B-spline-enhanced space-fractional finite element method with application to limit state analysis of 3D scale-sensitive truss structures

Abstract

The present paper proposes a novel B-spline-based space-fractional finite element formulation for analyzing three-dimensional scale-sensitive truss structures. The formulation is developed within the framework of space-fractional continuum mechanics, which generalizes the classical local theory by incorporating spatial nonlocality through fractional differentiation to capture scale effects. A key novelty of the proposed approach is the use of B-spline shape functions, whose overlapping nature enables the sharing of degrees of freedom between adjacent elements, thereby ensuring inter-element continuity. This property is particularly important in nonlocal formulations, as it prevents artificial discontinuities at element boundaries and ensures consistent information transfer between neighboring regions, enabling a representation of long-range interactions. As a result, the proposed approach allows the use of substantially lower polynomial degrees while maintaining solution accuracy comparable to that of conventional high-order polynomial formulations. Building on previous one- and two-dimensional studies, the present work extends the formulation to spatial configurations and applies it to the limit-state analysis of 3D scale-sensitive truss structures. The numerical results demonstrate improved convergence and consistent reproduction of size-dependent softening behavior.