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.

MODELING OF UNSTEADY COUPLED MECHANODIFFUSION PROCESSES IN A CONTINUUM ISOTROPIC CYLINDER

We considered the one-dimensional polar-symmetric problem of stress-strain state determining of a continuum isotropic multicomponent cylinder. The cylinder is affected by unsteady surface elastic diffusive perturbations. The coupled system of elastic diffusion equations in the polar coordinate system is used as a mathematical model. The problem solution is sought in the integral form and is represented as convolutions of Green's functions with functions defining surface elastodiffusive perturbations. Mechanical loads and diffusion fields are considered as external influences. We used the Laplace transform by time, and Fourier series expansion in first kind Bessel functions to find the Green's functions. To calculate the coefficients of these series, we obtained formulas for transforming differential operators of the first, second, and third orders using the Hankel integral transform on a segment, which allowed us to reduce the initial boundary-value problem of mechanodiffusion to a system of linear algebraic equations. Laplace transforms of Green's functions are represented through rational functions of the Laplace transform parameter. The Laplace transform inversion is done analytically due to residues and operational calculus tables. As a result, Analytical expressions of surface Green's functions are obtained for the considering problem. Numerical study of the mechanical and diffusion fields interaction in a continuous isotropic cylinder is performed. We used two-component material as an example. The cylinder is under pressure uniformly distributed over the surface. The solution is presented in analytical form and in the form of three-dimensional graphs of the desired displacement fields and concentration increments as functions of time and radial coordinate. This calculation example allows us to demonstrate the coupling effect of mechanical and diffusion fields. It manifests itself as a change in the concentrations of the continuum components under the influence of external unsteady surface pressure.

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.

Morphological Instability of a Transversally Isotropic Solid Cylinder Under Stress

The linear stability of the surface of a transversally isotropic cylinder submitted to uniaxial stress has been theoretically investigated with respect to the development by surface diffusion of longitudinal fluctuations of its radius. The effect of stress has been characterized on the instability threshold.