The finite element method is a numerical technique used to solve engineering problems. Finite element analysis can be used to obtain solutions in solid mechanics, heat transfer, electromagnetism, and even fluid mechanics. FEA was developed initially for mechanics of materials. Even though the focus point will be for static stress, there are other types like dynamic, modal, and buckling. Finite element analysis is a powerful tool and should be handled with care.
Hooke’s law describes that an elastic body stretches in proportion to the force. The equation is F=kx, [Force = constant x distance stretched]. The FEM method divides a structure into smaller elements. These pieces are then reconnected using nodes. Imagine a cylinder fixed or constrained to the ground and divided into several thousand small box elements. Each box has 8 corners with 8 nodes. Now picture pressing down on top of that cylinder with a certain force. As the force moves through the initial element, it spreads to the other nodes. The governing equation will of course be Hooke’s law. This allows you to measure the behavior of each element and how it affects the other elements that are connected at the nodes. The appropriate forces and stress values can eventually be derived from this system.
In the past, engineers have always relied on hand calculations to analyze stress and strain. With the advent of computers and the advancement of technology, software now handles the heavy lifting. It is possible to solve simple one-dimensional problems, but what about measuring the stress and strain for complex structure like large brackets, car chassis, or even aircraft wings? This would yield millions of equations and would take a lifetime for any one individual to conquer.
Solidworks, Onshape, Catia, Creo, Ansys, Inventor, and Abaqus are some of the most well know and utilized parametric software and simulation packages used today. The following are basic steps to perform a sample simulation which are applicable for all software tools. Create a 2D sketch of a beam. Extrude the beam into a 3D object. Define the material properties of the beam. Set up the boundary conditions (ex. Cantilever: fix the beam at one end). Apply and define a force to the other end of the beam. Generate a mesh for the beam (Coarse mesh = less elements = less processing power and time | fine mesh = more elements = more processing power and time). Let the computer create the solution. Generate the post process results, charts, and graphics for various stresses, strains, and deformations. Analyze the results and compare it to your hand calculations. Rinse and repeat after optimization and fine tuning.
The ability to analyze stress and strain is one of the many important skills engineers have. Finite element analysis is widely used throughout all industries. Modern CAD and CAM software and sleek simulations packages help engineers perform these invaluable techniques. It is always important to remember to build a strong analytical foundation and understand why and how these methods are implemented as opposed to just using them.