ABSTRACT
In this chapter, the solution methods for a system of nonlinear equations are discussed in the context of nonlinear finite element analysis of solids and structural systems. We will only discuss the static cases. In general, the numerical solution of nonlinear structural analysis problems is usually carried out by means of an incremental solution procedure in which the load vector is applied in a series of small incremental steps. At the beginning of each incremental step, the geometry and material properties and incremental response of the structural system are computed as a linear system, often accompanied with corrective iterations. The equilibrium path of the structure is thereby followed in a series of small tangential linear steps. The standard incremental-iterative numerical solution procedure is called the Newton-Raphson method. The modified Newton-Raphson method characterized by infrequent update on the tangent stiffness matrix is more suitable for a moderate degree of structural nonlinearity. If it is desired to calculate structural response past limit points, special methods, such as an arc length method, are used. These methods allow the load increments to be automatically removed from the structure when appropriate.
