Abstract
This chapter reviews the formulation and logic for some of the more commonly accepted and used non-linear solution methods. The relative slope of the tangent along the equilibrium path is always used as a yardstick to check the state of stiffness of a structure. In some methods, when this relative stiffness is less than a certain value of its original stiffness, the method is converted to a pure incremental method, and when the stiffness is large, the iterative procedure can be activated since divergence is unlikely. The displacement control method possesses the capacity of traversing the limit point without destroying the symmetrical property of the tangent stiffness matrix. The arc-length method is based on using the complete displacement vector for the control of the advance of the equilibrium path. The arc distance, taken as the dot product of the displacement vectors, is fixed in a particular load cycle. The objective of an iterative process is to eliminate the residual displacement or the unbalanced forces, instead of meeting the constant work done or the constant arc-distance.
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