Analysis of Nanoplate with a Central Crack Under Distributed Transverse Load Based on Modified Nonlocal Elasticity Theory

Abstract

In this paper, using the complete modified nonlocal elasticity theory, the deflection and strain energy equations of rectangular nanoplates, with a central crack, under distributed transverse load were overwritten. First, the deflection of nanoplate was obtained using Levy's solution and consuming it; strain energy of nanoplate was found. As regards nonlocal elasticity theory wasn’t qualified for predicting the static behavior of nanoplates under distributed transverse load, using modified nonlocal elasticity theory, the deflection of nanoplate with a central crack for different values of the small-scale effect parameter was achieved. It was gained with the convergence condition for the complete modified nonlocal elasticity theory. To verify the result, the results for the state of the small-scale effect parameter were placed equal to zero (plate with macro-scale) and then were compared with the numerical results as well as the classical analytical solution results available in the valid references. It was shown that the complete modified nonlocal elasticity theory does not show any singularity at the crack-tip unlike the classical theory; therefore, the method presented is a suitable method for analysis of the nanoplates with a central crack.