Taking Young's modulus, thermal expansion coefficient and density to be the functions of the radial coordinate, a closed form solution of rotating circular disks made of functionally graded materials subjected to a constant angular velocity and a uniform temperature change is proposed in this paper. Excellent agreement with the solution from Mathematica 5.0 indicates the correctness of the proposed closed form solution. Distributions of the radial displacement and stresses in the disks are determined with the proposed approach and how material properties, temperature change, geometric size and different material coefficients affect deformations and stresses is investigated.
SUMMARYA simple and e cient numerical method is proposed to investigate deformations and stresses in elasticplastic rotating solid shafts. Using the assumption of plane strain, the governing equation is derived from the geometric relation, equilibrium equation, deformation theory, von Mises' yield criterion and non-linear stress-plastic strain relationship. By making use of the information of the second and third derivatives of the radial stress with respect to the radial co-ordinate and introducing a truncated Taylor's expansion, an iterative algorithm is presented which can solve elastic-plastic problems of rotating solid shafts quickly and e ectively. Two numerical examples are given to demonstrate accuracy, e ciency and capacity of the proposed method in both fully elastic and non-linear strain-hardening elastic-plastic analyses of rotating solid shafts. Excellent agreement is found between this method and ÿnite element approach.
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