Nonlocal elastic plate problems via iterative method

Elastostatics of nanoplates is addressed via an effective iterative procedure. An integral theory of elasticity is exploited to capture size effects in thin plates. The governing nonlocal elastic problem is represented by an integro-differential formulation, whose resolution is particularly demanding. Moreover, extending solution methodologies to general plate geometries and arbitrary boundary and loading conditions is a complex issue to address. To overcome these limitations, an effective iterative method is proposed. Such an algorithm relies solely on the solution of standard local elastostatic problems. Indeed, according to the iterative scheme, the nonlocal solution is obtained by solving a sequence of local problems. The presented methodology accommodates arbitrary nanoplate geometries and general kernels of the constitutive integral law, ensuring broad applicability and making it suitable for modeling a wide spectrum of nanoengineered systems.