caa a22 4500 44581196X CHVBK 20180317145214.0 cr unu---uuuuu 170323e20111001xx s 000 0 eng 10.1007/s00419-010-0495-7 doi (NATIONALLICENCE)springer-10.1007/s00419-010-0495-7 Thermal instability of functionally graded deep spherical shell [Elektronische Daten] [R. Shahsiah, M. Eslami, M. Sabzikar Boroujerdy] Thermal instability of deep spherical shells made of functionally graded material (FGM) is studied in this paper. The governing equations are based on the first-order theory of shells and the Sanders nonlinear kinematics equations. It is assumed that the mechanical properties are linear functions of thickness coordinate. The constituent material of the functionally graded shell is assumed to be a mixture of ceramic and metal. The analytical solutions are obtained for three types of thermal loadings including the uniform temperature rise (UTR), the linear radial temperature (LRT), and the nonlinear radial temperature (NRT). Results are validated with the known data in literature. Springer-Verlag, 2010 Thermal buckling nationallicence Spherical shells nationallicence Functionally graded material nationallicence a : Geometrical parameter as shown in Fig. 2 nationallicence E m , E c : Modulus of elasticity of metal and ceramic nationallicence h : Thickness nationallicence H : Geometrical parameter as shown in Fig. 2 nationallicence k ij : Curvature of middle surface nationallicence M ij : Moment resultant nationallicence ( M ij )1 : Moment resultant related to stable state nationallicence N ij : Force resultant nationallicence ( N ij )0 : Force resultant related to equilibrium state nationallicence ( N ij )1 : Force resultant related to stable state nationallicence $${N_{\theta_{0}}^{b},\,\,N_{\phi_{0}}^{b}}$$ : Circumferential and meridional prebuckling loads nationallicence R : Mean radius nationallicence $${r,\,\theta,\,\phi}$$ : Radial, circumferential, and meridional direction nationallicence T a : Inside temperature difference of the shell nationallicence T b : Outside temperature difference of the shell nationallicence u , v , w : Meridional, circumferential, and radial displacement nationallicence u 1, v 1, w 1 : Meridional, circumferential, and radial displacement related to stable state nationallicence z : Distance from the middle surface nationallicence α m , α c : Thermal expansion coefficient of metal and ceramic nationallicence β θ : Rotation of middle surface about the $${\phi}$$ direction nationallicence $${\beta_{\theta_{1}}}$$ : Rotation of middle surface about the $${\phi}$$ direction related to stable state nationallicence $${\beta_{\phi}}$$ : Rotation of middle surface about the θ direction nationallicence $${\beta_{\phi_{1}}}$$ : Rotation of middle surface about the θ direction related to stable state nationallicence $${\epsilon_{i}}$$ : Normal strain nationallicence $${(\epsilon_{i})_{m}}$$ : Normal strain of middle surface nationallicence $${(\epsilon_{i})_{m1}}$$ : Normal strain of middle surface related to stable state nationallicence γ ij : Shear strain nationallicence ( γ ij ) m : Shear strain of middle surface nationallicence ( γ ij ) m 1 : Shear strain of middle surface related to stable state nationallicence $${\phi_{L}}$$ : Supportive angle nationallicence T : Temperature difference nationallicence ν : Poisson's ratio nationallicence σ ii : Normal stress nationallicence τ ij : Shear stress nationallicence Shahsiah R. ME Department, I.A.U. Tehran Central Branch, Tehran, Iran aut Eslami M. Thermoelasticity Center of Excellence, ME Department, Amirkabir University of Technology, Tehran, Iran aut Sabzikar Boroujerdy M. Thermoelasticity Center of Excellence, ME Department, Amirkabir University of Technology, Tehran, Iran aut Archive of Applied Mechanics Springer-Verlag 81/10(2011-10-01), 1455-1471 0939-1533 81:10<1455 2011 81 419 https://doi.org/10.1007/s00419-010-0495-7 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00419-010-0495-7 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Shahsiah R. ME Department, I.A.U. Tehran Central Branch, Tehran, Iran aut NATIONALLICENCE 700 1- Eslami M. Thermoelasticity Center of Excellence, ME Department, Amirkabir University of Technology, Tehran, Iran aut NATIONALLICENCE 700 1- Sabzikar Boroujerdy M. Thermoelasticity Center of Excellence, ME Department, Amirkabir University of Technology, Tehran, Iran aut NATIONALLICENCE 773 0- Archive of Applied Mechanics Springer-Verlag 81/10(2011-10-01), 1455-1471 0939-1533 81:10<1455 2011 81 419 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer