Solid mechanics applications of boundary fitted coordinate systems

Abstract

A numerical method which utilizes the boundary fitted coordinate method is presented and applied to the solution of three solid mechanics problems. The three problems considered are the elastic torsion of uniform shafts of arbitrary cross section, the elastic torsion of non-uniform shafts of arbitrarily varying circular cross section, and the bending of thin isotropic elastic plates of arbitrary shape with simple or clamped boundaries. The boundary fitted coordinate method is utilized to transform the arbitrary simply connected or multiply connected region under study onto a fixed rectangular domain where computations are easily done. The governing equations and boundary conditions are transformed and solved on the rectangular domain by SOR iteration. Numerical results for all three problems show close agreement with analytical solutions, although there is local error introduced when the coordinate system is severely skewed. Numerical results check closely with experimental results obtained for problems which have no analytical solution.