**5. Mechanical testing of structure with different laminate lay-ups**

The mechanical testing of the structure with different lay-ups and ply stacking angles has been implemented using FE model (see **Figures 1**–**3**) by using three abovementioned types of static bending and torsion loading. These loads were applied separately; for each load scenario the total strain energy *Eel tot*, the maximum and averaged von Mises stress, two end deflections max(*vb*), max(*wb*) and torsion angles *θ* on the free face of the beam tip were calculated. At the solving of these subtasks a linear parametric solver was used. Results of these testing were used for the refinement of the "candidates," that is, select lay-ups that provide the minimum strain energy, bending and torsion deformations. Our study demonstrated a strong coupling of total strain energy of deformed structure with the values of maximum beam deflection (bending load cases) and maximum torsion angles (twisting load case). Moreover, two very interesting and important facts were established. First, we found that sensitivity of both maximum and averaged von Mises stress to the structural symmetry of orthotropic material is noticeably less comparing to the total elastic strain energy. Thereby we do not give here any von Mises dependencies. Second result is the practically independent response of the structure on the twisting load of the lay-ups II, III and IV. The reason for this is the practical identity of the shear modulus of these lay-up schemes at the same lamina angular orientation (see **Figure 7b**–**d**).

The calculated dependencies of maximum deflections and torsion angles of the loaded beams on the lay-up parameters are present in **Figure 9**. These results together with the angular dependencies of elastic moduli that are partially presented in **Figure 8** allowed to select eight "candidates" for further optimization. These candidates had to have acceptable values for the total strain energy and rigidity under all loading scenarios.

> distributed forces oriented along y and z axis and twisting torque applied to the external surface and given by Eqs. (1) and (2). The studied responses included total strain energy, the maximum bending deflections and objective, which was accepted in the normalized dimen-

Optimization of Lay-Up Stacking for a Loaded-Carrying Slender Composite Beam

http://dx.doi.org/10.5772/intechopen.76566

47

**Figure 9.** Dependencies of maximum deflections and torsion angles of the loaded beams.

*Obj* = *θ*/6 + max(*vb*) + max(*wb*)/1.5 (5)

sionless form.
