5. Principal stresses.

**Figure C5.**

*Principal stresses around the single hole in an elastic plate subjected to far-field stress. These solutions are obtained by applying Eqs. (37) and (38) using the tensor stress components in Figures C4.*

6. Displacement field with respect to different values of Poisson's ratio.

In **Figures C5** and **C6**, we show the impact of the Poisson's ratio on the plane strain and plane stress displacement considering the model Case 1–1 of the elastic plate with a single hole. The model inputs are fixed as given in **Table 1** except for the Poisson's ratio that takes three different values *ν* ¼ 0, 0*:*2, and 0.4. We can see from **Figure C6** the following results (as presented before in Case 2–2 results):


Therefore, this impact will extend to the resulting plane strain and plane stress solutions for the strain and stress tensor components computed based on the displacement results. This impact can be also generalized to the model of the elastic plate with 5-holes presented in Case 2–2. **Tables 3** and **4** illustrate, numerically, the impact of Poisson's ratio on the maximum and minimum values of the tangential stress (*σθ*) around the rim of the central hole in model Case 1–1 and model Case 2–2, respectively.

*Asymptotic Solutions for Multi-Hole Problems: Plane Strain versus Plane Stress Boundary… DOI: http://dx.doi.org/10.5772/intechopen.105048*

#### **Figure C6.**

*The plane strain and plane stress displacement solutions against different values of Poisson's ratio: ν* ¼ 0 *first column, ν* ¼ 0*:*2 *second column, and ν* ¼ 0*:*4 *third column. The first two rows are for the displacement in x*�*direction and the last two rows are for the displacement in y*�*direction.*
