Methods of Nonlinear Analysis
Materials such as metals, soils, and rocks (e.g., lime stones) are inherently nonlinear and plastic. Except in a limited class of problems, the behavior of structures made of these materials cannot be predicted without the consideration of their nonlinear plastic stress–strain behavior. Contrary to linear elastic problems, nonlinear problems require iterative methods for obtaining the solution, both at the global (structure) and local (Gauss point) levels. There are several methods of carrying out the iterations. In this chapter, we will describe (1) a class of methods called the Newton’s methods which form the basis for commonly used global and local iterative algorithms, and (2) Euler methods of solving initial value problems, which form the basis for the commonly used local iterative algorithms.
- Griffiths, D.V. and Smith, I.M. (1991). Numerical Methods for Engineers. CRC Press, Boca Raton, FL.Google Scholar