Finite element method in structural mechanics

Summary

The finite element method in structural mechanics is the finite element method applied to the equilibrium of elastic bodies and structures. The body is cut into small elements, and the displacement is approximated by simple functions on each element. The minimum total potential energy principle then turns the equilibrium problem into a linear system $K d = F$. Here $K$ is the global stiffness matrix, $d$ the vector of nodal displacements and $F$ the vector of nodal loads. It is the standard tool for computing deformations and stresses in engineering design.