A CONTROL VOLUME PROCEDURE FOR SOLVING THE ELASTIC STRESS-STRAIN EQUATIONS ON AN UNSTRUCTURED MESH

A robust and accurate control volume procedure for solving the elastic stress-strain equations for two-dimensional arbitrarily complex geometries is described. The method is implemented for triangular and/or quadrilateral irregular meshes as well as rectangular regular meshes and is thus a control volume-unstructured mesh (CV-UM) procedure. The procedure is compared favorably to conventional finite element (FE) approaches with regard to accuracy on a number of standard test problems that demonstrate the ability of the CV-UM procedure to model constraints on the boundary and within the domain, boundary loads, body forces throughout the domain induced by a temperature distribution, multimaterial problems, and irregular geometries. For static problems the CV-UM algorithm requires about twice as much CPU time as the conventional FE analysis to achieve convergence on the same mesh. However, it is expected that as the solution procedure is optimized, this overhead will reduce by a further factor of 2.