Finite element codes or programs fall within two main groups:
1. general-purpose systems with large finite element libraries, sophisticated modelling capabilities and a range of analysis types
2. specialised systems for particular applications, e.g. air flow around/over electronic components.
While FEA systems usually offer many analysis areas, the most relevant to this course (and the most commonly used in engineering generally) are linear static structural, linear steady-state thermal, linear dynamic and, to a lesser degree, non-linear static structural. As has been mentioned, quite often, areas of analysis are coupled. For example, a common form of coupled analysis is thermal stress analysis, where the results of a thermal load case are transferred to a stress analysis. Perhaps a loaded component is subject to heat and prevented from expanding because of its physical restraints, which results in a thermally induced strain and consequent stresses within the component.
Some general capabilities of FEA codes for these main areas are summarised in Box 1. These are derived from the NAFEMS booklet by Baguley and Hose (1994). It is advisable to become familiar with these capabilities so that, faced with a particular problem, you will at least have an indication of the required form of analysis. For example, say your problem involved ‘large displacement’. In general, this would indicate that, ultimately, you would need to perform a non-linear analysis. (The meanings of the technical terms in Box 1 will be explained as and when needed in your study of the course.)
1. Linear static structural capabilities
· homogeneous/non-homogeneous materials
· isotropic/orthotropic/anisotropic materials
· temperature-dependent material properties
· spring supports
· support displacements: point, line, pressure loads
· body forces (accelerations)
· initial strains (e.g. concrete prestressing tension)
· expansion
· fracture mechanics
· stress stiffening.
2. Non-linear static structural capabilities
· material non-linearities (e.g. plasticity, creep)
· large strain (gross changes in structure shape)
· large displacements
· gaps (compression only interfaces)
· cables (tension only members)
· friction
· metal forming.
3. Linear dynamic capabilities
· natural frequencies and modes of vibration
· response to harmonic loading
· general dynamic loading
· response spectrum loading
· power spectral density loading
· spin softening.
4. Non-linear dynamic capabilities
· time history response of non-linear systems
· large damping effects
· impact with plastic deformation.
5. Linear steady-state thermal capabilities
· homogeneous/non-homogeneous materials
· isotropic/orthotropic/anisotropic materials
· temperature-dependent material properties
· conduction
· isothermal boundaries
· convection
· heat fluxes
· internal heat generation.
6. Non-linear thermal capabilities
· radiation (steady state)
· phase change (transient).
Results of finite element analyses
The amount of information that can be produced by an FEA system, especially for non-linear analysis, is enormous, and, for the first-time user, can be daunting. For the main areas we are considering, most general-purpose finite element codes provide the capability to determine the items in Box 2, again adapted from Baguley and Hose (1994). Results can be presented in various forms such as tabulated numerical data, line graphs, charts and multicoloured contour plots.
7. Typical information generated by a stress analysis
· deflections
· reactions at supports
· stress components
· principal stresses
· equivalent stresses (Tresca, von Mises, etc.)
· strains
· strain energies
· path integrals and stress intensity for fracture mechanics
· linearised stresses
· buckling loads
· buckling mode shapes.
8. Typical information generated by a dynamic analysis
· natural frequencies
· natural mode shapes
· phase angles
· participation factors
· dynamic analysis
· responses to loading
· displacements
· velocities
· accelerations
· reactions
· stresses
· strains.
9. Typical information generated by a thermal stress analysis
· temperatures
· heat fluxes.
10. General information generated by a thermal stress analysis
· displaced shape plots
· symbols showing the magnitude of reaction forces, heat fluxes, etc.
· contour plots of stresses, strains, displacements, temperatures, etc.
· vector plots showing the direction and magnitude of principal stresses, etc.
It cannot be emphasised strongly enough that while most FEA systems produce vast amounts of data and pretty, highly persuasive pictures, it is the user’s responsibility to ensure correctness and accuracy. They are, in the end, approximate models and solutions, albeit highly sophisticated ones, and it is the user’s responsibility to ensure that results are valid. In the absence of such awareness, the system degenerates into a ‘black box’ category, and the solution it provides will almost certainly be wrong, despite the impressive-looking results.
To summarise: modelling is an important part of modern engineering. FEA is a powerful tool for evaluating a design and for making comparisons between various alternatives. It is not the universal panacea that replaces testing, nor should it allow users to design products without a thorough understanding of the engineering and physical principles involved.
The qualification of assumptions is the key to successful use of FEA in any product design. To achieve this, it is essential to:
· appreciate the physics and engineering inherent in the problem
· understand the mechanics of the materials being modelled
· be aware of the failure modes that the products might encounter
· consider the manufacturing and operating environment of the product and how these might impinge on the performance
· assume that the FEA results are incorrect until they can be verified
· pay close attention to boundary conditions, loads and material models.
Remember that there is an assumption behind every decision, both implicit and explicit, that is made in finite element modelling.
