Space-Fractional Finite Element Formulation for 3D Nonlocal Frames
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This talk introduces a nonlocal finite element for the static analysis of three-dimensional frame structures exhibiting scale-dependent behavior. The formulation is developed within the framework of space-fractional continuum mechanics, which generalizes the classical local theory by introducing spatial nonlocality through a fractional integro-differential operator to capture scale effects. The finite element is formulated using Timoshenko beam theory combined with Saint-Venant torsion theory, accounting for bi-directional bending, shear deformations, and torsion. For the numerical implementation, B-spline shape functions are used to provide smooth displacement fields and facilitate interactions between elements. This feature is particularly important in nonlocal formulations, where the response at a point depends on its surroundings. Representative numerical examples of three-dimensional frames illustrate the performance of the proposed formulation. A comprehensive parametric study is conducted to examine the influence of the nonlocal parameters on the structural response. The results indicate that the proposed formulation captures the characteristic size-dependent behavior, showing a general softening trend as nonlocal effects become more pronounced. ACKNOWLEDGEMENTS This research was funded in whole by the National Science Centre, Poland, grant number 2022/45/N/ST8/02421. For the purpose of Open Access, the authors have applied a CC-BY public copyright license to any Author Accepted Manuscript (AAM) version arising from this submission.
