PSI - Issue 47

3

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. 1 . Coordinate system and configuration of the FG nanobeam: bulk continuum (mixture of ceramic and metal) and surface layer.

2.1. Displacement field The Cartesian components � � � � , � and � � � � , � of the displacement field of the FG nanobeam along and directions, respectively, in presence of a loading discontinuity at the point of abscissa �� (Figure 2) can be expressed as � �� �� � �� ��� ; � � , � � � � � 0 � �� (4a) � �� �� � �� ��� ; � � , � � � � � �� �� (4b) where � � � and � � � are the transverse displacements of the geometric center O belonging to the first and the second part of the FG nanobeam, respectively. The corresponding non-zero strain, � � � � , � , can be expressed, respectively, as � � � � � � �� � � � 0 � �� (5a) � � � � � � �� � � � �� �� (5b) being � � � the geometrical bending curvature ( � � 1,2 ).