Linear Analysis of Nonlinear Properties

doi:10.1117/3.2317988.ch15

Book: Opto-structural Analysis

Author(s): John W. Pepi

Published: 2018

https://doi.org/10.1117/3.2317988.ch15

Author Affiliations +

Abstract

In Chapter 1 we found that both load-induced and thermally induced stress is readily calculated for linear elastic material properties using Hooke’s law. In some cases, however, material behavior is nonlinear, and hence one needs to make use of nonlinear theory. Since this is now a departure from the usual Hookean approach, the use of plastic analysis may be required. However, we can avoid this complexity in some situations. In Chapter 4 we saw an example of nonlinear behavior of the CTE with temperature, which we handle quite nicely using secant CTE properties. We discuss this application and extend it to apply to a nonlinear elastic modulus. A theoretical approach is presented to calculate stresses for nonlinear, non-Hookean materials.