Journal of Theoretical
and Applied Mechanics

57, 1, pp. 49-58, Warsaw 2019
DOI: 10.15632/jtam-pl.57.1.49

### Investigation of flexibility constants for a multi-spring model: a ‎solution for buckling of cracked micro/nanobeams

In this paper, a multi-spring model is used for modelling of the crack in a micro/nanobeam
under axial compressive load based on a modified couple stress theory. This model inc-
ludes an equivalent rotational spring to transmit the bending moment and an equivalent
longitudinal spring to transmit the axial force through the cracked section, which leads to
promotion of the modelling of discontinuities due to the presence of the crack. Moreover,
this study considers coupled effects between the bending moment and axial force on the
discontinuities at the cracked section. Therefore, four flexibility constants appear in the con-
tinuity conditions. In this paper, these four constants are obtained as a function of crack
depth, separately. This modelling is employed to solve the buckling problem of cracked
micro/nanobeams using a close-form method, Euler-Bernoulli theory and simply suppor-
ted boundary conditions. Finally, the effects of flexibility constants, crack depth and crack
location on the critical buckling load are studied.
Keywords: flexibility constants, multi-spring model, MCST, buckling, crack

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