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Anisotropic and Non-homogeneous Bodies

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Treatise on Classical Elasticity

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Abstract

We remind that between the fundamental hypotheses of the theory of elasticity presented in Sect. 2.1.2.2 are that of isotropy and homogeneity; the study made till now has respected these hypotheses. Hereafter we will consider the cases in which these hypotheses are no more respected.

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References

A. Books

  1. Beju, I., Soós, E., Teodorescu, P.P.: Euclidean Tensor Calculus with Applications. Abacus Press, Tunbridge Wells (1983). (Ed. Tehnică, Bucureşti)

    Google Scholar 

  2. Brilla, J.: Anizotropické steny (Anisotropic Plates). Slov. Akad. Vied., Bratislava (1958)

    Google Scholar 

  3. Cristescu, N.D., Crăciun, E.M., Soós, E.: Mechanics of Elastic Composites. Chapman and Hall/CRC, Boca Raton (2004)

    MATH  Google Scholar 

  4. Hearmon, R.F.S.: An Introduction to Applied Anisotropic Elasticity. Clarendon Press, Oxford (1961)

    Google Scholar 

  5. Lekhnitskiĭ, S.G.: Teoriya uprugosti anizotropnogo tela (Theory of Elasticity of Anisotropis Bodies). Ogiz, Moskva-Leningrad (1947)

    Google Scholar 

  6. Love, A.-E.-H.: A Treatise on the Mathematical Theory of Elasticity, 4th edn. Cambridge University Press, Cambridge (1934)

    Google Scholar 

B. Papers

  1. Bekhterev, P.: Analiticheskoe issledovanie obobshchenovo zakona Guka (Analytical study of the generalized hooke law). J. Russk. fiz.-khim. obshchestva. VII (1925)

    Google Scholar 

  2. Bishop, R.E.D.: Dynamical problems of plane stress and plane strain. Q.J. Mech. Appl. Math. VI, 250 (1953)

    Article  MATH  Google Scholar 

  3. Chentsov, N.G.: Issledovanie faneri, kak ortotropnoi plastinki (Application of bodies as orthotropic plates). Tekhn. Zametki Tsagi. (1936)

    Google Scholar 

  4. Cristea, M.: Legea lui Hooke plană neizotropă (Plane anisotropic hooke’s law). Com. Acad. Rom. I, 1007 (1951)

    MathSciNet  Google Scholar 

  5. Fridman, M.M.: Matematicheskaya teoriya anizotropnykh sred (Mathematical theory of anisotropic media). Prikl. Mat. Mekh. XIV, 321 (1950)

    Google Scholar 

  6. Green, A.E.: A note on stress systems in aelotropic materials. Proc. Roy. Soc. 162, 173 (1939). (173, 416, 420 (1920))

    ADS  Google Scholar 

  7. Iacovache, M. Aplicarea funcţiilor monogene în sensul lui Feodorov în teoria elasticităţii corpurilor cu izotropie transversă (Application of the monogenic functions in the sense of feodorov in the theory of elasticity of the bodies with transverse isotropy). Rev. Univ. şi Polit., Bucureşti. 58 (1952)

    Google Scholar 

  8. Lang, H.A.: The affine transformation for orthotropic plane-stress and plane-strain problems. J. Appl. Mech. 23, 1 (1956)

    MathSciNet  MATH  Google Scholar 

  9. Marguerre, K.: Ebenes und achsensymmetrisches Problem der Elastizitätstheorie. Z.A.M.M. 13, 437 (1933)

    Google Scholar 

  10. Mikhlin, S. G.: Ploskaya deformatsya v anizotropnoŭ srede (Plane deformation in anisotropic media). Tr. seism. inst., ANSSSR. t (1936)

    Google Scholar 

  11. Moisil, A.: Asupra ecuaţiilor echilibrului elastic plan pentru corpurile cu izotropie transversă (On the equations of plane elastic equilibrium for bodies with transverse isotropy). Lucr. Ses. Acad. Rom. 308 (1950)

    Google Scholar 

  12. Rabinovich, A. L.: Ob uprugikh postoiannykh i prochnosti anizotropnykh materialov (On elastic strength of anisotropic materials). Trudy. Tsagi. (1946)

    Google Scholar 

  13. Reissner, E.: A contribution to the problem of elasticity of nonisotropic materials. Phil. Mag. (1940)

    Google Scholar 

  14. Reissner, H.: Z.A.M.M. 11, 1 (1931)

    Article  Google Scholar 

  15. Savin, G. N.: Osnovnaya ploskaya zadacha teorii uprugosti dlya anizotropnoŭ sredy (odnosvyaznaya becknechnaya oblast’) (Fundamental plane problem of the theory of elasticity for an isotropic body (Simple connected infinite domain)). Tr. Inst. Stroit. Mekh., ANSSSR (1938)

    Google Scholar 

  16. Savin, G.N.: Ob odnom metode resheniya osnovnoĭ ploskoĭ staticheskoĭ zadachi teorii uprugosti anizotropnoĭ sredy (On a method of solving the fundamental plane statical problem of the theory of elasticity of the anisotropic media). Tr. Inst. Matem. ANSSSR (1939)

    Google Scholar 

  17. Sokolnicoff, I.S.: Approximate methods of solution of twodimensional problems in anisotropic elasticity. Proc. Symp. Appl. Math. (1950)

    Google Scholar 

  18. Teodorescu, P. P.: Asupra problemei plane a elasticităţii unor corpuri anizotrope. I. Relaţii între eforturi unitare şi deformaţii specifice (On the plane problem of elasticity of some anisotropic bodies. I. Relations between stresses and strains). Com. Acad. Rom. VII, 395 (1957)

    Google Scholar 

  19. Teodorescu, P. P.: Asupra problemei plane a elasticităţii unor corpuri anizotrope. II. Corpuri cu izotropie transversă (On the plane problem of elasticity of some anisotropic bodies. II. Bodies with transverse isotropy). Com. Acad. Rom. VII, 401 (1957)

    Google Scholar 

  20. Teodorescu, P. P.: Asupra problemei plane a elasticităţii unor corpuri anizotrope. III. Corpuri ortotrope (On the plane problem of elasticity of some anisotropic bodies. III. Orthotropie bodies). Com. Acad. Rom. VII, 503 (1957)

    Google Scholar 

  21. Teodorescu, P. P.: Asupra problemei plane a elasticităţii unor corpuri anizotrope. IV. Corpuri cu un plan de simetrie elastică (On the plane problem of elasticity of some anisotropic bodies. IV. Bodies with a plane of elastic symmetry). Com. Acad. Rom. VII, 509 (1957)

    Google Scholar 

  22. Teodorescu, P. P: Asupra problemei plane a elasticităţii unor corpuri anizotrope. V. Corpuri cu o axă de simetrie elastică de ordinul al treilea (On the plane problem of elasticity of some anisotropic bodies. V. Bodies with an axis of elastic symmetry of third order). Bul. Acad. Rom. VII, 641 (1957)

    Google Scholar 

  23. Teodorescu, P. P.: Asupra problemei plane a elasticităţii unor corpuri anizotrope. VI. Corpuri cu o axă de simetrie elastică de ordinul patru (On the plane problem of elasticity of some anisotropic bodies. VI. Bodies with an axis of elastic symmetry of fourth order). Bul. Acad. Rom. VII, 753 (1957)

    Google Scholar 

  24. Teodorescu, P. P.: Asupra problemei plane a elasticităţii unor corpuri anizotrope. VII. Corpuri acţionate de forţe masice oarecare (On the plane problem of elasticity of some anisotropic bodies. VII. Bodies acted upon by arbitrary volume forces). Com. Acad. Rom. VIII, 887 (1958)

    Google Scholar 

  25. Teodorescu, P.P.: Asupra problemei plane a elasticităţii unor corpuri anizotrope. VIII. Influenţa variaţiei de temperatură (On the plane problem of elasticity of some anisotropic bodies. VIII. Influence of the temperature variation). Com. Acad. Rom. VIII, 1119 (1958)

    Google Scholar 

  26. Teodorescu, P. P.: Asupra problemei plane a elasticităţii unor corpuri anizotrope. IX. Cazul micilor mişcări elastice (On the plane problem of elasticity of some anisotropic bodies. IX. Case of small elastic motions). Com. Acad. Rom. VIII, 1243 (1958)

    Google Scholar 

  27. Teodorescu, P. P.: Ůber das Kinetische Problem nichthomogener elasticher Körper. Bull. Acad. Pol. Sci., sér. Sci. Techn. XII, 595 (1964)

    Google Scholar 

  28. Teodorescu, P. P., Predeleanu, M.: Quelques considérations sur le problème des corps élastiques hétérogènes (Non-homogeneity in Elasticity and Plasticity). In: IUTAM-Symposium, pp. 31 (1958)

    Google Scholar 

  29. Teodorescu, P. P., Predeleanu, M.: Quelques considérations sur le problème des corps élastiques hétérogènes. Bull. Acad. Pol. Sci., sér. Sci. Techn. VII, 81 (1959)

    Google Scholar 

  30. Teodorescu, P. P., Predeleanu, M.: Ůber das ebene Problem nichthomogeneuer elastischer Körper. Acta Techn. Acad. Sci. Hung. XXVII, 349 (1959)

    Google Scholar 

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  1. Faculty of Mathematics, University of Bucharest, Str. Popa Soare 38, Bucharest, 023984, Romania

    Petre P. Teodorescu

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  1. Petre P. Teodorescu
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Teodorescu, P.P. (2013). Anisotropic and Non-homogeneous Bodies. In: Treatise on Classical Elasticity. Mathematical and Analytical Techniques with Applications to Engineering. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-2616-1_14

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  • DOI: https://doi.org/10.1007/978-94-007-2616-1_14

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