Computational & Technology Resources
an online resource for computational,
engineering & technology publications 

CivilComp Proceedings
ISSN 17593433 CCP: 83
PROCEEDINGS OF THE EIGHTH INTERNATIONAL CONFERENCE ON COMPUTATIONAL STRUCTURES TECHNOLOGY Edited by: B.H.V. Topping, G. Montero and R. Montenegro
Paper 160
Application of the Finite Volume Method for Shell Analysis: A Membrane Study F. Hatami, N. Fallah and S. Pourzeynali
Department of Civil Engineering, University of Guilan, Rasht, Iran F. Hatami, N. Fallah, S. Pourzeynali, "Application of the Finite Volume Method for Shell Analysis: A Membrane Study", in B.H.V. Topping, G. Montero, R. Montenegro, (Editors), "Proceedings of the Eighth International Conference on Computational Structures Technology", CivilComp Press, Stirlingshire, UK, Paper 160, 2006. doi:10.4203/ccp.83.160
Keywords: shell, membrane, finite volume, cell centred, cylinder.
Summary
The work presented in references [1,2,3] have demonstrated excellent performance of the finite
volume method in computational structural mechanics, which is encouraging for
the further application of the method to other complex structural problems. This
paper applies a cell centred finite volume method for the analysis of shell
structures. In the formulation presented here the membrane behaviour is considered.
In this way, the midsurface of a shell is discretised into a number of arbitrary flat
elements. In the cell centred finite volume method each element is considered as a
control volume or cell, which its centre is located at the element centre. One cell is
connected to the neighbouring cells by its boundary faces. The cells' centres are
considered as the computational points. In the formulation presented three degrees
of freedom are assigned to the each cell centre, i.e. displacements along the , and
global coordinate system. The equilibrium equations governing the conservation of
forces are written in the discretised form for the cells. To evaluate stress components
at the common face of the two adjacent cells, the idea of an interim element is used [4].
The interim elements are fournode isoparametric elements in which bilinear
variations are assumed for the unknown variables. The derivative of displacement
components is evaluated in the natural space of the interim elements and then
mapped back to global coordinate system. To transfer the boundary conditions to the
cells lying next to the domain boundaries the point cells are used, which are located
at the domains. The equations describing the boundary conditions and the
equilibrium equations corresponding to the internal cells provide a system of
simultaneous linear equations, which relates the unknown displacements to one another.
Iterative solver technique is used for the solution of this system of equations
and the displacements at the computational points are calculated.
To verify the proposed formulation a test case is studied by using a computer code developed based on the formulation presented. The test case concerns a cantilever cylindrical shell subjected to internal pressure loading. The results obtained are compared with the available reference solutions. The comparison between the predicted results and the reference solutions reveals that the method is able to predict accurate displacement fields. Future research aims to include the bending effects in the formulation. References
purchase the fulltext of this paper (price £20)
go to the previous paper 
