The finite element method (FEM) is a numerical method to solve partial differential equations (PDE). This method enables to investigate the interaction between analysing of structure and default external boundary conditions. By applying of this method respectively the deformation of a component part as result of a working load can be clarified. The following procedure is fundamental for this method:
1. Pre-processing
- Modelling or import of geometry
- Allocation of material properties
- Geometry based FEM-mesh generation with a grid engine system
- Definition of boundary conditions
- Determination of load dimensions
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2. Solver
- Setting up the system of equations
- Solving the system of equations
- Calculation of desired load dimensions (e.g. mechanical properties or variables, temperature distribution)
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3. Postprocessing
- Import of load parameters
- Display of load parameters corresponding to the possibilities of the post processor
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Pre-processor, solver and postprocessor are normally single program modules. In the following the procedure is shown for a circular disc. In a first step the 3D model of the disc constructed with a CAD program is imported in the finite element analysis software. Afterwards the imported model obtains boundary conditions and is meshed by a grid engine. The figures left and right shown below contrast a rough with a fine grid. These figures do not show the assigned material properties of the disc. This Step already carried out in the pre-processing procedure. The figure in the middle below represents the deformation of the disc as result of post processing. Each colour corresponds to a deformation magnitude.
The diagram of deformation (unsmoothed) below demonstrates that the deformation is determined by articular degrees of freedom in the mesh knots. By a higher number of mesh or finite elements the calculated result describes the real deformation more exactly. However, because of calculation complexity an exorbitant number of mesh knots is to avoid.
Finite element analysis (FEA) is a modern engineering tool to optimize apparatuses, reactors, membrane elements and membrane modules. This way the constructional elements can be designed much smaller.
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