Generalized coupled thermoelasticity of functionally graded cylindrical shells

Abstract

SUMMARYIn this paper, the response of a circular cylindrical thin shell made of the functionally graded material based on the generalized theory of thermoelasticity is obtained. The governing equations of the generalized theory of thermoelasticity and the energy equations are simultaneously solved for a functionally graded axisymmetric cylindrical shell subjected to thermal shock load. Thermoelasticity with second sound effect in cylindrical shells based on the Lord-Shulman model is compared with the Green-Lindsay model. A second-order shear deformation shell theory, that accounts for the transverse shear strains and rotations, is considered. Including the thermo-mechanical coupling and rotary inertia, a Galerkin finite element formulation in space domain and the Laplace transform in time domain is used to formulate the problem. The inverse Laplace transform is obtained using a numerical algorithm. The shell is graded through the thickness assuming a volume fraction of metal and ceramic, using a power law distribution. The effects of temperature field for linear and non-linear distributions across the shell thickness are examined. The results are validated with the known data in the literature.

Thermoelastic Interactions on Two-Temperature Generalized Thermoelasticity in an Infinite Medium with a Cylindrical Cavity

“…Several investigations were then carried out based on these generalized theories of thermoelasticity. A few relevant to the present study are [6][7][8][9][10][11][12][13].…”

Thermoelastic Analysis of Functionally Graded Cylindrical Panels with Piezoelectric Layers

“…Countermeasures against these limitations have encouraged the development of different coupled thermoelasticity theories [1][2][3]. Among them, the Lord and Shulman (L-S) generalized thermoelasticity theory is one of the simplest formulations applied in the literature [4][5][6][7][8][9][10][11][12][13][14], which includes a relaxation time and a coupling between thermal and mechanical energies [1]. In this framework, some interesting thermoelastic studies based on an uncoupled classical thermoelasticity theory of FG cylindrical panels and shells can be found in [15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31].…”

Transient analysis of rotating functionally graded truncated conical shells based on the Lord–Shulman model

“…Different types of boundary conditions at the edges z ¼0 and β L cos can be considered which can be obtained by combining the conditions stated in Eqs. (9) and (10). For example, for the FG truncated conical shell with clamped and simply supported edges, one may consider, Clamped edge:…”

“…In comparison with the research works in these topics, only limited studies can be found on the coupled thermoelasticity of stationary FG cylindrical shells [8][9][10][11][12][13][14]. In these interesting studies [8][9][10][11][12][13][14], the coupled thermoelastic responses of functionally graded cylindrical shells subjected to the thermal load with prescribed temperature or convection on the external surfaces of FG shells were presented.…”