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Some Solutions for Anisotropic Heterogeneous Shells Based on Classical Model

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Abstract

Results for stationary deformation of anisotropic inhomogeneous shells of various classes are presented by using classical Kirchhoff-Love theory and the numerical approaches outlined in Chap. 2 of this book. The stress-strain problems for shallow, noncircular cylindrical shells and shells of revolution are solved. Various types of boundary conditions and loadings are considered. Distributions of stress and displacement fields in shells of the aforementioned type are analyzed for various geometrical and mechanical parameters. The practically important stress problem of a high-pressure glass-reinforced balloon is solved. Dynamical characteristics of an inhomogeneous orthotropic plate under various boundary conditions are studied. The problem of free vibrations of a circumferential inhomogeneous truncated conical shell is solved. The effect of variation in thicknesses, mechanical parameters, and boundary conditions on the behavior of natural frequencies and vibration modes of a plate and cone is analyzed. Much attention is given to the validation of the reliability of the results obtained by numerical calculations.

  • Stress-strain state
  • Free vibrations
  • Anisotropy
  • Heterogeneity
  • Rectangular plates
  • Shallow
  • Spherical
  • Conical and noncircular shells

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References

  1. Ding K, Tang L (1999) The solution of weak formulation for axisymmetric problem of orthotropic cantilever cylindrical shell. Appl Math Mech 20(6):615–621

    MATH  CrossRef  Google Scholar 

  2. Donnell LG (1976) Beams, plates and shells. McGraw-Hill, New York

    MATH  Google Scholar 

  3. Flügge W (1967) Stresses in shells. Springer, Berlin

    Google Scholar 

  4. Grigorenko AY, Mal’tsev SA (2009) Natural vibrations of thin conical panels of variable thickness. Int Appl. Mech. 45(11):1221–1231

    MATH  MathSciNet  CrossRef  Google Scholar 

  5. Grigorenko AY, Tregubenko TV (2000) Numerical and experimental analysis of natural vibration of rectangular plates with variable thickness. Int Appl Mech 36(2):268–270

    CrossRef  Google Scholar 

  6. Grigorenko YM (1973) Izotropnyye i anizotropnyye sloistyye obolochki vrashcheniya peremennoy zhestkosti (Isotropic and anisotropic laminated shells of revolution with variable stiffness). Naukova Dumka, Kiev

    Google Scholar 

  7. Grigorenko YM, Grigorenko AY, Zakhariichenko LI (2005) Stress-Strain analysis of orthotropic closed and open noncircular cylindrical shells. Int Appl Mech 41(7):778–785

    CrossRef  Google Scholar 

  8. Grigorenko YM, Grigorenko AY, Zakhariichenko LI (2006) Stress-strain solutions for circumferentially corrugated elliptic cylindrical shells. Int Appl Mech 42(9):1021–1028

    CrossRef  Google Scholar 

  9. Grigorenko YM, Vasilenko AT (1997) Solution of problems and analysis of the stress-strain state of nonuniform anisotropic shells (survey). Int Appl Mech 33(11):851–880

    CrossRef  Google Scholar 

  10. Grigorenko YM, Zakhariichenko LI (1998) Solution of the problem of the stress state of noncircular cylindrical shells of variable thickness. Int Appl Mech 34(12):1196–1203

    CrossRef  Google Scholar 

  11. Johns IA (1999) Analysis of laminated anisotropic plates and shells using symbolic computation. Int J Mech Sci 41(4–5):397–417

    Google Scholar 

  12. Korn GA, Korn TM (1968) Mathematical handbook for scientists and engineers. Definitions, theorems, and formulas for reference and review. McGraw-Hill, New York

    MATH  Google Scholar 

  13. Li L, Babuska I, Chen J (1997) The boundary buyer for p–model plate problems. Pt 1. Asymptotic analysis. Acta Mech 122(1–4):181–201

    MATH  MathSciNet  CrossRef  Google Scholar 

  14. Librescu L, Hause T (2000) Recent developments in the modeling and behavior of advanced sandwich constructions (survey). Compos Struct 48:1–17

    CrossRef  Google Scholar 

  15. Librescu L, Schmidt R (1991) Substantiation of a shear deformable theory of anisotropic composite laminated shells accounting for the interminated continuity conditions. Int J Eng Sci 29(6):669–683

    MATH  MathSciNet  CrossRef  Google Scholar 

  16. Noor AK, Burton WS (1992) Computational models for hightemperature multilayered composite plates and shells. Appl Mech Rev 45(10):419–446

    CrossRef  Google Scholar 

  17. Ramm E (1977) A plate/shell element for large deflections and rotations. In: Bathe A et al (eds) Formulations and computational algorithms in finite element analysis. MIT Press, Cambridge

    Google Scholar 

  18. Soldatos KP (1999) Mechanics of cylindrical shells with non-circular cross-section. A survey. Appl Mech Rev 52(8):237–274

    CrossRef  Google Scholar 

  19. Sun BH, Zhang W, Yeh KY, Rimrott FDJ (1996) Exact displacement solution of arbitrary degree paraboidal shallow shell of revolution made of linear elastic materials. Int J Solids Struct 33(16):2299–2308

    MATH  CrossRef  Google Scholar 

  20. Vlasov VZ (1964) General theory of shells and Its application to engineering. NASA Technical Translation, NASA-TT-F-99, Washington

    Google Scholar 

  21. Zang R (1999) A novel solution of toroidal shells under axisymmetric loading. Appl Math Mech 20(5):519–526

    CrossRef  Google Scholar 

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Correspondence to Alexander Ya. Grigorenko .

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Grigorenko, A.Y., Müller, W.H., Grigorenko, Y.M., Vlaikov, G.G. (2016). Some Solutions for Anisotropic Heterogeneous Shells Based on Classical Model. In: Recent Developments in Anisotropic Heterogeneous Shell Theory. SpringerBriefs in Applied Sciences and Technology(). Springer, Singapore. https://doi.org/10.1007/978-981-10-0353-0_3

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  • DOI: https://doi.org/10.1007/978-981-10-0353-0_3

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