ABSTRACT
This chapter presents several techniques that can be used in analysis of structures in general, considering material nonlinearity. Except for simple structures, use of a computer is necessary to perform nonlinear analysis, generally requiring iterations. Understanding of nonlinear behavior can be enhanced by the use of computer programs which permit the introduction of loads in multi-stages, allow changing the number of iteration cycles, and give the out-of-balance forces at the end of each iteration cycle. This requires nonlinear analysis involving iteration, which can be done using Newton-Raphson's technique. The equilibrium equations are based on trial displacement values, whose accuracy is improved by iterations, so as to satisfy the equilibrium of the nodes or the members in their displaced positions or their deformed shapes. Nonlinearity caused by large deformations is referred to as geometric nonlinearity. Nonlinearity can also arise when the stress–strain relationship of the material is nonlinear in the elastic or in the plastic range; this is called material nonlinearity.
