Refined geometrically nonlinear theories of anisotropic laminated shells
Author:
Liviu Librescu
Journal:
Quart. Appl. Math. 45 (1987), 1-22
MSC:
Primary 73L10
DOI:
https://doi.org/10.1090/qam/885164
MathSciNet review:
885164
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S. A. Ambartsumian, Theory of anisotropic shells, NASA Techn. Transl. F-118, 1964
- S. A. Ambartsumyan, Obshchaya teoriya anizotropnykh obolochek, Izdat. “Nauka”, Moscow, 1974 (Russian). MR 0416168
Ia. M. Grigorenko, Isotropic and anisotropic multilayered shells of revolution of variable rigidity, Naukova Dumka (in Russian), Kiev, 1973
J. R. Vinson and T. W. Chou, Composite materials and their use in structures, John Wiley & Sons, New York, Toronto, 1974
L. Librescu, Elastostatics and kinetics of anisotropic and heterogeneous shell-type structures, Noordhoff Internat. Publishing, Leyden, 1975
R. B. Rikards and G. A. Teters, Stability of shells made of composite materials (in Russian), Zinatne, Riga, 1974
E. I. Grigoliuk and F. A. Kogan, Present status of the multilayered shell theory (in Russian), Prikladnaia Mechanika 8, 6, 1972
C. W. Bert and P. H. Francis, Composite material mechanics; Structural mechanics, AIAA Journ. 12 (1974)
C. W. Bert, Comparison of new plate theories applied to laminated composites, in Mechanics of Composite Materials, G. J. Dvorak (Ed.). ASME Winter Annual Meeting, Boston, MA, Nov. 1983, 1–9
J. N. Reddy, Finite-element modeling of layered, anisotropic composite plates and shells: A review of recent research, Shock and Vibration Digest 13 (1981)
A. E. Green and P. M. Naghdi, A theory of laminated composite plates, IMA J. Appl. Math. 29, 1–23 (1982)
E. I. Grigoliuk and P. P. Chulkov, On the theory of multilayered shells, in Contributions to the Theory of Aircraft Structures, Delft Univ., 171–183, 1972
L. Librescu, Nonlinear theory of elastic, anisotropic multilayered shells (in Russian), in Selected Topics in Applied Mechanics, Ed. L. I. Sedov, pp. 453–466, Nauka, Moskow, 1974
L. Librescu, Improved linear theory of elastic anisotropic multilayered shells (in Russian), Mekhanika Polimerov, Part I, No. 6, 1038–1050, Dec. Nov.-Dec. 1975, and Part II, No. 1 100–109, Jan.-Feb., 1976 (English Translat. by Plenum Publ. Corp.)
G. A. Wempner, Theory for moderately large deflections of sandwich shells with dissimilar facings, Internat. J. Solids and Structures 3, 367–392 (1967)
- Eric Reissner, Finite deflections of sandwich plates, J. Aeronaut. Sci. 15 (1948), 435–440. MR 27215
I. K. Ebcioglu, Nonlinear theory of sandwich panels, in Developments in Theoretical and Applied Mechanics, Vol. 4, Ed. Daniel Frederik, Pergamon Press, Oxford and New York, 611–637, 1970
P. C. Yang, C. H. Norris and Y. Stavsky, Elastic-wave propagation in heterogeneous plates, Internat. J. Solids and Structures 2, 665–684 (1966)
J. M. Whitney and N. J. Pagano, Shear deformation in heterogeneous anistropic plates, J. Appl. Mech., 1031–1036 (1970)
R. B. Nelson and D. R. Lorch, A refined theory for laminated orthotropic plates, J. Appl. Mech. 41, 177–183 (1974)
K. H. Lo, R. M. Christensen, and E. M. Wu, A higher-order theory of plate deformation, Part 2, Laminated plates, ASME Journal of Applied Mechanics 44, 669–676 (1977)
J. N. Reddy and W. C. Chao, Nonlinear oscillation of laminated anisotropic, rectangular plates, ASME Journal of Applied Mechanics 49, 396–401 (1982)
J. A. Zukas and J. R. Vinson, Laminated transversal isotropic cylindrical shells, ASME Journal of Applied Mechanics 38, 400–407 (1971)
J. M. Whitney and C. T. Sun, A refined theory for laminated anisotropic, cylindrical shells, ASME Journal of Applied Mechanics, 471–476 (1974)
P. M. Naghdi, Foundations of elastic shell theories, in Progr. Solid Mechanics, Ed. I. N. Sneddon and R. Hill, 4, 1963
E. Reissner, On a variational theory for finite elastic deformation, J. Math. Phys. 32, 129–135 (1953)
L. M. Habip, Theory of elastic shells in the reference state, Ing. Archiv. 34, 228–237 (1965)
- A. E. Green and J. E. Adkins, Large elastic deformations, Clarendon Press, Oxford, 1970. Second edition, revised by A. E. Green. MR 0269158
- H. Leipholz, Theory of elasticity, Noordhoff International Publishing, Leyden, 1974. Mechanics of Elastic Stability, No. 1; Monographs and Textbooks on Mechanics of Solids and Fluids. MR 0413649
B. Budiansky, Remarks on theories of solid and structural mechanics, in Problems of Hydrodynamics and Continuum Mechanics, SIAM, 77–83 (1969)
- P. M. Naghdi and R. P. Nordgren, On the nonlinear theory of elastic shells under the Kirchhoff hypothesis, Quart. Appl. Math. 21 (1963), 49–59. MR 145743, DOI https://doi.org/10.1090/S0033-569X-1963-0145743-4
P. M. Naghdi, On the non-linear thermoelastic theory of shells, in Non-Classical Shell-Problems, North-Holland, Amsterdam, R.W.N., Warsaw, 5–26, 1964
L. E. Malvern, Introduction to the mechanics of a continuous medium, Prentice-Hall, Englewood Cliffs, 1969
- A. E. Green and W. Zerna, Theoretical elasticity, Oxford, at the Clarendon Press, 1954. MR 0064598
- M. Brull and L. Librescu, Strain measures and compatibility equations in the linear high-order shell theories, Quart. Appl. Math. 40 (1982/83), no. 1, 15–25. MR 652046, DOI https://doi.org/10.1090/S0033-569X-1982-0652046-4
- W. T. Koiter, A consistent first approximation in the general theory of thin elastic shells, Proc. Sympos. Thin Elastic Shells (Delft, 1959) North-Holland, Amsterdam, 1960, pp. 12–33. MR 0142241
- B. Budiansky and J. L. Sanders Jr., On the “best” first-order linear shell theory, Progress in Applied Mechanics, Macmillan, New York, 1963, pp. 129–140. MR 0158595
- F. B. Hildebrand, E. Reissner, and G. B. Thomas, Notes on the foundations of the theory of small displacements of orthotropic shells, Tech. Notes Nat. Adv. Comm. Aeronaut. 1949 (1949), no. 1833, 59. MR 0030886
J. N. Reddy, An accurate prediction of natural frequencies of laminated plates by a high-order theory, in Advances in Aerospace Structures and Materials, (Ed. Umar Yuceoglu) 1983 Winter Annual Meeting of ASME, Boston, MA., November, 1983 (Report)
- W. L. Wainwright, On a nonlinear theory of elastic shells, Internat. J. Engrg. Sci. 1 (1963), 339–358 (English, with French, German, Italian and Russian summaries). MR 0160366, DOI https://doi.org/10.1016/0020-7225%2863%2990012-0
L. Librescu, A physically nonlinear theory of elastic shells and plates, the Love-Kirchhoff hypothesis being eliminated, Rev. Roum. Sci. Techn-Mec. Appl. 15, 1263–1284 (1970)
V. Biricikoglu and A. Kalnins, Large elastic deformation of shells with the inclusion of transverse normal strain, Int. J. Solids Structures 7, 431–444 (1971)
Y. Yokoo and H. Matsunaga, A general nonlinear theory of elastic solids, Internat. J. Solids and Structures 10, 261–272 (1974)
L. M. Habip and I. K. Ebcioglu, On the equations of motion of shells in the reference state, Ing. Archiv. 34 (1965)
L. Ia. Ainola, Nonlinear Timoshenko type theory of elastic shells (in Russian), Izv. Akad. Nauk. Eston. SSR, 14, 337–344 (1965)
K. Z. Galimov, The theory of shells with transverse shear effect (in Russian), Kazan Univ., 1977
K. Z. Galimov, The bases of the nonlinear theory of thin shells, (in Russian), Kazan Univ., 1975
I. Oshima, Y. Seguchi and A. Shindo, On nonlinear shell theories, Bull. of the J.S.M.E. 13, 1155–1164 (1970)
I. K. Ebcioglu, Non-linear theory of shells, Internat. J. Non-linear Mech. 6, 469–478 (1970)
C. I. Wu and J. Vinson, Influences of large amplitudes, transverse shear deformation and rotatory inertia on lateral vibrations of transversely istropic plates, J. Appl. Mech. 36, 254–260 (1969)
K. Summo, Nonlinear theory of thin elastic shells based on Kirchhoff hypothesis, Recent Researches of Structural Mechanics, Uno Shoten, Tokyo, 231–244, 1968
T. Nakamura, Foundation of geometrically nonlinear theory of the continuum based on Kirchhoff-Love assumptions, Report of the Institute of Industrial Science, Univ. of Tokyo, 20, 1–49 (1971)
R. Harnach and W. B. Kratzig, Allgemeine Theorie geometrish nichtlinearer insbesondere leighter Flachentragwerke, Mitteilung Nr. 73–6, April, Inst, für Konstruktiven Ingenieurbau, Ruhr-Univ. Bochum, 1976
- W. T. Koiter, On the nonlinear theory of thin elastic shells. I, II, III, Nederl. Akad. Wetensch. Proc. Ser. B 69 (1966), 1–17, 18–32, 33–54. MR 0192706
- J. Lyell Sanders Jr., Nonlinear theories for thin shells, Quart. Appl. Math. 21 (1963), 21–36. MR 147023, DOI https://doi.org/10.1090/S0033-569X-1963-0147023-4
J. G. Wempner, Mechanics of solids with applications to thin bodies, McGraw-Hill, 1973
R. G. Jeffers and M. A. Brull, A large deflection theory for thin elastic shells, Israel J. Tech. 13, 111–121 (1975); Proc. XVII Isr. Annu. Conf. Aviation and Astronautics, May 1975
S. A. Ambartsumian, Theory of anisotropic shells, NASA Techn. Transl. F-118, 1964
S. A. Ambartsumian, General theory of anisotropic shells (in Russian), Nauka, Moskow 1974
Ia. M. Grigorenko, Isotropic and anisotropic multilayered shells of revolution of variable rigidity, Naukova Dumka (in Russian), Kiev, 1973
J. R. Vinson and T. W. Chou, Composite materials and their use in structures, John Wiley & Sons, New York, Toronto, 1974
L. Librescu, Elastostatics and kinetics of anisotropic and heterogeneous shell-type structures, Noordhoff Internat. Publishing, Leyden, 1975
R. B. Rikards and G. A. Teters, Stability of shells made of composite materials (in Russian), Zinatne, Riga, 1974
E. I. Grigoliuk and F. A. Kogan, Present status of the multilayered shell theory (in Russian), Prikladnaia Mechanika 8, 6, 1972
C. W. Bert and P. H. Francis, Composite material mechanics; Structural mechanics, AIAA Journ. 12 (1974)
C. W. Bert, Comparison of new plate theories applied to laminated composites, in Mechanics of Composite Materials, G. J. Dvorak (Ed.). ASME Winter Annual Meeting, Boston, MA, Nov. 1983, 1–9
J. N. Reddy, Finite-element modeling of layered, anisotropic composite plates and shells: A review of recent research, Shock and Vibration Digest 13 (1981)
A. E. Green and P. M. Naghdi, A theory of laminated composite plates, IMA J. Appl. Math. 29, 1–23 (1982)
E. I. Grigoliuk and P. P. Chulkov, On the theory of multilayered shells, in Contributions to the Theory of Aircraft Structures, Delft Univ., 171–183, 1972
L. Librescu, Nonlinear theory of elastic, anisotropic multilayered shells (in Russian), in Selected Topics in Applied Mechanics, Ed. L. I. Sedov, pp. 453–466, Nauka, Moskow, 1974
L. Librescu, Improved linear theory of elastic anisotropic multilayered shells (in Russian), Mekhanika Polimerov, Part I, No. 6, 1038–1050, Dec. Nov.-Dec. 1975, and Part II, No. 1 100–109, Jan.-Feb., 1976 (English Translat. by Plenum Publ. Corp.)
G. A. Wempner, Theory for moderately large deflections of sandwich shells with dissimilar facings, Internat. J. Solids and Structures 3, 367–392 (1967)
E. Reissner, Finite deflections of sandwich plates, J. Aeron. Sci. 15 435–440 (1948)
I. K. Ebcioglu, Nonlinear theory of sandwich panels, in Developments in Theoretical and Applied Mechanics, Vol. 4, Ed. Daniel Frederik, Pergamon Press, Oxford and New York, 611–637, 1970
P. C. Yang, C. H. Norris and Y. Stavsky, Elastic-wave propagation in heterogeneous plates, Internat. J. Solids and Structures 2, 665–684 (1966)
J. M. Whitney and N. J. Pagano, Shear deformation in heterogeneous anistropic plates, J. Appl. Mech., 1031–1036 (1970)
R. B. Nelson and D. R. Lorch, A refined theory for laminated orthotropic plates, J. Appl. Mech. 41, 177–183 (1974)
K. H. Lo, R. M. Christensen, and E. M. Wu, A higher-order theory of plate deformation, Part 2, Laminated plates, ASME Journal of Applied Mechanics 44, 669–676 (1977)
J. N. Reddy and W. C. Chao, Nonlinear oscillation of laminated anisotropic, rectangular plates, ASME Journal of Applied Mechanics 49, 396–401 (1982)
J. A. Zukas and J. R. Vinson, Laminated transversal isotropic cylindrical shells, ASME Journal of Applied Mechanics 38, 400–407 (1971)
J. M. Whitney and C. T. Sun, A refined theory for laminated anisotropic, cylindrical shells, ASME Journal of Applied Mechanics, 471–476 (1974)
P. M. Naghdi, Foundations of elastic shell theories, in Progr. Solid Mechanics, Ed. I. N. Sneddon and R. Hill, 4, 1963
E. Reissner, On a variational theory for finite elastic deformation, J. Math. Phys. 32, 129–135 (1953)
L. M. Habip, Theory of elastic shells in the reference state, Ing. Archiv. 34, 228–237 (1965)
A. E. Green and J. E. Adkins, Large elastic deformation and nonlinear continuum mechanics, Clarendon Press, Oxford, 1970
H. Leipholz, Theory of elasticity, Noordhoff Intern. Publ., 1974
B. Budiansky, Remarks on theories of solid and structural mechanics, in Problems of Hydrodynamics and Continuum Mechanics, SIAM, 77–83 (1969)
P. M. Naghdi and R. P. Nordgren, On the nonlinear theory of elastic shells under the Kirchhoff hypothesis, Quart. Appl. Math. 21, 49–59 (1963)
P. M. Naghdi, On the non-linear thermoelastic theory of shells, in Non-Classical Shell-Problems, North-Holland, Amsterdam, R.W.N., Warsaw, 5–26, 1964
L. E. Malvern, Introduction to the mechanics of a continuous medium, Prentice-Hall, Englewood Cliffs, 1969
A. E. Green and W. Zerna, Theoretical elasticity, Clarendon Press, Oxford, 1954
M. Brull and L. Librescu, Strain measures and compatibility equations in the linear high-order shell theories, Quart. Appl. Math vol. 40, 15–25 (1982)
W. T. Koiter, A consistent first approximation in the general theory of thin elastic shells, Part I. Foundations and linear theory, technology, Univ. Delft, August 1959
B. Budiansky and J. L. Sanders, Jr., On the “best” first-order linear shell theory, in Progress in Applied Mechanics, Prager Univerity Volume, Macmillan, New York, 129–140, 1963
F. B. Hildebrand, E. Reissner and G. B. Thomas, Notes on the foundations of the theory of small displacements of orthotropic shells,NACA-TN-1633, 1949
J. N. Reddy, An accurate prediction of natural frequencies of laminated plates by a high-order theory, in Advances in Aerospace Structures and Materials, (Ed. Umar Yuceoglu) 1983 Winter Annual Meeting of ASME, Boston, MA., November, 1983 (Report)
W. L. Wainwright, On a nonlinear theory of elastic shells, Int. J. Eng. Sci. 1, 339–358 (1963)
L. Librescu, A physically nonlinear theory of elastic shells and plates, the Love-Kirchhoff hypothesis being eliminated, Rev. Roum. Sci. Techn-Mec. Appl. 15, 1263–1284 (1970)
V. Biricikoglu and A. Kalnins, Large elastic deformation of shells with the inclusion of transverse normal strain, Int. J. Solids Structures 7, 431–444 (1971)
Y. Yokoo and H. Matsunaga, A general nonlinear theory of elastic solids, Internat. J. Solids and Structures 10, 261–272 (1974)
L. M. Habip and I. K. Ebcioglu, On the equations of motion of shells in the reference state, Ing. Archiv. 34 (1965)
L. Ia. Ainola, Nonlinear Timoshenko type theory of elastic shells (in Russian), Izv. Akad. Nauk. Eston. SSR, 14, 337–344 (1965)
K. Z. Galimov, The theory of shells with transverse shear effect (in Russian), Kazan Univ., 1977
K. Z. Galimov, The bases of the nonlinear theory of thin shells, (in Russian), Kazan Univ., 1975
I. Oshima, Y. Seguchi and A. Shindo, On nonlinear shell theories, Bull. of the J.S.M.E. 13, 1155–1164 (1970)
I. K. Ebcioglu, Non-linear theory of shells, Internat. J. Non-linear Mech. 6, 469–478 (1970)
C. I. Wu and J. Vinson, Influences of large amplitudes, transverse shear deformation and rotatory inertia on lateral vibrations of transversely istropic plates, J. Appl. Mech. 36, 254–260 (1969)
K. Summo, Nonlinear theory of thin elastic shells based on Kirchhoff hypothesis, Recent Researches of Structural Mechanics, Uno Shoten, Tokyo, 231–244, 1968
T. Nakamura, Foundation of geometrically nonlinear theory of the continuum based on Kirchhoff-Love assumptions, Report of the Institute of Industrial Science, Univ. of Tokyo, 20, 1–49 (1971)
R. Harnach and W. B. Kratzig, Allgemeine Theorie geometrish nichtlinearer insbesondere leighter Flachentragwerke, Mitteilung Nr. 73–6, April, Inst, für Konstruktiven Ingenieurbau, Ruhr-Univ. Bochum, 1976
W. T. Koiter, On the nonlinear theory of thin elastic shells, Proc. Konink Ned. Akad. Wetensch. Ser. B. 69, 1–54 (1966)
J. L. Sanders, Jr., Nonlinear theories of thin shells, Quart. Appl. Math. 21, 21–36 (1963)
J. G. Wempner, Mechanics of solids with applications to thin bodies, McGraw-Hill, 1973
R. G. Jeffers and M. A. Brull, A large deflection theory for thin elastic shells, Israel J. Tech. 13, 111–121 (1975); Proc. XVII Isr. Annu. Conf. Aviation and Astronautics, May 1975
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© Copyright 1987
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