Finite-Element Method for the Determination of Thermal Stresses in Anisotropic Solids of Revolution

This paper considers two finite-element networks. The first network consists of triangular annuli forming a solid of revolution of any arbitrary cross section in the radial-longitudinal plane. The network has 2T symmetry with regard to material properties, external loadings, and temperatures. The second network consists of trapezoidal and triangular elements in the plane of the circle forming a right circular (actually, a polygon cross section) cylinder long in the longitudinal direction. The restriction of 2v symmetry is lifted for the second network and is replaced with the restriction that material properties, external loadings, and temperatures are independent of the longitudinal direction of the cylinder. Both methods were programmed on the I B M 370 computer. For the first method, two test plane strain problems are presented: one, a hollow cylinder subjected to a negative radial pressure and two, a 827 solid cylinder subjected to a linear radial temperature gradient. Comparisons of stresses and deflections with known plane strain solutions are excellent in both cases. In the second method, the solution of a long cylinder subjected to a linear radial thermal gradient is presented. Comparison with a known theoretical solution again was excellent. Results are presented for thermal stresses induced in a lithium tantalate crystal during the post-growth cooling stage. Lithium tantalate is in crystal class Csv. By aligning the trigonal axis of the crystal with the longitudinal axis of the cylinder, the problem can be analyzed by both methods.