Abstract
A general solution for the one-dimensional steady-state thermal and mechanical stresses in a hollow thick sphere made of porous functionally graded material (FGPM) is presented. The temperature distribution is assumed to be a function of radius, with general thermal and mechanical boundary conditions on the inside and outside surfaces of the sphere. The material properties, except Poisson's ratio, are assumed to vary along the radius r according to a power law function. The analytical solution of the heat conduction equation and the Navier equation lead to the temperature profile, radial displacement, radial stress, and hoop stress as a function of radial direction.
Highlights
Graded materials (FGMs) are made of a mixture with arbitrary composition of two different materials, and the volume fraction of each material changes continuously and gradually
Thick hollow sphere analysis made of Functionally graded materials (FGMs) under mechanical and thermal loads and in asymmetric and two-dimensional (r, θ) state was conducted investigating navier equations and using legendre polynomials [2]
Their assumed thermal boundary conditions are varied along the γ direction and the problem is solved with the potential function method
Summary
Graded materials (FGMs) are made of a mixture with arbitrary composition of two different materials, and the volume fraction of each material changes continuously and gradually. Shao and Wang presented three-dimensional solution to obtain stress fields in an FGM cylindrical plate with a finite length which is mechanical and thermal load tests and showed the results an a graph [10]. Takeuti and Tanigawa have employed the potential function method to obtain the analytical solution of a homogeneous spherical vessel with rotating heat source [12]. They considered the general form of thermal boundary conditions and analyzed the problem in transient condition with the potential functions method. This study investigates the effect of mechanical and thermal stresses on one-dimensional steady state in the poro FGM hollow sphere that fluid trapped in the poro medium which is located in undrained conditions
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