Thermal-Stress Analysis of Irregular Shapes

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Abstract
A method has been developed for determining the thermal stresses resulting from an axially symmetric temperature distribution in an irregularly shaped cylindrical vessel. It permits the calculation of the principal stresses, rotations, and displacements for all points within the cross section and on the boundary of the geometry being considered. Finite-difference techniques are used to solve the governing fourth-order differential equation that must be satisfied. The method was applied to geometries and temperature distributions for which classical analytical solutions are available, and the agreement was very good. An example is given for which the “isostress” and isothermal lines are plotted for an irregular geometry with varying temperature gradients in the radial and longitudinal directions.

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