Nonlinear Thermal Stress Analysis of Functionally Graded Thick Cylinders and Spheres
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RESEARCH PAPER
Nonlinear Thermal Stress Analysis of Functionally Graded Thick Cylinders and Spheres Durmuş Yarimpabuç1 Received: 13 February 2020 / Accepted: 21 September 2020 © Shiraz University 2020
Abstract Nonlinear thermal stress analysis in a functionally graded hollow thick cylinders and spheres under the effect of high temperatures and temperature differences is considered by taking into account the material properties of the body both temperature dependent and radially graded, except Poisson’s ratio which is taken to be constant for simplicity. These conditions result in nonlinear governing differential equation that is adopted to solve numerically. The effect of the temperature-dependent material properties on the temperature distribution, radial displacement, and thermal stresses is presented in a graphical form. The importance of the effect of temperature on the material is shown in functionally graded materials manufactured to be exposed to high temperature and temperature difference. Benchmark solutions available in the literature are used to validate the results and to emphasize the convergence of the numerical solutions. Keywords Nonlinear thermal stress analysis · Functionally graded material · Chebyshev pseudospectral method · Fixedpoint iteration List of Symbols E(r, T) Radial and temperature-dependent Young modulus Ei Young modulus of the material in the inner boundary k(r, T) Radial and temperature-dependent thermal conductivity ki Thermal conductivity of the material in the inner boundary mi Inhomogeneity parameters ni Nonlinearity parameters Pi Pressure in the inner surface ri , ro Inner and outer radius of the medium r, 𝜃 Polar coordinates T Temperature of the body Ti , To Inner and outer temperature of the body u Radial displacement
* Durmuş Yarimpabuç [email protected] 1
Department of Mathematics, Osmaniye Korkut Ata University, 80000 Osmaniye, Turkey
Greek Letters 𝛼(r, T) Radial and temperature-dependent linear thermal expansion coefficient 𝛼i Linear thermal expansion coefficient of the material in the inner boundary 𝜖r , 𝜖𝜃 Radial and tangential strains 𝜎rr , 𝜎𝜃𝜃 Radial and tangential stresses 𝜈 Poisson’s ratio
1 Introduction Thick cylinders and spheres are widely used in many engineering design applications as common structural components. These structures are generally subject to thermal stresses, temperature, and environmental factors. Therefore, their material design is an important issue, not only to withstand high pressures, radial loads, and radial temperature, but also high temperatures, corrosion, erosion, and high fracture. In this context, functionally graded materials (FGMs) that are resistant to both internal and environmental conditions have been started to be developed and used in many areas (Koizumi 1997; Miyamoto et al. 1999). So, the thermal stress analysis of these intelligent materials has been an important issue addressed by many scientists in recent years. Even though it is based on mainly the principle of producing materia
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