Elastoplastic analysis in functionally graded thick-walled rotating transversely isotropic cylinder under a radial temperature gradient and uniform pressure

In this research paper, an analytical solution with numerical illustration is presented for elastoplastic analysis in a functionally graded thick-walled rotating transversely isotropic cylinder under a radial temperature gradient and uniform pressure using the transition theory of Seth and generalized strain measure theory. The theory of Seth requires no assumptions, such as infinitesimally small deformation or material incompressibility, or a yield criterion, and is important in determining elastoplastic transitional stresses and fully plastic stresses on the basis of Lebesgue strain measure. The combined impacts of an inhomogeneity parameter, uniform pressure, temperature, and angular speed are discussed numerically and shown graphically. It is concluded that a functionally graded thick-walled rotating cylinder made of steel subjected to a radial temperature gradient and uniform pressure is on safer than a cylinder made of titanium, owing to the percentage increase in pressure. This, in turn, brings to the concept of “stress saving,” which reduces the potential for thick-walled cylinder failure. The fully plastic circumferential stress with the application of thermal effects in a functionally graded cylinder is greater than that at room temperature on the inner surface, whereas fully plastic circumferential and radial stresses for a homogeneous cylinder are independent of thermal effects.

Torsional Vibrations of Fluid-Filled Multilayered Transversely Isotropic Finite Circular Cylinder

An analytical and numerical study for the torsional vibrations of viscous fluid-filled three-layer transversely isotropic cylinder is presented in this paper. The equations of motion of solid and fluid are respectively formulated using the constitutive equations of a transversely isotropic cylinder and the constitutive equations of a viscous fluid. The analytical solution of the frequency equation is obtained using the boundary conditions at the free surface of the solid layer and the boundary conditions at the fluid–solid interface. The frequency equation is deduced and analytically solved using the symbolic Software Mathematica. The finite element method using Comsol Multiphysics Software results are compared with present method for validation and an acceptable match between them were obtained. It is shown that the results from the proposed method are in good agreement with numerical solutions. The influence of fluid dynamic viscosity is thoroughly analyzed and the effect of the isotropic properties on the natural frequencies is also investigated.

The Refined Analysis of Axisymmetric Transversely Isotropic Cylinder under Radial Direction Surface Loading

In this paper, the axisymmetric deformation of one cylinder with transversely isotropic is researched. According to the general solution of deformation body with transversely isotropic and the Lur’e method, the exact deformation field and exact stress field are represented by unknown functions with single independent variables. Based on boundary conditions of radial direction surface loading, the unknown functions can be ascertained. By dropping terms of high order, the approximate solution is derived, and the department field and the stress field for a circular cylinder under radial direction surface loading can be obtained. After simplifying, the states with isotropic can be obtained.

STRESS ANALYSIS OF TRANSVERSELY ISOTROPIC CYLINDER UNDER ARBITRARY AXISYMMETRIC LOAD

Power series method is used to analyze the distribution of stresses of the transversely isotropic cylinder under arbitrary axisymmetrical normal load. The stress function and normal load are expanded as the form of Fourier series. Unknown parameters in equations are determined using boundary conditions and final solutions of stress and displacement are obtained accordingly. The analysis of stresses obtained from different material parameters shows that the axial stress is significantly affected by Young's modulus and the circumference stress is sensitive to the variation of Poisson's ratio.