Thermo-magnetic analysis of thick-walled spherical pressure vessels made of functionally graded materials
|
摘要
This study presents an analytical solution of thermal and mechanical displacements, strains, and stresses for a thick-walled rotating spherical pressure vessel made of functionally graded materials(FGMs). The pressure vessel is subject to axisymmetric mechanical and thermal loadings within a uniform magnetic field. The material properties of the FGM are considered as the power-law distribution along the thickness. Navier's equation, which is a second-order ordinary differential equation, is derived from the mechanical equilibrium equation with the consideration of the thermal stresses and the Lorentz force resulting from the magnetic field. The distributions of the displacement,strains, and stresses are determined by the exact solution to Navier's equation. Numerical results clarify the influence of the thermal loading, magnetic field, non-homogeneity constant, internal pressure, and angular velocity on the magneto-thermo-elastic response of the functionally graded spherical vessel. It is observed that these parameters have remarkable effects on the distributions of radial displacement, radial and circumferential strains, and radial and circumferential stresses.
This study presents an analytical solution of thermal and mechanical displacements, strains, and stresses for a thick-walled rotating spherical pressure vessel made of functionally graded materials(FGMs). The pressure vessel is subject to axisymmetric mechanical and thermal loadings within a uniform magnetic field. The material properties of the FGM are considered as the power-law distribution along the thickness. Navier's equation, which is a second-order ordinary differential equation, is derived from the mechanical equilibrium equation with the consideration of the thermal stresses and the Lorentz force resulting from the magnetic field. The distributions of the displacement,strains, and stresses are determined by the exact solution to Navier's equation. Numerical results clarify the influence of the thermal loading, magnetic field, non-homogeneity constant, internal pressure, and angular velocity on the magneto-thermo-elastic response of the functionally graded spherical vessel. It is observed that these parameters have remarkable effects on the distributions of radial displacement, radial and circumferential strains, and radial and circumferential stresses.
This study presents an analytical solution of thermal and mechanical displacements, strains, and stresses for a thick-walled rotating spherical pressure vessel made of functionally graded materials(FGMs). The pressure vessel is subject to axisymmetric mechanical and thermal loadings within a uniform magnetic field. The material properties of the FGM are considered as the power-law distribution along the thickness. Navier's equation, which is a second-order ordinary differential equation, is derived from the mechanical equilibrium equation with the consideration of the thermal stresses and the Lorentz force resulting from the magnetic field. The distributions of the displacement,strains, and stresses are determined by the exact solution to Navier's equation. Numerical results clarify the influence of the thermal loading, magnetic field, non-homogeneity constant, internal pressure, and angular velocity on the magneto-thermo-elastic response of the functionally graded spherical vessel. It is observed that these parameters have remarkable effects on the distributions of radial displacement, radial and circumferential strains, and radial and circumferential stresses.
引文
[1]KOIZUMI,M.FGM activities in Japan.Composites:Part B,28(1-2),1-4(1996)
[2]HOSSEINI,M.,DINI,A.,and EFTEKHARI,M.Strain gradient effects on the thermoelastic analysis of a functionally graded micro-rotating cylinder using generalized differential quadrature method.Acta Mechanica,228(5),1-18(2017)
[3]REDDY,J.N.and CHIN,C.D.Thermomechanical analysis of functionally graded cylinders and plates.Journal of Thermal Stresses,21(6),593-626(1998)
[4]MIYAMOTO,Y.,KAYSSER,W.,RABIN,B.,KAWASAKI,A.,and FORD,R.Functionally Graded Materials:Design,Processing and Applications,Kluwer,London(1999)
[5]DINI,A.and ABOLBASHARI,M.H.Hygro-thermo-electro-elastic response of a functionally graded piezoelectric cylinder resting on an elastic foundation subjected to non-axisymmetric loads.International Journal of Pressure Vessels and Piping,147,21-40(2016)
[6]CHEN,Y.and SHI,Z.F.Analysis of a functionally graded piezothermoelastic hollow cylinder.Journal of Zhejiang University-Science A,6(9),956-961(2005)
[7]MOHSENIZADEH,M.,GASBARRI,F.,MUNTHER,M.,BEHESHTI,A.,and DAVAMI,K.Additively-manufactured lightweight metamaterials for energy absorption.Materials and Design,139,521-530(2018)
[8]DI BARBA,P.,DUGHIERO,F.,and SIENI,E.Magnetic field synthesis in the design of inductors for magnetic fluid hyperthermia.IEEE Transactions on Magnetics,46(8),2931-2934(2010)
[9]KIRSCHVINK,J.L.Uniform magnetic fields and double-wrapped coil systems:improved techniques for the design of bioelectromagnetic experiments.Bioelectromagnetics,13(5),401-411(1992)
[10]MIRZAEVA,G.,SUMMERS,T.,and BETZ,R.A laboratory system to produce a highly accurate and uniform magnetic field for sensor calibration.2012 IEEE International Conference on Industrial Technology,Institute of Electrical and Electronics Engineers(IEEE),New York,1020-1025(2012)
[11]MODI,A.,SINGH,R.,CHAVAN,V.,KUKREJA,K.,GHODE,S.,MANWAR,K.,and KAZI,F.Hexagonal coil systems for uniform magnetic field generation.2016 IEEE Asia-Pacific Conference on Applied Electromagnetics,Institute of Electrical and Electronics Engineers(IEEE),New York,47-51(2016)
[12]TUTUNCU,N.and OZTURK,M.Exact solutions for stresses in functionally graded pressure vessels.Composites Part B:Engineering,32(8),683-686(2001)
[13]DAI,H.L.,FU,Y.M.,and DONG,Z.M.Exact solutions for functionally graded pressure vessels in a uniform magnetic field.International Journal of Solids and Structures,43(18-19),5570-5580(2006)
[14]SANTOS,H.,SOARES,C.M.M.,SOARES,C.A.M.,and REDD,J.N.A semi-analytical finite element model for the analysis of cylindrical shells made of functionally graded materials under thermal shock.Composite Structures,86(1-3),10-21(2008)
[15]DAI,H.L.,YANG,L.,and ZHENG,H.Y.Magnetothermoelastic analysis of functionally graded hollow spherical structures under thermal and mechanical loads.Solid State Sciences,13(2),372-378(2011)
[16]KELES,I.and TUTUNCU,N.Exact analysis of axisymmetric dynamic response of functionally graded cylinders(or disks)and spheres.Journal of Applied Mechanics,78(6),061014(2011)
[17]OOTAO,Y.and ISHIHARA,M.Exact solution of transient thermal stress problem of a multilayered magneto-electro-thermoelastic hollow sphere.Applied Mathematical Modelling,36(4),1431-1443(2012)
[18]HOSSEINI,M.and DINI,A.Magneto-thermo-elastic response of a rotating functionally graded cylinder.Structural Engineering and Mechanics,56(1),137-156(2015)
[19]YUAN,K.Magneto-thermo-elastic stresses in an infinitely long cylindrical conductor carrying a uniformly distributed axial current.Applied Scientific Research,26(1),307-314(1972)
[20]LUTZ,M.P.and ZIMMERMAN,R.W.Thermal stresses and thermal expansion in a uniformly heated functionally graded cylinder.Journal of Thermal Stresses,22(2),177-188(1999)
[21]RUHI,M.,ANGOSHTARI,A.,and NAGHDABADI,R.Thermoelastic analysis of thick-walled finite-length cylinders of functionally graded materials.Journal of Thermal Stresses,28(4),391-408(2005)
[22]JABBARI,M.,BAHTUI,A.,and ESLAMI,M.R.Axisymmetric mechanical and thermal stresses in thick long FGM cylinders.Journal of Thermal Stresses,29(7),643-663(2006)
[23]DAI,H.L.and FU,Y.M.Magnetothermoelastic interactions in hollow structures of functionally graded material subjected to mechanical loads.International Journal of Pressure Vessels and Piping,84(3),132-138(2007)
[24]ZENKOUR,A.M.Stress distribution in rotating composite structures of functionally graded solid disks.Journal of Materials Processing Technology,209(7),3511-3517(2009)
[25]PENG,X.L.and LI,X.F.Thermal stress in rotating functionally graded hollow circular disks.Composite Structures,92(8),1896-1904(2010)
[26]AKBARZADEH,A.H.and CHEN,Z.T.Magnetoelastic field of a multilayered and functionally graded cylinder with a dynamic polynomial eigenstrain.Journal of Applied Mechanics,81(2),021009(2013)
[27]ZENKOUR,A.M.On the magneto-thermo-elastic responses of FG annular sandwich disks.International Journal of Engineering Science,75,54-66(2014)
[28]KHOSHGOFTAR,M.J.,MIRZAALI,M.J.,and RAHIMI,G.H.Thermoelastic analysis of nonuniform pressurized functionally graded cylinder with variable thickness using first order shear deformation theory(FSDT)and perturbation method.Chinese Journal of Mechanical Engineering,28(6),1149-1156(2015)
[29]JABBARI,M.,SOHRABPOUR,S.,and ESLAMI,M.R.Mechanical and thermal stresses in a functionally graded hollow cylinder due to radially symmetric loads.International Journal of Pressure Vessels and Piping,79(7),493-497(2002)
[30]JABBARI,M.,SOHRABPOUR,S.,and ESLAMI,M.R.General solution for mechanical and thermal stresses in a functionally graded hollow cylinder due to nonaxisymmetric steady-state loads.Journal of Applied Mechanics,70(1),111-118(2003)
[31]TOKOVYY,Y.V.and MA,C.C.Analysis of 2D non-axisymmetric elasticity and thermoelasticity problems for radially inhomogeneous hollow cylinders.Journal of Engineering Mathematics,61(2-4),171-184(2007)
[32]ASGHARI,M.and GHAFOORI,E.A three-dimensional elasticity solution for functionally graded rotating disks.Composite Structures,92(5),1092-1099(2010)
[33]YAS,M.H.and ARAGH,B.S.Three-dimensional analysis for thermoelastic response of functionally graded fiber reinforced cylindrical panel.Composite Structures,92(10),2391-2399(2010)
[34]AKBARZADEH,A.H.and CHEN,Z.T.Magnetoelectroelastic behavior of rotating cylinders resting on an elastic foundation under hygrothermal loading.Smart Materials and Structures,21(12),125013(2012)
[35]AKBARZADEH,A.H.and CHEN,Z.T.Hygrothermal stresses in one-dimensional functionally graded piezoelectric media in constant magnetic field.Composite Structures,97,317-331(2013)
[36]ZENKOUR,A.M.Hygrothermoelastic responses of inhomogeneous piezoelectric and exponentially graded cylinders.International Journal of Pressure Vessels and Piping,119,8-18(2014)
[37]SAADATFAR,M.and AGHAIE-KHAFRI,M.Hygrothermal analysis of a rotating smart exponentially graded cylindrical shell with imperfect bonding supported by an elastic foundation.Aerospace Science and Technology,43,37-50(2015)
[38]DAI,H.L.,FU,Y.M.,and YANG,J.H.Electromagnetoelastic behaviors of functionally graded piezoelectric solid cylinder and sphere.Acta Mechanica Sinica,23(1),55-63(2007)
[39]OBATA,Y.and NODA,N.Steady thermal stresses in a hollow circular cylinder and a hollow sphere of a functionally gradient material.Journal of Thermal Stresses,17(3),471-487(1994)
[40]LUTZ,M.P.and ZIMMERMAN,R.W.Thermal stresses and effective thermal expansion coefficient of a functionally gradient sphere.Journal of Thermal Stresses,19(1),39-54(1996)
[41]SAADATFAR,M.and RASTGOO,A.Stress in piezoelectric hollow sphere with thermal gradient.Journal of Mechanical Science and Technology,22(8),1460-1467(2009)
[42]BARATI,A.R.and JABBARI,M.Two-dimensional piezothermoelastic analysis of a smart FGMhollow sphere.Acta Mechanica,226(7),2195-2224(2015)
[43]ESLAMI,M.R.,BABAEI,M.H.,and POULTANGARI,R.Thermal and mechanical stresses in a functionally graded thick sphere.International Journal of Pressure Vessels and Piping,82(7),522-527(2005)
[44]IACCARINO,G.L.and BATRA,R.C.Analytical solution for radial deformations of functionally graded isotropic and incompressible second-order elastic hollow spheres.Journal of Elasticity,107(2),179-197(2011)
[45]SAADATFAR,M.and AGHAIE-KHAFRI,M.Hygrothermomagnetoelectroelastic analysis of a functionally graded magnetoelectroelastic hollow sphere resting on an elastic foundation.Smart Materials and Structures,23(3),035004(2014)
[46]PRAVEEN,G.N.and REDDY,J.N.Nonlinear transient thermoelastic analysis of functionally graded ceramic-metal plates.International Journal of Solids and Structures,35(33),4457-4476(1998)
[2]HOSSEINI,M.,DINI,A.,and EFTEKHARI,M.Strain gradient effects on the thermoelastic analysis of a functionally graded micro-rotating cylinder using generalized differential quadrature method.Acta Mechanica,228(5),1-18(2017)
[3]REDDY,J.N.and CHIN,C.D.Thermomechanical analysis of functionally graded cylinders and plates.Journal of Thermal Stresses,21(6),593-626(1998)
[4]MIYAMOTO,Y.,KAYSSER,W.,RABIN,B.,KAWASAKI,A.,and FORD,R.Functionally Graded Materials:Design,Processing and Applications,Kluwer,London(1999)
[5]DINI,A.and ABOLBASHARI,M.H.Hygro-thermo-electro-elastic response of a functionally graded piezoelectric cylinder resting on an elastic foundation subjected to non-axisymmetric loads.International Journal of Pressure Vessels and Piping,147,21-40(2016)
[6]CHEN,Y.and SHI,Z.F.Analysis of a functionally graded piezothermoelastic hollow cylinder.Journal of Zhejiang University-Science A,6(9),956-961(2005)
[7]MOHSENIZADEH,M.,GASBARRI,F.,MUNTHER,M.,BEHESHTI,A.,and DAVAMI,K.Additively-manufactured lightweight metamaterials for energy absorption.Materials and Design,139,521-530(2018)
[8]DI BARBA,P.,DUGHIERO,F.,and SIENI,E.Magnetic field synthesis in the design of inductors for magnetic fluid hyperthermia.IEEE Transactions on Magnetics,46(8),2931-2934(2010)
[9]KIRSCHVINK,J.L.Uniform magnetic fields and double-wrapped coil systems:improved techniques for the design of bioelectromagnetic experiments.Bioelectromagnetics,13(5),401-411(1992)
[10]MIRZAEVA,G.,SUMMERS,T.,and BETZ,R.A laboratory system to produce a highly accurate and uniform magnetic field for sensor calibration.2012 IEEE International Conference on Industrial Technology,Institute of Electrical and Electronics Engineers(IEEE),New York,1020-1025(2012)
[11]MODI,A.,SINGH,R.,CHAVAN,V.,KUKREJA,K.,GHODE,S.,MANWAR,K.,and KAZI,F.Hexagonal coil systems for uniform magnetic field generation.2016 IEEE Asia-Pacific Conference on Applied Electromagnetics,Institute of Electrical and Electronics Engineers(IEEE),New York,47-51(2016)
[12]TUTUNCU,N.and OZTURK,M.Exact solutions for stresses in functionally graded pressure vessels.Composites Part B:Engineering,32(8),683-686(2001)
[13]DAI,H.L.,FU,Y.M.,and DONG,Z.M.Exact solutions for functionally graded pressure vessels in a uniform magnetic field.International Journal of Solids and Structures,43(18-19),5570-5580(2006)
[14]SANTOS,H.,SOARES,C.M.M.,SOARES,C.A.M.,and REDD,J.N.A semi-analytical finite element model for the analysis of cylindrical shells made of functionally graded materials under thermal shock.Composite Structures,86(1-3),10-21(2008)
[15]DAI,H.L.,YANG,L.,and ZHENG,H.Y.Magnetothermoelastic analysis of functionally graded hollow spherical structures under thermal and mechanical loads.Solid State Sciences,13(2),372-378(2011)
[16]KELES,I.and TUTUNCU,N.Exact analysis of axisymmetric dynamic response of functionally graded cylinders(or disks)and spheres.Journal of Applied Mechanics,78(6),061014(2011)
[17]OOTAO,Y.and ISHIHARA,M.Exact solution of transient thermal stress problem of a multilayered magneto-electro-thermoelastic hollow sphere.Applied Mathematical Modelling,36(4),1431-1443(2012)
[18]HOSSEINI,M.and DINI,A.Magneto-thermo-elastic response of a rotating functionally graded cylinder.Structural Engineering and Mechanics,56(1),137-156(2015)
[19]YUAN,K.Magneto-thermo-elastic stresses in an infinitely long cylindrical conductor carrying a uniformly distributed axial current.Applied Scientific Research,26(1),307-314(1972)
[20]LUTZ,M.P.and ZIMMERMAN,R.W.Thermal stresses and thermal expansion in a uniformly heated functionally graded cylinder.Journal of Thermal Stresses,22(2),177-188(1999)
[21]RUHI,M.,ANGOSHTARI,A.,and NAGHDABADI,R.Thermoelastic analysis of thick-walled finite-length cylinders of functionally graded materials.Journal of Thermal Stresses,28(4),391-408(2005)
[22]JABBARI,M.,BAHTUI,A.,and ESLAMI,M.R.Axisymmetric mechanical and thermal stresses in thick long FGM cylinders.Journal of Thermal Stresses,29(7),643-663(2006)
[23]DAI,H.L.and FU,Y.M.Magnetothermoelastic interactions in hollow structures of functionally graded material subjected to mechanical loads.International Journal of Pressure Vessels and Piping,84(3),132-138(2007)
[24]ZENKOUR,A.M.Stress distribution in rotating composite structures of functionally graded solid disks.Journal of Materials Processing Technology,209(7),3511-3517(2009)
[25]PENG,X.L.and LI,X.F.Thermal stress in rotating functionally graded hollow circular disks.Composite Structures,92(8),1896-1904(2010)
[26]AKBARZADEH,A.H.and CHEN,Z.T.Magnetoelastic field of a multilayered and functionally graded cylinder with a dynamic polynomial eigenstrain.Journal of Applied Mechanics,81(2),021009(2013)
[27]ZENKOUR,A.M.On the magneto-thermo-elastic responses of FG annular sandwich disks.International Journal of Engineering Science,75,54-66(2014)
[28]KHOSHGOFTAR,M.J.,MIRZAALI,M.J.,and RAHIMI,G.H.Thermoelastic analysis of nonuniform pressurized functionally graded cylinder with variable thickness using first order shear deformation theory(FSDT)and perturbation method.Chinese Journal of Mechanical Engineering,28(6),1149-1156(2015)
[29]JABBARI,M.,SOHRABPOUR,S.,and ESLAMI,M.R.Mechanical and thermal stresses in a functionally graded hollow cylinder due to radially symmetric loads.International Journal of Pressure Vessels and Piping,79(7),493-497(2002)
[30]JABBARI,M.,SOHRABPOUR,S.,and ESLAMI,M.R.General solution for mechanical and thermal stresses in a functionally graded hollow cylinder due to nonaxisymmetric steady-state loads.Journal of Applied Mechanics,70(1),111-118(2003)
[31]TOKOVYY,Y.V.and MA,C.C.Analysis of 2D non-axisymmetric elasticity and thermoelasticity problems for radially inhomogeneous hollow cylinders.Journal of Engineering Mathematics,61(2-4),171-184(2007)
[32]ASGHARI,M.and GHAFOORI,E.A three-dimensional elasticity solution for functionally graded rotating disks.Composite Structures,92(5),1092-1099(2010)
[33]YAS,M.H.and ARAGH,B.S.Three-dimensional analysis for thermoelastic response of functionally graded fiber reinforced cylindrical panel.Composite Structures,92(10),2391-2399(2010)
[34]AKBARZADEH,A.H.and CHEN,Z.T.Magnetoelectroelastic behavior of rotating cylinders resting on an elastic foundation under hygrothermal loading.Smart Materials and Structures,21(12),125013(2012)
[35]AKBARZADEH,A.H.and CHEN,Z.T.Hygrothermal stresses in one-dimensional functionally graded piezoelectric media in constant magnetic field.Composite Structures,97,317-331(2013)
[36]ZENKOUR,A.M.Hygrothermoelastic responses of inhomogeneous piezoelectric and exponentially graded cylinders.International Journal of Pressure Vessels and Piping,119,8-18(2014)
[37]SAADATFAR,M.and AGHAIE-KHAFRI,M.Hygrothermal analysis of a rotating smart exponentially graded cylindrical shell with imperfect bonding supported by an elastic foundation.Aerospace Science and Technology,43,37-50(2015)
[38]DAI,H.L.,FU,Y.M.,and YANG,J.H.Electromagnetoelastic behaviors of functionally graded piezoelectric solid cylinder and sphere.Acta Mechanica Sinica,23(1),55-63(2007)
[39]OBATA,Y.and NODA,N.Steady thermal stresses in a hollow circular cylinder and a hollow sphere of a functionally gradient material.Journal of Thermal Stresses,17(3),471-487(1994)
[40]LUTZ,M.P.and ZIMMERMAN,R.W.Thermal stresses and effective thermal expansion coefficient of a functionally gradient sphere.Journal of Thermal Stresses,19(1),39-54(1996)
[41]SAADATFAR,M.and RASTGOO,A.Stress in piezoelectric hollow sphere with thermal gradient.Journal of Mechanical Science and Technology,22(8),1460-1467(2009)
[42]BARATI,A.R.and JABBARI,M.Two-dimensional piezothermoelastic analysis of a smart FGMhollow sphere.Acta Mechanica,226(7),2195-2224(2015)
[43]ESLAMI,M.R.,BABAEI,M.H.,and POULTANGARI,R.Thermal and mechanical stresses in a functionally graded thick sphere.International Journal of Pressure Vessels and Piping,82(7),522-527(2005)
[44]IACCARINO,G.L.and BATRA,R.C.Analytical solution for radial deformations of functionally graded isotropic and incompressible second-order elastic hollow spheres.Journal of Elasticity,107(2),179-197(2011)
[45]SAADATFAR,M.and AGHAIE-KHAFRI,M.Hygrothermomagnetoelectroelastic analysis of a functionally graded magnetoelectroelastic hollow sphere resting on an elastic foundation.Smart Materials and Structures,23(3),035004(2014)
[46]PRAVEEN,G.N.and REDDY,J.N.Nonlinear transient thermoelastic analysis of functionally graded ceramic-metal plates.International Journal of Solids and Structures,35(33),4457-4476(1998)