18.2 Brief summary of FEA

• FEA consists of a discretization of a body into “elements” which can be more easily analyzed.

• The elements are connected by “nodes” (These connections is called the “element connectivity”)

• the nodes possess “degrees of freedom” which are the unknowns of the problem. (\(\{q\}\))

• Inside the elements, the degrees of freedom are interpolated. (\(\{u\}=\{N^T\}\{q\}\))

• The loads (forces, moments, etc) are also discretized and are applied at the nodes (\(\{F\}\))

• The elements have “stiffness” (\([K]\)) that relates the loads to the displacements

• The element stiffnesses and forces are “assembled” into global matrices.

• Solving the problem reduces to solving a problem of the form: \[[K]\{q\}=\{F\}\] \[\{q\}=[K]^{-1}\{F\}\]

• Boundary conditions are enforced on the degrees of freedom.

  • Penalty method

  • Elimination method/Matrix Partitioning