Axially symmetric thermal stress of a penny-shaped crack subjected to general temperature
The authors consider in the cylindrical coordinates \((r, \varphi, z)\) the thermoelastic equations \(2(1 - \nu) ({\partial^2u \over \partial r^2} + {1 \over r} {\partial u \over \partial r} - {u \over r^2}) + (1 - 2 \nu) {\partial^2u \over \partial z^2} + {\partial^2w \over \partial r \partial z} = 2(1 + \nu) \alpha {\partial \theta \over \partial r}\), \((1 - 2 \nu) ({\partial^2w \over \partial r^2} + {1 \over r} {\partial w \over \partial r}) + 2 (1 - \nu) {\partial^2w \over \partial z^2} + {\partial \over \partial z} ({\partial u \over \partial r} + {u \over r}) = 2(1 + \nu) \alpha {\partial \theta \over \partial z}\), with respect to the displacement \((u,w)\), and the temperature distribution \(\theta\) satisfying the Laplace equation. All functions are independent of \(\varphi\). Different boundary conditions are considered for \(0 < r < a\) and \(r > a\). The problem has been solved in closed form using Hankel transforms and Abel integral equations.
scientific article; zbMATH DE number 755127