Analytical solutions for strain-driven Timoshenko nanobeam bending using generalized functions.

AbstractStatic nanobeam bending problems have yielded conflicting results from many researchers. Methods suggested by numerous researchers have shown inconsistencies in capturing size effects and satisfying essential and natural boundary conditions for nanobeam configurations when subjected to different types of loading. This work proposes an alternative approach using Eringen’s strain-driven integral nonlocal elasticity to arrive at analytical solutions. The theory of generalized functions and the Dirac-delta identity are used to revisit Timoshenko nanobeam modeling aspects, focusing on nanobeam elastostatics. Proposed analytical solutions for fundamental and derived quantities based on the strain-driven nonlocal model have been compared with the results of existing approaches. A crucial drawback with the strain-driven models of Eringen in both integral and differential form is its inability to satisfy equilibrium equations, which is addressed extensively in this work. [ABSTRACT FROM AUTHOR]