Design Theory and Methods using CAD/CAE

4.2. Simple Bar Example

In this section, we introduce basic concept in structural analysis that is essential for DSA. We use a simple bar example to illustrate the concept for the purpose of avoiding complex mathematical formulations that would dilute our focus. The bar example and formulation discussed in this section will be used in the next section to illustrate some of the solution techniques for sensitivity analysis.

We start by deriving a governing equation in the differential form with which we are familiar. Then, in Section 4.2.2, we introduce the energy equation that is equivalent to the differential governing equation but is more relaxed in the smoothness requirement on the solution function. The energy form is more general and is suitable ...