An operational calculus-based approach to a general bending theory of nonlocal elastic beams

• A general beam theory within the framework of nonlocal elasticity theory is developed via Lurie's operational method.
• This beam theory does not require any ad hoc assumptions.
• The explicit solutions involving trigonometric expansions are presented.

This paper is concerned with obtaining exact solutions for the bending problem of an elastic nanobeam by using the Lurie's operational method. Within the framework of nonlocal elasticity theory, a general governing equation, capable of capturing the size effect, is first constructed in a systematic and straightforward manner. Then a solution methodology is described. Some explicit solutions involving trigonometric expansions are also presented and compared with other well known beam theories. The results indicate that this general beam theory can provide more accurate results, which can be served as benchmarks for other theoretical or numerical methods.