Nonlocal finite element formulation in modeling micro and nano scaled mechanical systems

Experimental studies have shown that the mechanical behaviors of nano- and micro-scale structures are different from structures having conventional dimensions (centimeters, meter). Experimental study on nanostructures and nanostructures is both costly and time consuming. For this reason, by using higher-order elasticity theories, the results have been theoretically tried to be obtained closer (simulated by mechanical model) and many higher order theories taking the size effect into account have been emerged. In this thesis, nonlocal elasticity theory was used to investigate the dimensional effect. Using the nonlocal elasticity theory, bending, vibration and buckling differential equations are obtained in detail. These differential equations are also solved using Galerkin weighted residual method which is one of the finite element methods which is an approximate solution method. Indeed in finite element method the calibration of small scale parameter from nonlocal elasticity theory is made for vibration analysis of nanorod. Protein microtubules and silicon carbide nanotube is choosen to perform analyzes. Variable parameters on the analyzes have been examined in detail. In addition, the effect of parameters such as the length, diameter, and thickness and size effect parameter on the analyzes are examined in detail and the results are presented in tables and figures.