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All physical processes are inherently nonlinear to a certain extent. For example, when you stretch a rubber band, it gets harder to pull as the deflection increases; or when you flex a paper clip, permanent deformation is achieved. Several common every day applications like these exhibit either large deformations and/or inelastic material behavior. Failure to account for nonlinear behavior can lead to product failures, safety issues, and unnecessary cost to product manufacturers. Over the last decade, finite element analysis (FEA) stopped being regarded only as an analyst’s tool and entered the practical world of design engineering. CAD software now comes with built-in FEA capabilities and design engineers use FEA as an everyday design tool in support of the product design process. However, until recently, most FEA applications undertaken by design engineers were limited to linear analysis. Such linear analysis provides an acceptable approximation of real-life characteristics for most problems design engineers encounter. Nevertheless, occasionally more challenging problems arise, problems that call for a nonlinear approach. Historically, engineers were reluctant to use nonlinear analysis, because of its complex problem formulation and long solution time. That’s changing now, as nonlinear FEA software interfaces with CAD and has become much easier to use. In addition, improved solution algorithms and powerful desktop computers have shortened solution times. A decade ago, engineers recognized FEA as a valuable design tool. Now they are starting to realize the benefits and greater understanding that nonlinear FEA brings to the design process.

Methods of Nonlinear Analysis is devoted to nonlinear problems coming from different areas, with particular reference to those introducing new techniques capable of solving a wide range of problems. The book focuses on significant problems in pure and applied nonlinear analysis. It seeks to present the most significant advances in this field to a wide readership, including researchers and graduate students in mathematics, physics, and engineering.