Effect of Material Gradient on Stresses of FGM Rotating Thick-Walled Cylindrical Pressure Vessel with Longitudinal Variation of Properties under Non-uniform Internal and External Pressure
الموضوعات :Mehdi Jabbari 1 , Mohammad Zamani Nejad 2 , Mehdi Ghannad 3
1 - Mechanical Engineering Department, Yasouj University, Yasouj, Iran
2 - Mechanical Engineering Department, Yasouj University, Yasouj, Iran.
3 - Mechanical Engineering Faculty, Shahrood University, Shahrood, Iran
الکلمات المفتاحية: Thick cylindrical shell, Functionally graded material (FGM), Multi-layered method (MLM), Longitudinal variation of properties, Non-uniform pressure,
ملخص المقالة :
The present paper provides a semi-analytical solution to obtain the displacements and stresses in a functionally graded material (FGM) rotating thick cylindrical shell with clamped ends under non-uniform pressure. Material properties of cylinder are assumed to change along the axial direction according to a power law form. It is also assumed that the Poisson’s ratio is constant. Given the existence of shear stress in the thick cylindrical shell due to material and pressure changes along the axial direction, the governing equations are obtained based on first-order shear deformation theory (FSDT). These equations are in the form of a set of general differential equations with variable coefficients. Given that the FG cylinder is divided into n homogenous disks, n sets of differential equations with constant coefficients are obtained. The solution of this set of equations, applying the boundary conditions and continuity conditions between the layers, yields displacements and stresses. The problem was also solved, using the finite element method (FEM), the results of which were compared with those of the multi-layered method (MLM). Finally, some numerical results are presented to study the effects of applied pressure, non-homogeneity index, and power law index of FGM on the mechanical behavior of the cylindrical shell.
[1] M. Z. Nejad, M. Gharibi, “Effect of material gradient on stresses of thick FGM spherical pressure vessels with exponentially-varying properties”, J. Adv. Mat. and Proc., Vol. 2, no. 3, 2014, pp. 39-46.
[2] M. Z. Nejad, M. Jabbari, M. Ghannad, “Elastic analysis of FGM rotating thick truncated conical shells with axially-varying properties under non-uniform pressure loading”, Compos. Struct., Vol. 122, 2015, pp. 561-569.
[3] H. L. Dai, Y. N. Rao, “Dynamic thermoelastic behavior of a double-layered hollow cylinder with an FGM layer”, J. Therm. Stresses, Vol. 36, no. 9, 2013, pp. 962-984.
[4] M. Z. Nejad, M. Jabbari, M. Ghannad, “Elastic analysis of axially functionally graded rotating thick cylinder with variable thickness under non-uniform arbitrarily pressure loading”, Int. J. Eng. Sci., Vol. 89, 2015, pp. 86-99.
[5] M. Jabbari, M. Z. Nejad, M. Ghannad, “Thermo-elastic analysis of axially functionally graded rotating thick cylindrical pressure vessels with variable thickness under mechanical loading”, Int. J. Eng. Sci., Vol. 96, 2015, pp. 1–18.
[6] G. Lamé, B. Clapeyron, “Mémoire sur l'équilibre intérieur des corps solides homogènes”, Journal für die reine und angewandte Mathematik, 1831, pp. 145-169.
[7] P. M. Naghdi, R. M. Cooper, “Propagation of elastic waves in cylindrical shells, including the effects of transverse shear and rotatory inertia”, J. Acous. Soc. America, Vol. 28, no. 1, 1956, pp. 56-63.
[8] I. Mirsky, G. Hermann, “Axially motions of thick cylindrical shells”, J. Appl. Mech., Vol. 25, 1958, pp. 97-102.
[9] F. Erdogan, G. Gupta, “The stress analysis of multi-layered composites with a flaw”,, Int. J. Solids Struct., Vol. 7, no. 1, 1971, pp. 39-61
[10] K. Shirakawa, “Displacements and stresses in cylindrical shells based on an improved theory”, Int. J. Mech. Sci., Vol. 26, no. 2, 1984, pp. 93-103.
[11] J. N. Reddy, “A refined nonlinear theory of plates with transverse shear deformation”,, Int. J. Solids Struct., Vol. 20, no. 9/10, 1984, pp. 881-896
[12] C. O. Horgan, A. M. Chan, “The pressurized hollow cylinder or disk problem for functionally graded isotropic linearly elastic materials”, J. Elast., Vol. 55, no. 1, 1999, pp. 43-59.
[13] F. I. Niordson, “An asymptotic theory for circular cylindrical shells”, Int. J. Solids Struct., Vol. 37, no. 13, 2000, pp. 1817-1839.
[14] T. Y. Ng, K. Y. Lam, K. M. Liew, J. N. Reddy, “Dynamic stability analysis of functionally graded cylindrical shells under periodic axial loading”, Int. J. Solids Struct., Vol. 38, no. 8, 2001, pp. 1295–1309.
[15] E. Pan, A. K. Roy, “A simple plane-strain solution for functionally graded multilayered isotropic cylinders”, Struc. Eng. Mech., Vol. 24, no. 6, 2006, pp. 727-740.
[16] H. Xiang, Z. Shi, T. Zhang, “Elastic analyses of heterogeneous hollow cylinders”, Mech. Res. Commun., Vol. 33, no. 5, 2006, pp. 681-691.
[17] J. H. Kang, “Field equations, equations of motion, and energy functionals for thick shells of reVolution with arbitrary curvature and variable thickness from a three-dimensional theory”, Acta Mech., Vol. 188, no. 1-2, 2007, pp. 21-37.
[18] M. Z. Nejad, G. H. Rahimi, M. Ghannad, “Set of field equations for thick shell of revolution made of functionally graded materials in curvilinear coordinate system”, Mechanika, Vol. 77, no. 3, 2009, pp. 18-26.
[19] H. Santos, C. M. M. Soares, C. A. M. Soares, J. N. Reddy, “A semi-analytical finite element model for the analysis of cylindrical shells made of functionally graded materials”, Compos. Struct., Vol. 91, no. 4, 2009, pp. 427-432.
[20] N. Tutuncu, B. Temel, “A novel approach to stress analysis of pressurized FGM cylinders, disks and spheres”, Compos. Struct., Vol. 91, no. 3, 2009, pp. 385-390.
[21] M. Z. Nejad, G. H. Rahimi, “Elastic analysis of FGM rotating cylindrical pressure vessels”, J. Chin. Ins. Eng., Vol. 33, no. 4, 2010, pp. 525-530.
[22] A. G. Arani, Z. K., M. R. M. Maraghi, A. R. Shajari, “Thermo-piezo-magneto-mechanical stresses analysis of FGPM hollow rotating thin disk”, Int. J. Mech. Mater. Des., Vol. 6, 2011, pp. 341-349,
[23] M. Ghannad, M. Z. Nejad, “Complete elastic solution of pressurized thick cylindrical shells made of heterogeneous functionally graded materials”, Mechanika, Vol. 18, no. 6, 2012, pp. 640-649.
[24] V. V. Zozulya, “A high-order theory for functionally graded axially symmetric cylindrical shells”, Arc. App. Mech., Vol. 83, no. 3, 2013, pp. 331-343.
[25] M. Ghannad, M. Z. Nejad, “Elastic analysis of pressurized thick hollow cylindrical shells with clamped-clamped ends”, Mechanika, Vol. 5, no. 85, 2010, pp. 11-18.
[26] M. Ghannad, M. Z. Nejad, “Elastic solution of pressurized clamped-clamped thick cylindrical shells made of functionally graded materials”, J. Theor. App. Mech., Vol. 51, no. 4, 2013, pp. 1067-1079.
[27] M. Ghannad, H. Gharooni, “Displacements and stresses in pressurized thick FGM cylinders with varying properties of power function based on HSDT”, J. Sol. Mech., Vol. 4, no. 3, 2012, pp. 237-251.
[28] M. J. Khoshgoftar, G. H. Rahimi, M. Arefi, “Exact solution of functionally graded thick cylinder with finite length under longitudinally non-uniform pressure”, Mech. Res. Commun., Vol. 51, 2013, pp. 61-66.
[29] M. Ghannad, G. H. Rahimi, M. Z. Nejad, “Determination of displacements and stresses in pressurized thick cylindrical shells with variable thickness using perturbation technique”, Mechanika, Vol. 18, no. 1, 2012, pp. 14-21.
[30] M. Ghannad, G. H. Rahimi, M. Z. Nejad, “Elastic analysis of pressurized thick cylindrical shells with variable thickness made of functionally graded materials”, Comp. Part B- Eng., Vol. 45, no. 1, 2013, pp. 388-396.
[31] K. Asemi, M. Salehi, M. Akhlaghi, “Elastic solution of a two-dimensional functionally graded thick truncated cone with finite length under hydrostatic combined loads”, Acta Mech., Vol. 217, no. 1-2, 2011, pp. 119-134.
[32] M. Z. Nejad, M. Jabbari, M. Ghannad, “A semi-analytical solution for elastic analysis of rotating thick cylindrical shells with variable thickness using disk form multilayers”, Sci. Wor. J., 2014, Article ID, 932743, pp. 1-10.
[33] A. G. Arani, E. Haghparast, Z. K. Maraghi, S. Amir, “Static stress analysis of carbon nano-tube reinforced composite (CNTRC) cylinder under non-axisymmetric thermo-mechanical loads and uniform electro-magnetic fields”, Comp. Part B- Eng., Vol. 68, 2014,136-145.
[34] R. C. Batra, “Material tailoring in finite torsional deformations of axially graded Mooney–Rivlin circular cylinder”, Math. Mech. Sol., Vol. 20, no. 2, 2015, pp. 183-189.
[35] M. Z. Nejad, M. Jabbari, M. Ghannad, “Elastic analysis of rotating thick cylindrical pressure vessels under non-uniform pressure: linear and non-linear thickness”, Periodica Poly. Mech.Eng., Vol. 59, no. 2, 2015, pp. 5-73.
[36] M. Shariati, H. Sadeghi, M. Ghannad, H. Gharooni, “Semi analytical analysis of FGM thick-walled cylindrical pressure vessel with longitudinal variation of elastic modulus under internal pressure”, J. Sol. Mech., Vol. 7, no. 2, 2015, pp. 131-145.
[37] S. Vlachoutsis, “Shear correction factors for plates and shells”, Int. J. Numer. Methods Eng., Vol. 33, 1992, pp. 1537–1552.
G. R. Buchanan, C. B. Y. Yii, “Effect of symmetrical boundary conditions on the vibration of thick hollow cylinders”, App. Acou., Vol. 63, no. 5, 2002, pp. 547-566.
