PSI - Issue 47

Rosa Penna et al. / Procedia Structural Integrity 47 (2023) 789–799 Author name / Structural Integrity Procedia 00 (2019) 000–000

797 9

� � �� � � � � � � �� � � � � � �� � � � � � �� � � � � � � �� � � � � � �� � � �

0 � � � � (27c) � � � � 1 (27d)

4. Results and discussion In this paragraph, the results of a parametric analysis are presented to show the effectiveness of the surface stress-drivel model (SSDM) for the study of the bending behavior of a straight Bernoulli-Euler FG nanobeam, with length L=10 nm, ���� 0.1 . The material properties of the nanobeam are listed in Table 1. Table 1. Material parameters of metal (m) and ceramic (c). Material Parameters Values Unit Ceramic 210 [GPa]

�� � � � � �� �� ��

‐ 10.6543

[N/m]

(Si)

0.6048

[N/m]

70

[GPa]

Metal

5.1882

[N/m]

(Al)

0.9108 [N/m] In order to validate the proposed SSDM model, a numerical analysis has been carried out for a Simply Supported (S-S) FG nanobeam by considering three different loading configurations: (i) a non-uniform distributed load � � ��� � 0.1 � � 0 � � , � ��� � 10 � � � � �� , (ii) a concentrated force at the abscissa d ��� 10 � and (iii) a concentrated couple at the abscissa d ��� 100 � . The obtained numerical results have been always compared to those derived by employing the Stress-Driven Model (SDM) without considering surface energy effects. In Figures 3-5 the curves of the non-dimensional deflections corresponding to the SSDM (continuous) and SDM (dashed) are plotted for each statical scheme by setting � ∊ {0.10, 0.30, 0.50} and k ∊ � 1,2 � and show the combined effects of the nonlocal parameter, � , of the surface energy and of the material gradient index, k, on the bending behavior of the FG nanobeams.

(a) (b) Figure 3. Combined effects of the nonlocal parameter, � , the surface energy and the material gradient index, k, on non-dimensional deflection, � , of a Simply-Supported (S-S) FG nanobeam subjected to a transverse discontinuous distributed load for both SSDM and SDM models of elasticity for k=1 (a) and k=2 (b).