The finite element method (FEM) is the dominant discretization technique in structural mechanics. The basic concept in the physical interpretation of the FEM is the subdivision of the mathematical model into disjoint (non-overlapping) components of simple geometry called finite elements or elements for short. The response of each element is expressed in terms of a finite number of degrees of freedom characterized as the value of an unknown function, or functions, at a set of nodal points. The response of the mathematical model is then considered to be approximated by that of the discrete model obtained by connecting or assembling the collection of all elements.

Because FEM is a discretization method, the number of degrees of freedom of a FEM model is necessarily finite.

FEM Solution Process Procedures

• Divide structure into pieces (elements with nodes) (discretization/meshing)
• Connect (assemble) the elements at the nodes to form an approximate system of equations for the whole structure (forming element matrices)
• Solve the system of equations involving unknown quantities at the nodes (e.g., displacements)
• Calculate desired quantities (e.g., strains and stresses) at selected elements