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