JP Journal of Solids and Structures
Volume 4, Issue 1, Pages 9 - 26
(March 2010)
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HIGHER ORDER FINITE VOLUME FORMULATION FOR THE SOLUTION OF CLASSICAL 1D AND 2D ELASTICITY
G. I. Tsamasphyros and C. D. Vrettos
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Abstract:
One of the major disadvantages in implementing the finite volume method for the solution of linear differential equations is the difficulty in forming higher order approximation shape functions. In the present work, the equations of classical elasticity are solved, via the finite volume method in 1D and 2D, with a second degree approximation of the displacement field using higher order h-elements. The method uses the node centered approach. The term node centered is used instead of the term vertex centered because the finite volumes are formed around both vertex nodes as well as midside nodes of the elements. Numerical implementation has demonstrated very good agreement with analytic solutions as well as with finite element solutions. The key of success within the suggested formulation lies in the choice of the finite volume tessellation within the elements. |
| Keywords and phrases: finite volume, classical elasticity, higher order interpolation, vertex centered scheme. |
| Communicated by M. Misbahul Amin |
| Number of Downloads: 151 | Number of Views: 463 |
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