| dc.description.abstract | A flat shell finite element is usually developed by superimposing plate bending and membrane components. In a normal analysis of the shell element, it is assumed to possess five degrees of freedom (DOF) per node composed of three displacements u, v and w, in the axial directions of x, y, z and two in-plane rotations ex and ey, at each typical node i. The sixth degree of freedom ez, which represents the node's normal rotation, is usually not required by conventional theory and is thus ignored. However, when dealing with finite element models, computational and modeling problems can be caused by a failure to include this degree of freedom in the analysis.
This thesis presents the formulation and testing of a thin flat rectangular shell finite element with six DOF per node, instead of the usual five. It has been introduced by assuming discrete Kirchhoff plate assumptions with the membrane element. Allman's physical interpretation of the drilling freedom is adopted in the formulation.
An existing open source program with sufficient finite element libraries has been utilized as a tool in which to implement the formulation. The work proceeds to be tested with numerical examples given for
· A square plate with various loadings,
· A cantilever beam with a piont load?
· A flat slab slab with two panels
· A folded plate.
The accuracy and efficiency of the flat shell finite element has been compared with the fesd module in Prokon ver 1.8 (which does not have the drilling freedom) for the case studies. It is clear that the drilling freedom improves the accuracy and efficiency of the finite element model, making the flat plate a higher order element without the need for mid-side nodes, mid-element nodes nor extreme mesh refinement. It also shows a high and consistent convergence rate to the actual solution. | en_US |
