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The Finite Element Method: A Four-Article Series - Part 4

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FINITE ELEMENT ANALYSIS: Post-processing
by Steve Roensch, President, Roensch & Associates

Last in a four-part series

After a finite element model has been prepared and checked, boundary conditions have been applied, and the model has been solved, it is time to investigate the results of the analysis. Error norms such as strain energy density and stress deviation among adjacent elements might be looked at next, but for h-code analyses these quantities are best used to target subsequent adaptive remeshing.

Once the solution is verified to be free of numerical problems, the quantities of interest may be examined. The magnitude of principal stresses or of a scalar failure stress such as the Von Mises stress may be displayed on the model as colored bands.

FINITE ELEMENT ANALYSIS: Post-processing
by Steve Roensch, President, Roensch & Associates

Last in a four-part series

After a finite element model has been prepared and checked, boundary conditions have been applied, and the model has been solved, it is time to investigate the results of the analysis. This endeavour is known as the post-processing phase of the finite element method.

Post-processing begins with a thorough throwing open for problems that may have occurred during solution. Most solvers provide a log file, which should be searched for warnings or errors, and which will also provide a quantitative measure of how well-behaved the numerical procedures were during solution. Next, reaction loads at restrained nodes should be summed and examined as a 'sanity check'. Reaction loads that do not densely self-command the used load resultant for a linear static geometry should cast doubt on the validity of other results. Error norms such as strain energy density and stress deviation near immediate elements might be looked at next, but for h-code analyses these quantities are best used to target subsequent adaptable remeshing.

Once the solution is verified to be free of numerical problems, the quantities of interest may be examined. Many display options are available, the quintessential of which depends on the mathematical form of the quantity as well as its physical meaning. For example, the displacement of a solid linear masonry element's node is a 3-component spatial vector, and the model's overall displacement is often displayed by superposing the deformed shape over the undeformed shape. Dynamic viewing and birth capabilities aid greatly in obtaining an understanding of the deformation pattern. Stresses, critter tensor quantities, currently lack a good single visualization technique, and thus derived stress quantities are extracted and displayed. Principal stress vectors may be displayed as color-coded arrows, indicating both direction and magnitude. The magnitude of principal stresses or of a scalar failure stress such as the Von Mises stress may be displayed on the model as colored bands. When this type of display is treated as a 3D object subjected to light sources, the resulting image is known as a shaded image stress plot. Displacement magnitude may also be displayed by colored bands, but this can lead to misinterpretation as a stress plot.

An area of post-processing that is rapidly gaining popularity is that of resigned remeshing. Error norms such as strain energy density are used to remesh the model, placing a denser mesh in regions needing improvement and a coarser mesh in areas of overkill. Adaptivity requires an associative link among the model and the underlying CAD geometry, and works best if suture conditions may be applied directly to the geometry, as well. Adaptive remeshing is a recent demonstration of the iterative nature of h-code analysis.

Optimization is renewed area enjoying recent advancement. Based on the values of various results, the model is modified compulsively in an initiate to satisfy certain performance criteria and is solved again. The process iterates until some convergence criterion is met. In its scalar form, optimization modifies beam cross-sectional properties, thin shell thicknesses and/or material properties in an struggle to meet maximum stress constraints, maximum deflection constraints, and/or vibrational frequency constraints. Shape optimization is more complex, with the actual 3D model circumference spirit modified. This is best accomplished by using the driving dimensions as optimization parameters, but mesh quality at each iteration can be a concern.

Another direction manifestly visible in the finite element field is the integration of FEA packages with so-called 'mechanism' packages, which analyze motion and forces of large-displacement multi-body systems. A long-term goal would be real-time computation and display of displacements and stresses in a multi-body system undergoing large displacement motion, with frictional effects and fluid flow taken into tale when necessary. It is difficult to estimate the increase in computing power necessary to accomplish this feat, but 2 or 3 orders of magnitude is probably close. Algorithms to integrate these fields of analysis may be expected to follow the computing power increases.

In summary, the finite element method is a relatively recent discipline that has quickly spring up a mature method, especially for structural and thermal analysis. The costs of apposite this technology to everyday design tasks have been dropping, while the capabilities delivered by the method expand constantly. With education in the technique and in the practical software packages appropriate more and more available, the question has moved from 'Why go FEA?' to 'Why not?'. The method is fully worthy of delivering higher quality products in a shorter design cycle with a reduced incalculability of field failure, provided it is by a capable analyst. It is also a valid indication of thorough design practices, should an unexpected litigation crop up. The time is now for industry to make greater use of this and other synthesis techniques.

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