*2.4. Proposed Algorithm*

After the principal stress and directions are found, the orthotropic directions can be oriented according to the principal directions. The semi-major axis is directed to the 1st principal stress direction. The porosity is determined by von Mises stress and value [*σ*]inf. The [*σ*]inf is the infimum of the stress value and determines the value of the underload. So, porosity can be restored by the equation:

$$\lambda\left(\stackrel{\rightarrow}{\mathbf{x}}\right) = \begin{cases} 1 - \frac{[\sigma]\_{\text{inf}} - \sigma\_{V.M.}\binom{\rightarrow}{\mathbf{x}}}{[\sigma]\_{\text{inf}}}, \sigma\_{V.M.}\left(\stackrel{\rightarrow}{\mathbf{x}}\right) < [\sigma]\_{\text{inf}}\\ 1, \sigma\_{V.M.}\left(\stackrel{\rightarrow}{\mathbf{x}}\right) \ge [\sigma]\_{\text{inf}} \end{cases} \tag{14}$$

To determine the ellipticity coefficient, the 1st and the 3rd principal stresses were used:

$$\beta\left(\overrightarrow{\dot{\boldsymbol{x}}}\right) = \frac{\min\left( \left| \sigma\_1\left(\overrightarrow{\dot{\boldsymbol{x}}}\right) \right|, \left| \sigma\_3\left(\overrightarrow{\dot{\boldsymbol{x}}}\right) \right| \right)}{\max\left( \left| \sigma\_1\left(\overrightarrow{\dot{\boldsymbol{x}}}\right) \right|, \left| \sigma\_3\left(\overrightarrow{\dot{\boldsymbol{x}}}\right) \right| \right)}\tag{15}$$

Then, the stiffness constants can be calculated by porosity and the ellipticity coefficient and the stress-state problem can be solved. So, the algorithm can be described:

## **Algorithm of structural design**

