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.
Reference:
Suliman, R, Oxtoby, O.F, Malan, A.G and Kok, S. 2014. An enhanced finite volume method to model 2D linear elastic structures. Applied Mathematical Modelling, vol. 38(7-8), pp 2265-2279
Suliman, R., Oxtoby, O. F., Malan, A., & Kok, S. (2014). An enhanced finite volume method to model 2D linear elastic structures. http://hdl.handle.net/10204/7437
Suliman, Ridhwaan, Oliver F Oxtoby, AG Malan, and S Kok "An enhanced finite volume method to model 2D linear elastic structures." (2014) http://hdl.handle.net/10204/7437
Suliman R, Oxtoby OF, Malan A, Kok S. An enhanced finite volume method to model 2D linear elastic structures. 2014; http://hdl.handle.net/10204/7437.
Copyright: 2014 Elsevier. This is the pre/post print version of the work. The definitive version is published in Applied Mathematical Modelling, vol. 38(7-8), pp 2265-2279
Author:Suliman, Ridhwaan; Oxtoby, Oliver F; Malan, AG; Kok, SDate:Jan 2010This paper presents the formulation, implementation and evaluation of an enhanced matrix free edge-based finite volume approach to model the mechanics of solids undergoing large non-linear deformations. The developed technology is evaluated ...Read more
Author:Suliman, Ridhwaan; Oxtoby, Oliver F; Malan, AG; Kok, SDate:Jan 2011A strongly coupled finite volume-finite element fluid-structure interaction (FSI) scheme is developed. Both an edge-based finite volume and Galerkin finite element scheme are implemented and evaluated for modelling the mechanics of solids. ...Read more
Author:Suliman, Ridhwaan; Oxtoby, Oliver F; Malan, AG; Kok, SDate:Jul 2012This work details the development of a computational tool that can accurately model strongly-coupled fluid-structure interaction (FSI) problems, with a particular focus on thin-walled structures undergoing large, non-linear deformations. The ...Read more