PSI - Issue 6

Anatolii Bochkarev / Procedia Structural Integrity 6 (2017) 174–181

181

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A.O. Bochkarev / Structural Integrity Procedia 00 (2017) 000–000

3. Conclusions

The theory of the large deflection of a plate with surface stresses taken into account was constructed in the classical von K´arm´an form on the basis of the strain-consistent model of surface elasticity. By using the introduced effective elastic moduli, the state equations for the forces tensor and the moments tensor were written in classical form, and then it was shown that taking into account the surface stresses in the potential energy reduces to redefining the elastic moduli as their effective analogs. The developed theory was tested for solving classical problems of the compressive buckling of a rectangular nanoplate under the different flexural boundary conditions. During the analysis of the solutions three factors were identified that affect the value of the critical load of the compressive buckling of the nanoplate compared with the macroplate: the boundary conditions, depending on the effective Poisson ratio, which leads to a redistribution of the bending energy; the effective flexural stiffness; and the pre-tension. In most of the cases, the last factor was dominant and led to an increase in the critical load compared with the macroplate. However, in one case, the cumulative effect of all the factors led to a decrease in the critical load. Thus, the theory of complex bending, adapted to nanoplates, allowed taking advantage of the known methods of solving the classical theory of macro-plates and the scale of its results for the nanoplates.

Acknowledgements

This research was supported by the Russian Foundation for Basic Research, grant No. 14-01-00260.

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