The equations of the technical theory of shells with the effect of transverse shear deformation

Author:
Stanislaw A. Lukasiewicz

Journal:
Quart. Appl. Math. **28** (1971), 489-497

DOI:
https://doi.org/10.1090/qam/99774

MathSciNet review:
QAM99774

Full-text PDF Free Access

References | Additional Information

**[1]**L. H. Donnell,*Stability of thin-walled tubes under torsion*, NACA Report #479, 1933**[2]**M. Musthari,*Some generalizations of the theory of thin shells*, Izv. Fiz. Mat. O. Va. Kazan. Univ. (8)**11**(1938)**[3]**K. Marguerre,*Zur Theorie der gekrummten Platte grosser Formanderung*, Proc. Fifth Internat. Congress Applied Mechanics Cambridge, Mass., 1938, pp. 93-101**[4]**V. Z. Vlasov,*General theory of shells and its applications in technology*, Gittl, Moscow, 1949 (Russian) MR**0034685****[5]**S. Łukasiewicz,*Supplement to the technical theory of shells*, Rozprawy Inż.**11**, (1963)**[6]**F. B. Hildebrand, E. Reissner and G. B. Thomas,*Notes on the foundations of the theory of small displacements of orthotropic shells*, NACA Technical Notes #1833, 1949 MR**0030886****[7]**A. E. Green and W. Zerna,*Theoretical elasticity*, Clarendon Press, Oxford, 1954 MR**0064598****[8]**E. Reissner,*Stress-strain relations in the theory of thin elastic shells*, J. Math. Physics**31**, 109-119 (1952) MR**0048283****[9]**E. Reissner, Proc. Amer. Soc. Civ. Eng. EM**23**, 1962**[10]**P. M. Naghdi,*Note on the equations of shallow elastic shells*, Quart. Appl. Math.**14**, 331-333 (1956) MR**0087336****[11]**P. M. Naghdi,*On the theory of thin elastic shells*, Quart. Appl. Math.**14**, 369-380 (1957) MR**0084284****[12]**J. P. Wilkinson and A. Kalnins,*On nonsymmetric dynamic problems of elastic spherical shells*, J. Appl. Mech.**32**, 525 (1965)**[13]**J. P. Wilkinson and A. Kalnins,*Deformation of open spherical shells under arbitrarily located concentrated loads*, J. Appl. Mech.**33**, 305-312 (1966)**[14]**L. S. D. Morley,*An improvement on Donnell's approximation for thin-walled circular cylinders*, Quart. J. Mech. Appl. Math.**12**, 89-99 (1959) MR**0101675****[15]**S. Łukasiewicz,*The equations of the theory of non-shallow thin shells*, Arch Bud. Masz.**12**(1965)**[16]**S. Łukasiewicz,*On the technical theory of non-shallow shells*, Arch. Bud. Masz.**15**(1968)

Additional Information

DOI:
https://doi.org/10.1090/qam/99774

Article copyright:
© Copyright 1971
American Mathematical Society