 6, Nov.–Dec. (1984), 392–404. |
| [21] | Whitney, J.M. and C.E. Browning,J. Compos. Mater.,6 (1973), 300–303. · doi:10.1177/002199837200600211 |
| [22] | Berghaus, D.G. and R.W. Aderholdt,Exp. Mech.,15, 4, Jul. (1975), 173–176. · doi:10.1007/BF02410338 |
| [23] | Spilker, R.L. and S.C. Chou,J. Compos. Mater.,14 (1980), 2–20. |
| [24] | Chien, W.Z.,On the Generalized Variational Principles, Knowledge Press, Shanghai (1985). (in Chinese) · Zbl 0615.73069 |
| [25] | Tsai, S.W. and H.T. Hahn,Introduction to Composite Materials. Technomic Publishing Co. Inc. (1980). |
| [26] | Christensen, R.M.,Mechanics of Composite Materials, John Wiley and Sons Inc. (1979). · Zbl 0393.46049 |
| [27] | Hull, D.,An Introduction to Composite Materials, Cambridge University Press (1981). · Zbl 0472.76009 |
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