A New Approach in Cell Centred Finite Volume Formulation for Plate Bending Analysis

摘要

In this paper a novel approach is developed in the application of cell centred finite volume method for plate bending analysis. The essence of this new approach lies in the use of interim elements and evaluating derivatives of unknown variables using the natural coordinate system of the interim elements. Mindlin-Reissner plate theory is applied in which the lateral shear effects are taken into account. The plate is meshed by elements that have arbitrary number of sides. These multi-faced elements are considered as control volumes or cells. The conservation of resultant forces, equilibrium equations, is written in the discretized form for the each cell. To evaluate the resultant forces on the faces of the cell, in the equilibrium equations, a 4-node interim element is used that enclosed the face. The interim element is isoparametric and its vertices are the centres of the two adjacent cells lying on either side of the face and the nodes at each end of the face. Shape functions are used to interpolate the unknown variables in the interim elements, and hence across the enclosed faces. The interpolation functions are defined in the natural coordinate system of the interim element. The derivative of unknown variables is evaluated in the natural coordinate of the interim element and then mapped back to global coordinate system. The equilibrium equations of a cell are approximated at the integration points, which are located in the interim elements. In this approach stress continuity will be guaranteed on common faces of the adjacent cells, which is a prominent feature of the finite volume method. To incorporate the boundary conditions point cells are used to transfer the boundary conditions to the adjacent cells. To demonstrate the capability of the present method in the predictions of accurate results a thin plate is analyzed and the results are compared with the analytical predictions. Further studies of the present method show the formulation is capable to analyze thin and thick plates. It is noticeable that the formulation does not show shear locking problem in the thin plate analysis, which occurs in the Mindlin based finite element formulation for the thin plate analysis. This extended studies cannot be included in this paper regards to the paper length.