On the nonlocal bending problem with fractional hereditariness

Nonlocal hereditariness in Bernoulli–Euler beam is investigated in this paper. An approach to solve that problem is proposed and some analytical solutions are provided. To this aim, time-dependent hereditary behavior is modeled by means of non-integer order operators of the fractional linear viscoelasticity. While, space-dependent nonlocal phenomena are simulated through the integral stress-driven formulation. These two approaches are combined providing a new model able to simulate nonlocal viscoelastic bending problem. Several application samples of the proposed formulation and a thorough parametric study are presented showing the influences of hereditariness and nonlocal effects on the mechanical bending response. Proposed formulation can be useful for design and optimization of structures used in advanced applications when local elastic theory cannot be adopted.