Abstract
The stress-strain state of a shallow shell with rectangular planform and varying thickness is analyzed in a refined formulation for different boundary conditions. A numerical-and-analytic method is developed based on the spline-approximation and discrete-orthogonalization methods. The stress-strain state of shallow shells with thickness varied without change in weight is analyzed
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References
V. Z. Vlasov, General Theory of Shells [in Russian], Gl. Izd. Tekhn.-Teor. Lit., Moscow-Leningrad (1949).
Ya. M. Grigorenko and A. T. Vasilenko, Theory of Shells of Variable Stiffness [in Russian], Naukova Dumka, Kyiv (1981).
Ya. M. Grigorenko, Yu. N. Shevchenko, A. T. Vasilenko, et al., Numerical Methods [in Russian], A.S.K., Kyiv (2002).
A. A. Nazarov, Fundamentals of the Theory and Methods of Design of Shallow Shells [in Russian], Stroiizdat, Leningrad (1966).
B. L. Pelekh, Theory of Shells with Finite Shear Stiffness [in Russian], Naukova Dumka, Kyiv (1973).
P. M. Varvak and A. F. Ryabov (eds.), A Handbook of the Theory of Elasticity [in Russian], Budivel’nyk, Kyiv (1971).
C. R. Calladine, Theory of Shell Structures, Cambridge Univ. Press, Cambridge (1983).
Y. K. Cheung, Finite Strip Method in Structure Analysis, Pergamon Press, Oxford (1976).
G. R. Cowper, G. M. Lindberg, and M. D. Olson, “Shallow shell finite element of triangular shape,” Int. J. Solids Struct., No. 6, 1133–1156 (1970).
S. C. Fan and Y. K. Cheung, “Analysis of shallow shells by spline finite strip method,” Eng. Struct., No. 5, 255–263 (1983).
W. Flügge, Stresses in Shells, Springer-Verlag, Berlin (1973).
P. L. Gould, Analysis of Shells and Plates, Springer-Verlag, New York (1988).
A. Ya. Grigorenko and T. L. Efimova, “Application of spline-approximation for solving the problems on natural vibrations of rectangular plates of variable thickness,” Int. Appl. Mech., 41, No. 10, 1161–1169 (2005).
Ya. M. Grigorenko, A. Ya. Grigorenko, and L. I. Zakhariichenko, “Calculation of stress-strain state of orthotropic closed and open non-circular cylindrical shells,” Int. Appl. Mech., 41, No. 7, 778–785 (2005).
Ya. M. Grigorenko, N. N. Kryukov, and N. S. Yakovenko, “Solving the boundary problems of the theory of layered orthotropic trapezoidal plates of variable thickness on the base of spline-approximation,” Int. Appl. Mech., 41, No. 4, 413–420 (2005).
Ya. M. Grigorenko and S. N. Yaremchenko, “Refined design of corrugated noncircular cylindrical shells,” Int. Appl. Mech., 41, No. 1, 7–13 (2005).
Ya. M. Grigorenko and L. I. Zakhariichenko, “Study into the effect of circumferential variation in thickness and load on the deformation,” Int. Appl. Mech., 38, No. 10, 1229–1236 (2002).
E. Reissner, “Effect of transverse shear deformation on the bending of elastic plates,” Trans. ASME, J. Appl. Mech., No. 12, 69–77 (1945).
Z. Rychter, “Family of shear deformation theories for shallow shells,” Adv. Mech., No. 98, 221–232 (1993).
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Translated from Prikladnaya Mekhanika, Vol. 43, No. 10, pp. 80–91, October 2007.
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Grigorenko, A.Y., Yaremchenko, N.P. Stress-strain state of shallow shells with rectangular planform and varying thickness: Refined formulation. Int Appl Mech 43, 1132–1141 (2007). https://doi.org/10.1007/s10778-007-0113-8
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DOI: https://doi.org/10.1007/s10778-007-0113-8