Keywords: shell, membrane, finite volume, cell centred, cylinder.

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 mid-surface 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 four-node 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.

1

G.A. Taylor, C. Bailey and M. Cross, "A vertex-based finite volume method applied to non-linear material problems in computational solid mechanics", Int. J. Numer. Meth. Eng. 2003; 56: 507-529. doi:10.1002/nme.574

2

N. Fallah, "A cell vertex and cell centred finite volume method for plate bending analysis", Journal of computer methods in applied mechanics and engineering, 2004; 193: 3457-3470. doi:10.1016/j.cma.2003.08.005

3

I. Bijelonja, I. Demirdzic, S. Muzaferija, "A finite volume method for large strain analysis of incompressible hyperelastic materials", Int. J. Numer. Meth. Eng. 2005; 64: 1594-1609. doi:10.1002/nme.1413

4

N. Fallah, "Using shape function in cell centred finite volume formulation for two dimensional stress analysis", Lecture series on computer and computational sciences, ICCMSE 2005, Vol. 4A, 183-186.

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