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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(a) (b) Figure 4. Combined effects of the nonlocal parameter, � , the surface energy and the material gradient index, k, on non-dimensional deflection, � , of a Simply-Supported (S-S) FG nanobeam subjected to a concentrated load for both SSDM and SDM models of elasticity for k=1 (a) and k=2 (b).

(a) (b) Figure 5. Combined effects of the nonlocal parameter, � , the surface energy and the material gradient index, k, on non-dimensional deflection, � , of a Simply-Supported (S-S) FG nanobeam subjected to a concentrated couple for both SSDM and SDM models of elasticity for k=1 (a) and k=2 (b). Conclusions The main outcomes of the present paper may be summarized as follows: (i) the effective surface parameters ( � , � ) depend on the variation of the material gradient, k , as well as on those of the bulk volume; (ii) as the value of the nonlocal parameter increases, the value of the deflection decreases both for the SSDM (with surface energy effects) model and for the SDM model (without surface energy effects); (iii) the values of the SSDM deflections evaluated in presence of surface effects are always lower than those obtained by the SDM model (without surface energy effects). In conclusion, the novel proposed surface stress-driven model, which combine the stress-driven formulation of elasticity with the surface elasticity theory, is here extended in order to analyses the coupled effects of the nonlocal parameter, � , the surface energy and the material gradient index, k , on the bending response of Bernoulli-Euler FG nanobeams with internal load discontinuities such as a non-uniform distributed load and/or a concentrated force or couple at an internal point of the nanobeam axis.