MasterFrame: Finite Element Analysis - Overview
The Finite Element module adds to the analytic capabilities of MasterFrame, by allowing the analysis of continuum structures, such as floor plates and wall elements. This analysis of such plate structural elements is achieved by the subdivision of the plate into a finite number of smaller elements, from which the analysis method derives it's name. Finite element surfaces can be analysed on their own, for example, in the case of a raft structure, or incorporated as part of a MasterFrame model, with 2D finite element surfaces being combined with 1D line elements. A range of loads can be applied directly to the FE surface, or, alternatively, loads can be applied to the line members and the reactions taken on the FE surface automatically.
The FE module uses 8-noded quadrilateral shell elements to model a plate as a 2-dimensional surface. The modelling of a planar surface is based on the centreline of the element. The shell element combines both plate bending and plane stress elements to model the in-plane membrane stiffness. This element also utilizes the Mindlin-Reissner plate theory (an extension of the Kirchoff plate theory) to take account of transverse shear deformations through the thickness of the element. This type of element is suited to modelling shell type structural components such as walls and slabs for use in a 1st order, linear elastic analysis. For limits of applicability of FE modelling in terms of span/depth for thick structural elements, see the following technical note here.
Elements are connected only at their nodes. In the case of an 8 sided nodes, this means that there is compatibility of displacements at the corners and mid way along each mid side. The pattern of displacements within each element, and hence the displacement of forces, is determined by the use of a shape function, which interpolates the solution between the node points of each element. Therefore, the accuracy of the analysis using the Finite Element Method is dependant upon the mesh size used. A smaller mesh will lead to a higher level of accuracy in the solution, but at the cost of a longer analysis time, since a finer mesh gives a larger number of nodes, so the resulting stiffness matrix is larger.
The software provides a number of option to control the size of the FE mesh. These options allow for a user defined global mesh size and then allows for mesh refinements to be specified at locations within the FE surface. The FE module uses a mesh generation algorithm to simply the process of creating the FE mesh.
The shell elements have the requirement to be planar. Hence, an FE surface must be a flat surface. However, the orientation relative to the global axes is not a limitation, so the FE module can analyse a flat surface at any orientation relative to the horizontal or vertical planes. However, the limitation that the elements much remain planar does mean that, at present, the current FE elements are not compatible with a P-delta analysis.