Meshfree Method for Static Analysis of Timoshenko Nano Beam Using Strain-Driven Nonlocal Model

Abstract Carbon nanotubes have found immense application in low-dimensional and miniaturized devices because of their exceptional structural and electrical attributes. Designing and using such a MEMS/ NEMS system requires numerical analysis. However, at these scales, they do not obey the local continuum theory. These common structures can be modeled as one-dimensional beams incorporating nonlocal constitutive models. Numerical methods inherently nonlocal in formulation can simulate nonlocal elastic solids effectively. Meshfree methods are efficient numerical methods that can capture nonlocal behavior through carefully constructed shape functions. This study explores the effectiveness of the Element-free Galerkin (EFG) method in simulating nonlocal elastic solids under static conditions. Timoshenko nanobeam is modeled using a strain-driven nonlocal model, and the solution to static beam bending is obtained using the EFG method. Standard boundary conditions with a uniformly distributed load throughout its length are selected for numerical case studies. Beam becomes softer with increase in nonlocal parameter. Displacement and rotations are plotted for various nonlocal parameter and compared against local results.