Whirlwind Introduction to the World of Finite Element Analysis (FEA)
The world of Finite Element Analysis is a deep rabbit hole that can lose many an engineer. To put it simply, FEA is a computational method used to solve engineering mechanics problems for almost any kind of part geometry.
Although the basic principles and mathematical discipline of FEA were developed decades ago, the discipline has only recently, within the last decade, taken off as computational power has increased. Although there is much that could be written about FEA theory in mathematical language that would confuse even the smartest engineer, the basic principles of the discipline are actually pretty easy to understand. The Finite Element Method (FEM) is a mathematical/mechanical approach to solve difficult geometric structural analysis problems that sometimes involve complex geometric shapes and structures by breaking the problem down into many smaller discrete chunks. These mathematical “chunks” are then solved piece by piece by the software and the results are then presented in colorful fringe plots that highlight “hotspots” of the particular engineering parameter of interest. The number of parameters that can be solved for depends on the loading configuration and material type, but typically for the simple linear static analyses, an engineer will solve for mechanical strain, stress, reaction loads, and gross deformation of the structure. There are, of course, many more advanced FEA solution techniques that have emerged over the years as a result of the rapid advent of computational power that can handle advanced mathematical analyses. These methods and software now enable the engineer to solve dynamic problems with non-linear material properties, but for the sake of illustration, only simple, linear materials, and static load FEA will be profiled here.
In this way, FEA is a great tool for engineers to employ to quickly assess the structural capabilities of particular part geometries when no suitable or applicable hand-calculation or analytical method to determine these parameters may exist. FEA can be a great quick check for an early conceptual design of a structure, or it can be used in more detail to assess the analytical structural margins of safety for a specific feature of a particular component. Although there is a lot left to be said about FEA methods and the software that are available, a quick “when-to” list of when FEA is most useful to the engineer will be of great value as a starting point.
Even in simple, linear static structural analyses, FEA is great for the following instances:
- Complex Geometric Parts– FEA is great for analyzing basic geometric shapes such as the interaction of multiple features such as fillets/holes, but it is also great for analyzing other complex geometric shapes with multiple angles of curvature. Although there are structural analytical methods and techniques that exist for single, simple geometric features such as holes and fillets, the only good way to really assess how multiple geometric features interact in full-scale geometry is with an FEA software tool.
- Material Interaction-FEA is a great tool for assessing the response of parts or subassemblies that may consist of multiple sections of distinct materials. Additionally, traditional analytical structural engineering methods become a great deal more complex when a non-isotropic material is introduced into the problem, and most times no analytical method exists to solve such problems. These problems are great candidates for an FEA because many FEA software and solution techniques handle non-isotropic materials. FEA is a great tool to quickly and efficiently assess these kinds of materials.
- Non-Uniform Loading Problems– (i.e., thermal and mechanical or multiple mechanical loads): For loading profiles that do not fit neatly into the analytical profile boxes, FEA is the best way to examine non-uniform loading profiles. Every engineer is probably familiar with the beam bending stress/strain/deflection profiles of engineering handbooks. While these lists are certainly impressive, they do not, by any stretch of the imagination, encompass every possible loading or constraint configuration. While this is a simplistic example, the principle behind it is easy to grasp. Additionally, even basic structural FEA software is able to relatively easily handle multiple types of loads, (such as pressure, thermal, inertial) together in a single analysis. The only way to effectively solve problems of this nature is to break the geometry up into small, “finite element” chunks to make the problem simpler.
- Non-Linear Analysis– While not all FEA software contains the computational engine to handle non-linear material response modeling, it is almost impossible to conduct this kind of analysis without the finite element method. The numerical equations are much too complex to be handled by any reasonable analytical method, which is why you won’t find an equivalent Roark’s Handbook of equations for non-linear stress/strain packed full of tools to conquer this type of analysis armed with pen and paper. Increasingly, more and more engineering industries are finding it necessary to perform more non-linear analyses as the analysis tools become readily available and materials are pushed beyond the realm of linear loading in “accident” scenarios such as dynamic impact analyses. In most cases, FEA software stands ready to answer the non-linear analysis call.
GIF by Fisher Unitech
There are volumes of additional information that could be written on this particular topic, but this should provide a solid introduction for the individual looking to learn a little bit about basic FEA methods and when they may be beneficial to employ. As computational power has increased over the past few decades, there are more and more types of engineering problems that FEA can tackle. It’s up to the engineer to pick up a piece of FEA software and dive in to see how deep the FEA pool actually is!
Cover Photo by Comsol