Understanding the Finite Element Method

thanks to curiositystream for sponsoring this video there are a lot of different analytical methods that engineers can use to solve structural mechanics problems whether it's to calculate the deflection of a beam or the stresses in a flat plate but we often encounter problems that can't be solved in this way typically because the geometry loads or materials

are too complex the finite element method is a powerful numerical technique that uses computational power to calculate approximate solutions to these types of problems it's widely used in all major engineering industries it could be used to check satellite components will survive the launch conditions for example

or to optimize the design of automotive components like the lower control arm of this car's suspension system finite element analysis software can be used to analyze a wide range of solid mechanics problems including static dynamic buckling and modal analyses but it can also be used for fluid flow heat transfer and electromagnetic problems

for this introduction to the finite element method we'll focus on how it applies to static linear elastic stress analysis imagine we want to analyze the brackets supporting this air conditioning unit the goal of a static stress analysis would typically be to calculate the stresses strains and displacements within the bracket these unknowns are called field

variables internal stresses develop within a body in such a way as to maintain equilibrium over any volume of the body so we can apply the concept of equilibrium to calculate the field variables this is easy to do for a simple beam we can use equilibrium to calculate the bending moment and shear force along it