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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Figure. 2 . FG nanobeam with loading discontinuities at the abscissa x=d.

2.2. Governing equation By using the virtual work principle, it is possible to obtain the following governing equation for each part of the FG nanobeam � � � �� � � � �� � ��� � 0 0 � � (6a) � � � �� � � � �� � ��� � 0 � � (6b) The corresponding boundary conditions at the FG nanobeam ends ( � 0 , ) can be chosen by specifying one element of each of the following two pairs of standard boundary conditions, SBCs (kinematic and static boundary conditions) � or � � � � � (7a) � � or � (7b) � or � � � � � (7c) � � or � (7d) In addition, it is necessary to satisfy the internal compatibility boundary conditions (ICBs) at the abscissa d � � � � � � � (8a) � � � � � � � (8b)