Abstract
The spatial axisymmetric creep problem for complex-shaped bodies of rotation from functionally graded materials is considered. For the variational problem statement, the Lagrangian-form functional is defined for kinematically possible displacement rates. For the main unknown creep parameters, namely displacements, stresses, and strains, the Cauchy problem in time scale is formulated for the spatial discretization points. In this case, the initial conditions for the unknown functions are derived by solving the problem of elastic deformation of the body. The numerical-andanalytical method was developed for solving a nonlinear initial boundary-value creep problem based on applying the R-function, Ritz, and Runge–Kutta–Merson methods. The advantages of the proposed method include: the accurate analytical account of the boundary value problem geometry features without their approximation, representation of an approximate solution in the analytical form, and automatic selection of a time step. The creep problem solutions are derived for a hollow straight cylinder and a complex-shaped body of rotation, namely a cylinder with an elliptical notch on the outer surface, loaded by constant internal pressure. The material creep is described by the Norton law. Several variation patterns of the material creep properties along the radial coordinate are considered. The effect of the material gradient properties and geometry on the stress-strain state of bodies of rotation is analyzed. It is shown that the above geometry effect in creep strongly depends on the material properties.
Published Version
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