What is an example of an engineering problem that may require nonlinear analysis?

A prime example of an engineering problem that requires nonlinear analysis is modeling the behavior of materials under extreme loading conditions. In such scenarios, materials often exhibit nonlinear elastic or plastic behavior when subjected to large forces, deformations, or changes in temperature. Traditional linear models may not accurately predict the material's response, as they assume a proportional relationship between stress and strain, which holds only within a certain limit of deformation.

Nonlinear analysis takes into account factors such as material yielding, buckling, and complex interactions that occur at higher stress levels. These interactions can significantly affect the performance and safety of structures or components, especially during events like seismic activities, impacts, or sudden load applications. Therefore, accurate modeling in these conditions ensures the reliability and longevity of engineering designs by accounting for the real-world complexities of material behavior beyond the linear assumptions.