How is the finite element method used in stress analysis?

The finite element method (FEM) is a powerful numerical technique used in stress analysis to approximate the behavior of complex structures by dividing them into a finite number of simpler, interconnected parts called elements.12

In this process, the domain of the structure is discretized into these elements, and the displacement field within each is interpolated based on displacements at specific points known as nodes. By ensuring the displacement field remains continuous across element boundaries, the strain at any point can be expressed as a function of these nodal displacements.1

To determine the stress, the method utilizes the material's stress-strain relations. The analysis requires that these stresses satisfy the principle of virtual work for any arbitrary variation of the nodal displacements. This mathematical requirement generates a system of simultaneous equations equal to the number of degrees of freedom in the model, which are then solved using numerical techniques programmed for computers. This approach allows engineers to analyze complex stress forces in structures—such as jet wing designs—that would be too complicated to solve using explicit analytical methods.12