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BUCKLING and VIBRATIONS OF FUNCTIONALLY GRADED PLATES and SHALLOW SHELLS WITH COMPLEX PLANFORM
Last modified: 2017-05-21
Abstract
Vibrations and buckling of FGM shallow shells of an arbitrary planform subjected to thermal environment are investigated with the use of R-functions theory and variational methods. Classical and first-order shear deformation shallow shells are employed. Material properties are assumed to be temperature-dependent and varying along the thickness direction accordingly to Voigt’s law. The developed method is based on the combined applications of R-functions theory, variational Ritz’s method. The effect of the temperature rise, geometry of the shell, and constituent volume fraction index is examined. The validation and accuracy of the proposed method were verified on a large number of the test problems. A comparison of the obtained results with available ones is also carried out for rectangular plates and shallow shells. The proposed method is demonstrated for FG clamped and simply-supported shallow shells of a complex planform also. The effect of the power-law index, properties of the constituent materials, curvature of the shell, boundary conditions, and geometry of the shell at different values of temperature at the top and bottom surfaces are analyzed
Reference
[1] Shen H.S. (2009) Functionally Graded M of plates and Shells. CRC Press, Florida.
[2] J.N.Reddy and C.D.Chin, (1998). Thermomech. Analysis of Functionally Graded Cylinders and Plates,J.Therm.Stresses, vol.21,pp.593-626
[3] J.Yang,H.-S.Shen. Free vibration and parametric resonance of shear deformable functionally graded cylindrical panels (2003).J.Sound and Vibration 261,871-893]
[4] R.Javaheri and M.R.Eslami (2002). Thermal Buckling of functionally graded plates,AIAAJ.,vol.40,pp.162-169,.]
V.R.Kar and S.Panda (2016) Geometrical nonlinear free vibration analysis of FGM spherical panel under nonlinear thermal loading with TD and TID properties. J. of thermal Stresses,V.39,No.8,942-959
[5] J. Awrejcewicz, L. Kurpa, O. Mazur, On the parametric vibrations and meshless discretization of orthotropic plates with complex shape. International Journal of Nonlinear Sciences and Numerical Simulation 11 (5) (2010) 371-386.
[6] J. Awrejcewicz, L. Kurpa, T. Shmatko, Investigating geometrically nonlinear vibrations of laminated shallow shells with layers of variable thickness via the R-functions theory. Composite Structures 125 (2015) 575–585.
[7] L. Kurpa, T. Shmatko, G. Timchenko, Free vibration analysis of laminated shallow shells with complex shape using the R-functions method. Composite Structures 93 (2010) 225–233.
[8] L.V. Kurpa, O.S. Mazur, Method of R-functions for investigating parametric vibrations of orthotropic plates with complex shape. Journal of Mathematical Sciences 171 (4) 2010 1-14.
[9] L.V. Kurpa, O.S. Mazur, V.V. Tkachenko, Parametric vibrations of multilayer plates of complex shape. Journal of Mathematical Sciences 174 (2) (2014) 101-114.
Reference
[1] Shen H.S. (2009) Functionally Graded M of plates and Shells. CRC Press, Florida.
[2] J.N.Reddy and C.D.Chin, (1998). Thermomech. Analysis of Functionally Graded Cylinders and Plates,J.Therm.Stresses, vol.21,pp.593-626
[3] J.Yang,H.-S.Shen. Free vibration and parametric resonance of shear deformable functionally graded cylindrical panels (2003).J.Sound and Vibration 261,871-893]
[4] R.Javaheri and M.R.Eslami (2002). Thermal Buckling of functionally graded plates,AIAAJ.,vol.40,pp.162-169,.]
V.R.Kar and S.Panda (2016) Geometrical nonlinear free vibration analysis of FGM spherical panel under nonlinear thermal loading with TD and TID properties. J. of thermal Stresses,V.39,No.8,942-959
[5] J. Awrejcewicz, L. Kurpa, O. Mazur, On the parametric vibrations and meshless discretization of orthotropic plates with complex shape. International Journal of Nonlinear Sciences and Numerical Simulation 11 (5) (2010) 371-386.
[6] J. Awrejcewicz, L. Kurpa, T. Shmatko, Investigating geometrically nonlinear vibrations of laminated shallow shells with layers of variable thickness via the R-functions theory. Composite Structures 125 (2015) 575–585.
[7] L. Kurpa, T. Shmatko, G. Timchenko, Free vibration analysis of laminated shallow shells with complex shape using the R-functions method. Composite Structures 93 (2010) 225–233.
[8] L.V. Kurpa, O.S. Mazur, Method of R-functions for investigating parametric vibrations of orthotropic plates with complex shape. Journal of Mathematical Sciences 171 (4) 2010 1-14.
[9] L.V. Kurpa, O.S. Mazur, V.V. Tkachenko, Parametric vibrations of multilayer plates of complex shape. Journal of Mathematical Sciences 174 (2) (2014) 101-114.