Exact nonlocal solutions of circular nanoplates subjected to uniformly distributed loads and nonlocal concentrated forces

Abstract

The nonlocal solutions of the bending problem of the circular elastic nanoplates subjected to uniformly distributed loads by using the Eringen's nonlocal theory are approximate. Seeking for an exact solution of the concerning problem by adding a concentrated force; a specific concentrated force which depends on the nonlocal parameter and, therefore, vanishes in the local case, is obtained. In this context; starting from the local bending solution of the simply supported circular nanoplates under uniformly distributed loads and evolving the solution step by step, exact nonlocal solutions of the bending problem of the simply supported and clamped circular nanoplates subjected to uniformly distributed loads and the concerning nonlocal concentrated forces acting at the centers of the circular nanoplates are obtained with the expectation that the exact nonlocal solution is not very different than the corresponding exact local solution. The closed-form solutions are checked to satisfy exactly the equations of equilibrium, constitutive equations and the boundary conditions of the relevant nonlocal problem. The application of the concerning specific concentrated force, in addition to the uniformly distributed load, is seen to make the radial bending moments for the simply supported circular nanoplate and the deflections for the clamped circular nanoplate free from the effects of the nonlocality.