An enhanced finite volume method to model 2D linear elastic structures

摘要

This paper details the evaluation and enhancement of the vertex-centred finite volumemethod for the purpose of modelling linear elastic structures undergoing bending. Amatrix-free edge-based finite volume procedure is discussed and compared with the traditionalisoparametric finite element method via application to a number of test-cases. It isdemonstrated that the standard finite volume approach exhibits similar disadvantages tothe linear Q4 finite element formulation when modelling bending. An enhanced finite volumeapproach is proposed to circumvent this and a rigorous error analysis conducted. It isdemonstrated that the developed finite volume method is superior to both standard finitevolume and Q4 finite element methods, and provides a practical alternative to the analysisof bending-dominated solid mechanics problems.