PSI - Issue 47

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

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�∗ �� � � �� � � � �∗ � � �� � � � � � � �� � � � � ��� � 0 �∗ �� � � � �∗ � � � � � � � � ��� � 0 � � (20b) with the corresponding constitutive and constitutive continuity boundary conditions (Eq.17) in addition to the standard and compatibility boundary conditions (Eq.7 and Eq.8). Now, by introducing the following dimensionless quantities � � (21a) � � (21b) � ∗ � ∗ (21c) � � (21d) � ∗ � ∗ � �∗ (21e) � ∗ � ∗ �∗ (21f) � � �∗ (21g) � � � �∗ (21h) � � ��� � � 1 � 3 ∗ (21i) � � ��� � � 2 � 3 ∗ (21l) �� � � �∗ (21m) � � � � �∗ (21n) � � (21o) the dimensionless governing equations incorporating surface energy effect of the bending problem for the two parts of the FG nanobeam can be formulated as follow �� � � � � � � � � � �� � � � � � � � ��� � 0 0 � � � � (22a) �� � � � � � � � � � �� � � � � � � � ��� � 0 � � � � 1 (22b) with the following boundary conditions in terms of dimensionless transverse displacements - SBCs 0 � � (20a)