Force-Based and Displacement-Based Finite Elements

The traditional displacement-based finite element method forms stiffness matrices for elements of a structure and assembles those elements into a global stiffness matrix that is then solved for the displacements and, subsequently, the forces. In the force-based method discussed in this book, a global equilibrium matrix is assembled from the equilibrium equations written at discrete nodes in the structure and then combined with compatibility equations to solve for the forces and, subsequently, the displacements. However, a global equilibrium matrix can also be assembled from element equilibrium matrices, in a process very similar to the displacement-based finite element method and is called here the force-based finite element method. Both force-based and displacement-based finite element methods are described with one-dimensional examples. Problems where there are nonzero-specified displacements are also considered. MATLAB displacement-based and force-based finite element scripts are presented.