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.
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References
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
Donnell LG (1976) Beams, plates and shells. McGraw-Hill, New York
Flügge W (1967) Stresses in shells. Springer, Berlin
Grigorenko AY, Mal’tsev SA (2009) Natural vibrations of thin conical panels of variable thickness. Int Appl. Mech. 45(11):1221–1231
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
Grigorenko YM (1973) Izotropnyye i anizotropnyye sloistyye obolochki vrashcheniya peremennoy zhestkosti (Isotropic and anisotropic laminated shells of revolution with variable stiffness). Naukova Dumka, Kiev
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
Grigorenko YM, Grigorenko AY, Zakhariichenko LI (2006) Stress-strain solutions for circumferentially corrugated elliptic cylindrical shells. Int Appl Mech 42(9):1021–1028
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
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
Johns IA (1999) Analysis of laminated anisotropic plates and shells using symbolic computation. Int J Mech Sci 41(4–5):397–417
Korn GA, Korn TM (1968) Mathematical handbook for scientists and engineers. Definitions, theorems, and formulas for reference and review. McGraw-Hill, New York
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
Librescu L, Hause T (2000) Recent developments in the modeling and behavior of advanced sandwich constructions (survey). Compos Struct 48:1–17
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
Noor AK, Burton WS (1992) Computational models for hightemperature multilayered composite plates and shells. Appl Mech Rev 45(10):419–446
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
Soldatos KP (1999) Mechanics of cylindrical shells with non-circular cross-section. A survey. Appl Mech Rev 52(8):237–274
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
Vlasov VZ (1964) General theory of shells and Its application to engineering. NASA Technical Translation, NASA-TT-F-99, Washington
Zang R (1999) A novel solution of toroidal shells under axisymmetric loading. Appl Math Mech 20(5):519–526
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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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