ABSTRACT
The numerical solution of nonlinear structural problems is generally carried out by means of an incremental-iterative solution procedure in which the external load is gradually incremented and equilibrium is sought at each load level via an iterative process. This chapter discusses the pure incremental method, incremental method with equilibrium corrections, Newton-Raphson incremental-iterative methods, and arc-length methods. A Newton-Raphson iteration will experience convergence difficulties in the close neighborhood of critical points due to ill conditioning of the tangent stiffness matrix. Slower convergence of the iterative solution process is often experienced "near" a critical point due to ill conditioning of the tangent stiffness matrix. Bergan proposed the use of a "current stiffness parameter" that can be computed from information already available from the incremental solution. Crisfield's modified arc-length method is often termed the "spherical method" since it seeks to find an intersection of the equilibrium path with a hypersphere of radius in (N + 1)-dimensional Euclidian space.
