Size dependent bending and vibration analysis of functionally graded micro beams based on modified couple stress theory and neutral surface position

Nonlocal integral thermoelasticity: A thermodynamic framework for functionally graded beams

“…For the present research, nonisothermal model [29] is of interest. But, when the nonlocal procedures are concerned, inclusion of the shift of neutral surface is much less common; for the isothermal strain gradient formulation see [35][36][37][38] and for the integral based [39]. For the gradient based thermoelastic beams including hygro effects, see [15].…”

Bending and free vibration analysis of functionally graded plates using a simple shear deformation theory and the concept the neutral surface position

“…Therefore, the stretching and bending equations of such plate are coupled. Morimoto et al [17], Abrate [18], Zhang and Zhou [19], Ould Larbi et al [20], Bousahla et al [21], Khalfi et al [22], Fekrar et al [23], Al-Basyouni et al [24] and Bourada et al [25] showed that there is no stretching-bending coupling in constitutive equations if the reference surface is properly selected.…”

Free vibration of anisotropic single-walled carbon nanotube based on couple stress theory for different chirality

“…By substituting equations (12) and (14) into equation (18) and by using the partial integration, the motion equations of anisotropic model of SWCNT based on the couple stress theory are extracted as follows…”

“…Elements for modeling nanostructures include nano-beams, nano-discs, and nano-shells. [8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23] Carbon nanotube (CNT) is one of the most commonly used elements in nanostructures which are used in a variety of composite materials and nano systems. CNTs are hollow cylinder made of the convolution of graphene sheets around an axis.…”