The governing equations of three dimensional elasticity problems include the six Beltrami-Michell stress compatibility equations, the three differential equations of equilibrium, and the six material constitutive relations; and these are usually solved subject to the boundary conditions. The system of fifteen differential equations is usually difficult to solve, and simplified methods are usual...

Abstract In this work, the Mellin transform method was used to obtain solutions for the stress field components in two dimensional (2D) elasticity problems in terms of plane polar coordinates. the Mellin transformation was applied to the biharmonic stress compatibility equation expressed in terms of the Airy stress potential function, and the boundary value problem transformed to an algebraic  ...

in the present work, the effect of fluid’s elasticity was investigated on the hydrodynamic instability of blasius flow. to determine the critical reynolds number as a function of the elasticity number, a two-dimensional linear temporal stability analysis was invoked. the viscoelastic fluid is assumed to obey the walters’ b fluid model for which base flow velocity profiles were fortunately avail...

In the present work, the effect of fluid’s elasticity was investigated on the hydrodynamic instability of Blasius flow. To determine the critical Reynolds number as a function of the elasticity number, a two-dimensional linear temporal stability analysis was invoked. The viscoelastic fluid is assumed to obey the Walters’ B fluid model for which base flow velocity profiles were fortunately avail...

In this paper, a semi-analytic thermal stress computation for single crystals with cubic anisotropy is developed, by introducing a new anisotropic factor. Based on a suitable splitting of the differential operators, a convergence series for general elasticity problem with cubic anisotropy is derived. Each term of the series is related to an isotropic elasticity problem. Using the analytic solut...