Computational aspects of the parametric finite-volume theory for functionally graded materials

Computational aspects of the recently developed parametric finite-volume theory for functionally graded materials are critically examined through comparison with the finite-element method for two problems which highlight the finite-volume theory's structural and microstructural modeling capabilities. The parametric version of the theory is based on a mapping of a reference square subvolume onto a quadrilateral subvolume in the actual discretized microstructure, which is also used to construct local stiffness matrices of quadrilateral subvolumes employed in the analysis. This formulation significantly advances the capability and utility of the finite-volume theory, enabling modeling of curved boundaries of functionally graded structural components, as well as inclusions employed for grading purposes, without the disadvantage of stress concentrations at the corners of rectangular subvolumes used in the standard version. Convergence of the results for local stress fields with mesh refinement to the exact analytical results and the corresponding execution times demonstrate that the parametric finite-volume theory is a very competitive alternative to the finite-element method for the considered class of problems.