Stress Analysis of Axisymmetric Solids with Asymmetric Properties

Abstract

The finite element method for the determination of stresses and displacements in arbitrary axisymmetric solids is extended to problems involving asymmetric mechanical and thermal loads and materials with asymmetric temperature dependent mechanical properties. All dependent variables, including the mechanical properties, are represented by a Fourier series expansion of the circumferential coordinate. Due to the mechanical property variation in the circumferential direction, the resulting equation set becomes fully coupled and must be solved simultaneously. By grouping all Fourier coefficients together at each nodal point, a banded stiffness matrix is achieved the efficient solution of which is feasible by the use of a blocked square root Cholesky method. A useroriented computer program based on the method of analysis is described and applied to several example problems to verify accuracy and demonstrate versatility of the program.