What questions should I
ask?
Better, stronger, lighter, safer, less costly--in less time. But how
do I get there from here? Computer simulation tools have been automated
to a level that produces significant competitive advantage for
companies designing mechanical products--and a significant competitive
disadvantage for those without them. Finite element analysis (FEA),
based on solid geometric modeling, provides the foundation for predicting
product performance throughout the entire design and manufacturing process
and into the hands of customers. Better, stronger, lighter, safer, less
costly, in less time--through Predictive Engineering.
But, it's not enough to merely add computer tools to your design process. It's important what you add and how you add those tools. Only you can ultimately answer these questions:
To reduce development time and cost, your company must make early commitments to final designs, straining your ability to apply engineering judgment, thus making the choice of modeling and analysis tools mission critical.
For 30 years FEA has played an important role in design and analysis of mechanical products. When used wisely and in conjunction with other tools such as closed-form solutions and structural testing, FEA can be an important complement to your engineering judgment.
The basic FEA process
The FEA process is a method of analyzing a part or assembly to ensure performance integrity over the product's lifetime. A geometric model is created, a finite element model is associated with the geometry, the operating environment is defined, and the structural response (deflection, stress, temperatures, etc.) is computed and presented for display. If the computed response--stress, for example--is greater than the allowable or maximum design value, the structure is redesigned and re-analyzed until an acceptable design is achieved. This redesign/re-analysis cycle can be automated via structural optimization.
Finite element analysis goes by many names: FEA, matrix structural analysis, beam analysis, computerized structural analysis, p-element analysis, and geometric element analysis, to name a few. Beam examples in strength of materials texts are also part of FEA. Regardless of the name, all types of finite element analyses involve the same basic steps described above.
What are the limits of finite element analysis?In FEA, the primary goal is to determine how a component or assembly will respond to a given set of environmental conditions. The results of the analysis can be used to verify the performance, and can also be used to improve and optimize the design. Of course, all of this relies on the assumptions that the design has been correctly modeled, the environment has been properly defined, and that the FEA software itself performs correctly.
Often the term accuracy is used in describing the results of finite element analysis. In this context, accuracy is not a measure of how well the system modeled real-world performance, it is simply a measure of how reliably the FEA software calculated a particular solution. The solution itself could be completely wrong due to errors in modeling the part or its environment, or errors in the software itself. How does an engineer determine if he has "accurately" calculated the wrong answer? The answer: Engineering judgment, a skill that can never be dismissed.
How do I know the answer is right?Beyond the engineer's modeling skill, however, the underlying technology within any FEA program affects the solution time, cost, and accuracy. While general users of a modern FEA program do not need to understand the details of element technology in order to achieve accurate results, they should understand that all elements and meshing methods are not equal and that the quality of the element formulations will have a direct effect on the time, cost, and accuracy of the results. The design and implementation of accurate and efficient elements requires substantial expertise by the FEA software developer.
What type of elements should I use?Plate and shell elements represent forces that vary over a surface. These two- and three-dimensional elements possess both membrane (in-plane) and bending (out-of-plane) behavior. Plates and shells are used to model automobiles, aircraft and spacecraft, computer cases, and sheet metal enclosures.
Solid elements represent a general, three-dimensional state of stress. Solid elements are used to model engine blocks, crankshafts, concrete arch dams, brackets, and test fixtures.
The original and traditional finite element science is based on what are known as "h-elements." These h-elements represent a part's geometry as an assembly of multiple small elements. Subdivision of the part's geometry into a series of discrete elements is called meshing. The relative simplicity of this representation allows efficient and direct solution of the analysis. In order to gain accuracy for complex geometries, additional elements must be added. This increase in the number of elements--either to represent complex geometry or to represent a highly varying stress gradient--increases the solution time and computer disk space required.
One way to minimize time and disk space is to add additional elements only in areas of the model where the current mesh cannot achieve the desired accuracy. Subdividing elements to achieve the desired accuracy is called adaptivity, and this has been the standard method for h-elements.
What's a p-element?One of the primary applications for p-elements is for complex stress fields where the geometry and environmental conditions must be represented very accurately. This includes modeling fillets instead of sharp corners and distributed loads and constraints instead of point loads and constraints. A more detailed model leads to more detailed results. With p-elements, adaptivity is achieved by increasing the p-level of selected elements, either by the user or automatically by the program, until the answers reach the specified convergence criterion--all without changing the mesh .
Which is better: 'h' or 'p'?Since solution time can increase dramatically as the p-level increases, good modeling judgment in the use of both h-elements and p-elements allows precise solutions for large problems without the performance overhead resulting from the use of only p-elements. A solution strategy that allows one model to simulate both detailed and gross behavior by using a coarse mesh and a fine mesh, or p-elements in selected regions of interest is called global/local analysis.
Most general problems have both global and local aspects; i.e. regions where h-elements and p-elements, respectively, are appropriate. Therefore the best approach is combined h- and p-adaptivity. This combination provides efficient answers to engineering problems with lower modeling cost, less solution time, and reduced computer disk space.
But we're ahead of ourselves. What role does geometry play?Fortunately, modern solid modeling programs allow complex designs and assemblies to be accurately modeled in a short period of time, compared to creating the individual finite elements. Often, existing designs in two- and three-dimensional wireframe CAD programs can be imported to speed model creation. Many systems include advanced automatic mesh generation and mapped meshing algorithms to help automate the creation of the mesh.
In addition to the time savings, having a precise mathematical definition of the design has several other advantages. By feeding the results of an analysis back to the design program, it is possible to update the design to improve its performance, reduce weight, or meet other design criteria.
Once I have geometry, how do I know how many elements to use?Meshing is the process of subdividing the geometry into a series of discrete elements. Meshing is done to represent complex geometry and provide more elements in regions of interest (typically, where stress gradients are greatest). Adequacy of the finite element mesh is often defined as solution convergence. "Convergence" means that as the number of h-elements are increased, or as the polynomial order of p-elements is increased, the solution approaches a given value. With simple academic problems, this given value can be calculated from textbook solutions, and convergence is often measured in terms of these known solutions.
Convergence may be achieved with relatively few h-elements, or it may require many elements, depending on the geometry of the structure, the applied load distribution, and the kind of elements used. Similarly, for p-elements, convergence may be achieved with relatively low p-levels or it may require higher p-levels.
How do I judge convergence?The most advanced error estimators require only a single analysis, not the difference between two analyses. Good FEA programs provide both the analysis results and the error estimation in a single analysis.
Can you make it 'automatic'?Consider several examples of multiple simultaneous operating environments. A computer printed circuit board must be able to withstand its own dead weight (static analysis), shock loads (transient response and/or response spectrum analysis), and induced temperatures (heat transfer plus thermal stress analysis). If the computer will be used aboard a helicopter it must be able to withstand sinusoidal vibration loads and accelerations (frequency response analysis); if the computer will be used aboard an aircraft it must be able to withstand wind gusts (random response analysis).
A car's engine block is also subjected to multiple operating environments, including several types of vibration (sinusoidal, impact, and random) and induced heat. Civil structures--buildings, dams, and bridges, for example--are also subjected to multiple operating environments: dead loads (static analysis and buckling), wind gusts (random response analysis), rotating machinery (frequency response analysis), and earthquakes (response spectrum analysis or transient analysis).
The operating environment includes all loads to which the product or structure will be subjected during its lifetime. Significant loads are induced during the manufacturing process (forging, stamping, welding, machining--many highly nonlinear), which not only induce stress on the structure during manufacture, but also create residual stresses that can affect the fatigue life of the part during operation. Similarly, significant loads can be induced during shipping. These manufacturing and shipping loads can often be greater than other operating loads.
Reality: Full System AnalysisSimilarly, the response of the car's engine block is highly dependent on the characteristics of the mounts supporting it and on the way loads are transmitted to the mounts (from the road through the tires through the suspension system through the car's body itself). Even civil structural response depends on more than the structure itself--the response is highly dependent on the way that the structure is attached to the foundation and on the stiffness characteristics of the foundation and soil.
What parts do not have attachment structures? The answer to that question is simple: Aircraft, spacecraft, and anything else in flight. However, they can exhibit fluid-structure coupling behavior!
Other than that, all structures are attached to something. Components in an aircraft are attached to the aircraft structure itself; instruments in a satellites are attached to the satellite structure itself; the satellite are attached to the launching rockets, at least during the most load-intensive part of its lifetime. Unless the structure being analyzed is totally unrestrained, as in flight, the attachment structure needs to be considered.
Therefore, it is not enough to simply model the part being analyzed--the attachment structure must also be considered because the attachment structure provides the correct boundary conditions and load paths to the part. In many cases a simplified model of the attachment structure can be formulated, which is facilitated by global/local analysis.
Reality, again: Nonlinear AnalysisLinear analysis means that the deflections and stresses are directly proportional to the applied loads. If the loads are doubled the deflections and stresses are doubled; if the loads are reversed and the magnitude multiplied by 100, the resulting deflections and stresses also reverse and are multiplied by 100.
Linearity is a good assumption only for very low levels of applied loads. For example, consider an empty aluminum soda can. If you gently press its sides and then release the force the can will spring back to its original undeformed state. However, if you apply a higher level of force the can will deform permanently. If you apply an even greater force, especially if the force is localized to a very tiny area, then you may be able to punch through the metal. Clearly, at large force levels the assumption of material linearity is not valid. The "oil-canning" ability of the structure is also a form of non-linearity--called "large deflection"--which requires special attention for finite element analysis.
Nonlinear properties are exhibited in several ways. Material non-linearity occurs when the stress exceeds the material's yield stress. In this case the material yields and, after still more load application, fractures. When contact occurs between a structure and another object--or with itself--during load application and deformation, another form of nonlinearity is caused. Geometric nonlinearity occurs when the structural stiffness is dependent upon the induced stresses and deformed shape. An example of this is an automobile tire: The tire has very little stiffness in its undeformed (uninflated) state, but has stiffness when it deforms (inflates).
Reality, once more: Can my computer handle all this?Discrepancies between the FEA and test results may occur due to:
Once these discrepancies are resolved, the FEA model can be updated so that its results match the test data. Note that resolving these discrepancies involves engineering judgment--a skill that can never be dismissed.
So, after all this, how do I know it's the right answer?"In the rush to automate, you must keep in mind that no technology available today can take the place of engineering judgement. The good news is that with today's modeling, meshing, and analysis software, engineers will spend less time worrying about the details of FEA, giving them more time to apply their engineering judgement.
When adopting FEA as an integral component of your design philosophy, you must not only consider your immediate needs, you must also anticipate your future requirements. While today's needs may only involve the static analysis of simple parts, success in this area will generate requirements for assembly modeling and more advanced analysis.
As the benefits of increased automation grow, thus do the demands for functionality, performance, reliability, and usability. And more choices appear in the marketplace. So, how do you cope? Here's a simple solution:
Ask good questions... demand realistic answers!As a proven technology, FEA has been and will continue to be used to help design everything from everyday consumer products to sophisticated airplanes and spacecraft. Advances in hardware and software will make this valuable tool available to an increasing number of engineers and designers. But in the final analysis, your engineering judgement will decide if the answer is correct.
For your reference: Finite Element Terms