What is Finite Element Analysis (FEA)?
FEA is short for Finite Element Analysis. It is a numerical method to approximate the solution to some given mathematical equations. This is done by discretizing a system into multiple, simple small sections called elements. This is useful because the behavior of each element is relatively easy to model, as opposed to that of a complex geometry. The equations governing the behavior of the individual elements are then assembled into a large matrix of equations which represents the response of the entire system.
What is a mesh in FEA?
The elements in which a geometry is divided are collectively referred to as the Mesh. Once the geometry has been fully subdivided into elements, we say that the geometry has been “meshed”.
Is meshing an art or a science?
It is both. The mathematical properties, limitations and capabilities of the various types of elements vary. Certain elements are better suited to represent particular physical phenomena, and geometry types. A firm knowledge of the science behind element formulations is essential in generating an acceptable mesh. However, there is a considerable degree of art involved in making your mesh “flow” smoothly with the geometry. It is the combined application of art, science, skill and experience which results in the most optimal meshes for a given geometry.
What is the underlying equation for structural FEA?
At its core, a structural FEA is approximates the solution to a simplified version of Hook’s Law:
{F} = [K]{X}
Where F and X refer to force and displacement respectively. K is a representation of the stiffness of the system.
What do we mean by “simplifying” a geometry for FEA?
By definition, an FEA is a simplification of the original problem statement. The FE program will “simplify” the geometry by dividing into simple elements. Any simplification that we can perform while defining the shape of the geometry, will assist the program in doing its job (and hence save time). Engineering and analytical judgment should dictate what simplifications are relevant and acceptable – Some examples of simplifications are deleting geometric features such as bolt holes, threads, chamfers and fillets.
2D vs 3D Analysis
2D and 3D refer to the geometries used for the analysis. Put simply, if the geometry has volume (as opposed to it being a 2D surface) you are running a 3D analysis. All real-life geometries are 3D. However, in many instances a 2D representation of the real geometry (and the corresponding loads) may be sufficient to provide the desired information. A 2-D analysis may run much quicker than a 3-D analysis.
Static vs Dynamic Analysis
In a dynamic analysis, the applied load is a function of time. Inertia and damping affects play a role in the system response. In a static analysis, we are only interested in the behavior of a system at a given point in time. In real life, all external loads are a function of time. However, in many engineering problems we are only interested in the system response at a static state of equilibrium.
Linear vs Non-Linear Analysis
In a linear analysis, the applied load results in a displacement which varies linearly with load. In a non-linear analysis, the load-displacement relationship is non-linear. In a linear structural analysis, the stiffness matrix is calculated only once. In a non-linear analysis the stiffness matrix is calculated at each equilibrium iteration.
What are the sources of Non-Linearity in an FEA?
There are three sources of non-linearity: Contact (components interact and load is transferred between them), Material (Stress-Strain curve used to model plasticity) and Geometry (large deformations causing change in stiffness).