Efficient nonlinear analysis by factored matrix modification

In a typical finite element analysis, the majority of computational effort is devoted to assembling and factoring a global system of equations. When significant nonlinearities occur, due to abrupt changes in material behavior or boundary conditions, the global equations must be modified. This paper presents a method for directly incorporating these nonlinear modifications into the previously factored matrix at a computational cost proportional to (1/bandwidth) times the initial solution. Because the computational cost of this method depends on the number of modifications rather than the number of times the matrix is factored, the nonlinear effects may be continuously incorporated into the global matrix during the analysis. This approach greatly reduces the amount of iteration and results in an equilibrium path which is closer to the true solution