Stress fields close to the boundary of a stochastically inhomogeneous half-plane during creep

Solution of the plane stochastic creep boundary value problem

“…(2.14), of the boundary-layer type under conditions (30 , there are multiple roots of the characteristic equation. The solution of this problem has been presented earlier6 and is not considered here.Substituting expressions (2.12), (2.13) and (2.16) into relation (2.10), we find the stress function Separating out the real part and introducing the…”

“…Under creep conditions, the development of analytical methods for solving of stochastic boundary-value problems encounters serious difficulties, due mainly to physical and statistical non-linearities. Boundary effects under creep conditions based on the solution of a stochastic boundary-value problem, has therefore only been investigated in the simplest cases 6,7 . A plane stochastic steady-state creep problem, ignoring the boundary effect, has been solved 8 using the eigenvalue representation of a stochastic function; in this case, the boundary conditions were replaced by the requirement that the functions were bounded at infinity.…”

Solution of the Stochastic Boundary-Value Problem of Steady-State Creep for a Thick-Walled Tube Using the Small-Parameter Method

“…To solve stochastic boundary-value problems in elastic and creep regions, the small-parameter method is used [6][7][8][9][10]. However, owing to substantial difficulties that arise in calculating the second and higher order moments of a random function, this method provides solutions of the stochastic boundary-value problems of steady-state creep only in the first approximation [6,8].…”

“…However, owing to substantial difficulties that arise in calculating the second and higher order moments of a random function, this method provides solutions of the stochastic boundary-value problems of steady-state creep only in the first approximation [6,8].…”

“…The necessity of considering the microheterogeneities of the material leads to stochastic boundary-value problems, in which statistical nonlinearity should be taken into account in addition to the physical nonlinearity of the governing equations. Because of these difficulties, stochastic boundary-value creep problems admit analytical solutions only in the simplest cases [6][7][8][9].…”