Strain measures and compatibility equations in the linear high-order shell theories

Authors:
M. Brull and L. Librescu

Journal:
Quart. Appl. Math. **40** (1982), 15-25

MSC:
Primary 73L99

DOI:
https://doi.org/10.1090/qam/652046

MathSciNet review:
652046

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**[1]**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, Mar. 1949 MR**0030886****[2]**P. M. Naghdi,*On the theory of thin elastic shells*, Quart. Appl. Math.**14**, 369-380. (1957) MR**0084284****[3]**J. E. Stoneking and A. P. Boresi,*A theory for free vibration of orthotropic shells of revolution*, Nucl. Eng. and Des.**17**, 271-285 (1970)**[4]**J. M. Whitney, and C. T. Sun,*A refined theory for laminated anisotropic cylindrical shells*, J. Appl. Mechan.**41**, 471-476 (1974)**[5]**E. Reissner,*Stress-strain relations in the theory of thin elastic shells*, J. Math, and Physics**31**, 109-119 (1952) MR**0048283****[6]**C. T. Sun and J. M. Whitney,*Axisymmetric vibrations of laminated composite cylindrical shells*, J. Acoust. Soc. Am.**55**, 1238-1246 (1974)**[7]**J. A. Zukas,*Effects of transverse normal and shear strains in orthotropic shells*, AIAAJ.**12**, 1753-1755 (1974)**[8]**W. H. Drysdale and A. R. Zak,*Structural problems in thick shells*, in*Thin-shell structures: theory, experiment, design*, pp. 453-463, Eds. Y. C. Fung and E. E. Sechler, Prentice-Hall Inc., Englewood Cliffs, 1974**[9]**V. Manea,*Some problems of the theory of elastic flat plates*(in Roumanian), Edit. Acad. Rep. Soc. Roum., pp. 193-221 (1966)**[10]**R. B. Nelson and D. R. Lorch,*A refined theory for laminated orthotropic plates*, J. Applied Mechanics**41**, 177-183.(1974)**[11]**K. H. Lo, R. M. Christensen, and E. M. Wu,*A high-order theory of plate deformation: Part 1: Homogeneous plates*, J. Appl. Mech.**44**, 4, 663-668 (1977)**[12]**K. H. Lo, R. M. Christensen, and E. M. Wu,*Stress solution determination for high order plate theory*, Int. J. Solid Structures**14**, 655-662 (1978)**[13]**L. Ia. Ainola,*Non-linear theory of Timoshenko type in elastic shells*(in Russian), Izv. A. N. Est. SSR., Ser. Fiz.-Matem. i. Techn.**14**, 337-344 (1965)**[14]**L. M. Habip and I. K. Ebicoglu,*On the equations of motion of shells in the reference state*, Ingenieur Archiv.**34**, (1965)**[15]**A. W. Leissa,*Vibrations of shells*, NASA SP-288, 1973**[15']**J. R. Vinson and T. W. Chou,*Composite materials and their use in strucutres*, Chapter 7, John Wiley & Sons, New York, Toronto, 1974**[16]**L. Librescu,*Improved linear theory of elastic anistropic multilayered shells*(in Russian), Mekhanika Polimerov, Part I, No. 6, 1038-1050, Nov. - Dec. 1975 and Part II, No. 1, 100-109, Jan. - Feb. 1976 (English Translat. by Plenum Publ. Corp.)**[17]**L. Librescu,*Non-linear theory of elastic anisotropic, multilayered shells*(in Russian), in*Selected topics in applied mechanics*, ed. L. I. Sedov. pp. 453-466, Nauka, Moskow, 1974**[18]**K. Z. Galimov,*The theory of shells with transverse shear deformation effect*(in Russian), Kazanskogo Universiteta, 1977**[19]**P. M. Nagdhi,*The theory of shells and plates*, in*Handbuch der Physik***VI**a/1 (ed. S.Flügge), Springer, Berlin, Heidelberg, New York, pp. 425-640 (1972)**[20]**L. Librescu,*Elastostatics and kinetics of anisotropic and heterogeneous shell-type structures*, Noordhoff, Leyden, 1975**[21]**P. M. Naghdi,*Foundations of elastic shell theory*, in*Progr. Solid Mech*., ed. I. N. Sneddon and R. Hill,**4**, 1 (1963) MR**0163488****[22]**L. Librescu,*A physically nonlinear theory of elastic shells and plates, the Love-Kirchoff hypothesis being eliminated*, Rev. Roum. Sci. Tech. - Mec. Appl.,**15**, 1263-1284 (1970)**[23]**P. M. Naghdi,*A new derivation of the general equations of elastic shells*, Int. J. Eng. Sci.**1**, 509-522 (1963) MR**0162420****[24]**P. M. Naghdi,*Further results in the derivation of the general equations of elastic shells*, Int. J. Eng. Sci.**2**, 269-273 (1964) MR**0167022****[25]**H. Leipholz,*Theory of elasticity*, Noordhoff, Leyden, 1974 MR**0413649****[26]**A. L. Gol'denveizer,*Qualitative investigation of the stress state in thin elastic shells*(in Russian), Prikl. Matem. i. Mechan.**IX**, 463-478 (1945)**[27]**E. Reissner,*A note on stress functions and compatibility equations in shell theory*, in*Topics in applied mechanics*, eds. D. Abir, F. Ollendorf, and M. Reiner, Elsevier, Amsterdam, 1965, pp. 23-32 MR**0191178****[28]**R. B. Rikards and G. A. Teters,*Stability of shells from composite materials*(in Russian), Publ. House, Zinatne-Riga, 1974, pp. 82-87.**[29]**W. T. Koiter,*A consistent first approximation in the general theory of thin elastic shells, Part I: foundations and linear theory*, Dept. Laboratorium voor Toegepaste Mechanica der Technische Hogeschool, August 5th, 1959 MR**0142241****[30]**W, T. Koiter,*A consistent first approximation in the general theory of thin elastic shells, Proc. IUTAM symposium on the theory of thin shells*(Ed. W. T. Koiter), North-Holland, Amsterdam, 1960 MR**0142241****[31]**B. Budiansky and J. L. Sanders, Jr.,*On the ``best'' first order linear shell theory, in The Prager anniversary volume*, 129-140, Macmillian, 1963 MR**0158595****[32]**P. M. Naghdi,*On a variational theorem in elasticity and its application to shell theory*, J. Appl. Mechan.**31**, 647-653 (1964) MR**0173390****[33]**I. N. Vekua,*The theory of thin shallow shells of variable thickness*(in Russian), The Mathematical Inst. of Tbilisi, Metzniereba, 1965 MR**0197007****[34]**N. K. Galimov,*On the applicability of Legendre polynomials in the substantiation of the theory of sandwich plates and shells*(in Russian) in*Issledovania po teorii plastin i obolocek*(ed. by K. Z. Galimov), X, 371-385, Univ. of Kazan, Kazan, 1973**[35]**G. Sansome,*Orthogonal functions*, Interscience, New York, 1959

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DOI:
https://doi.org/10.1090/qam/652046

Article copyright:
© Copyright 1982
American Mathematical Society