Towards a unified approach to nonlocal elasticity via fractional-order mechanics

This study presents a fractional-order continuum mechanics approach that allows combining selected characteristics of nonlocal elasticity, typical classical integral and gradient formulations, under single frame-invariant framework. The resulting generalized theory is capable capturing both stiffening softening effects it not subject to the inconsistencies often observed external loads boundary conditions. governing equations 1D are derived by continualization Lagrangian lattice long-range interactions. particularly well suited highlight connection between operators microscopic properties medium. also extended derive, means variational principles, 3D in strong form. positive definite potential energy, characteristic our fractional formulation, always ensures well-posed equations. aspect, combined with differ-integral nature operators, guarantees stability ability capture dispersion without requiring additional inertia terms. proposed formulation applied static free vibration analyses either Timoshenko beams or Mindlin plates. Numerical results, obtained finite element method, show able model response these slender structures. numerical results provide foundation critically analyze physical significance different parameters as their effect on structural elements.