Figure 4: beam dimensions Schematic
The governing equations for this analysis are the Bernoulli-Euler’s elastic curve theory [5] equations as shown below.
\(Moment\ of\ Inertia,\ I=\ \frac{\text{b\ x\ }h^{3}}{12}\) (1)
\(Maximum\ Deflection,\ \hat{y}=\frac{-WL^{3}}{3EI}\) (2)
\(Maximum\ Bending\ Stress.\ \sigma=\ \frac{M\hat{y}}{I}\) (3)
The first step is to generate a 3D Cad model as shown in figure 1. The constrains and loads are then applied to the beam (figure 2) after which a mesh is generated (figure 3).