# Methods of Nonlinear Analysis

Chapter

## Abstarct

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.

## Keywords

Gauss Point Tangent Stiffness Spring Force Raphson Method Tangent Stiffness Matrix
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

## References

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4. Simo, J.C. and Hughes, T.J.R. (1998). Computational Inelasticity. Springer, New York, 392 pages.
5. Zienkiewicz, O.C. (1977). The Finite Element Method. McGraw Hill, New York, 787 pages.