Formulation and experimental validation of space-fractional Timoshenko beam model with functionally graded materials effects

Abstract

In this study, the static bending behaviour of a size-dependent thick beam is considered including FGM (Functionally Graded Materials) effects. The presented theory is a further development and extension of the space-fractional (non-local) Euler–Bernoulli beam model (s-FEBB) to space-fractional Timoshenko beam (s-FTB) one by proper taking into account shear deformation. Furthermore, a detailed parametric study on the influence of length scale and order of fractional continua for different boundary conditions demonstrates, how the non-locality affects the static bending response of the s-FTB model. The differences in results between s-FTB and s-FEBB models are shown as well to indicate when shear deformations need to be considered. Finally, material parameter identification and validation based on the bending of SU-8 polymer microbeams confirm the effectiveness of the presented model.

Distillation of nonlocality in porous solids

“…Further, since the order map was determined from a linear response of the frame-invariant nonlocal model (see [7,19]), the map is also valid for any affine transformation; even via change in bulk material parameters [24]. It follows that the choice of the material parameters adopted in this study does not affect the order map, unless the isotropic bulk solid is modified to admit material heterogeneity or anisotropy which is an added source of nonlocal effects [7,20,30]. These results indicate that the VO approach potentially enables a parsimonious approach to describing heterogeneous nonlocality.…”

Cyclic Behavior of Masonry Shear Walls Retrofitted with Engineered Cementitious Composite and Pseudoelastic Shape Memory Alloy

“…Seismic activities can induce structural and non-structural damage both during and afterwards the event, which is mainly caused by perturbations in load-resisting elements of constructions, such as load-bearing walls and columns [1,2]. In most cases, seismic failures in structures are triggered by their limited resilience owing to deficient component size, material properties, and lack of structural flexibility or ductility [3,4].…”

Multiscale nonlocal beam theory: An application of distributed-order fractional operators

“…The rapid development of novel manufacturing techniques has greatly accelerated the discovery and fabrication of complex materials including, but not limited to, composites [1,2], metamaterials [3][4][5], and functionally graded materials [6,7]. While applications can span a diverse range such as wave-guiding [8], sensors and micro/nano-electromechanical devices [9], and even biological implants [10], all these materials are characterized by highly heterogeneous compositions and architectures.…”

“…However, recent studies focused on the deformation of heterogeneous solids (e.g. porous solids [14][15][16][17], granular solids [18][19][20], composites [21][22][23], functionally-graded solids [7,24], lattice structures [25,26], metamaterials [27][28][29]), and even intentionally designed nonlocal structures [30][31][32] have demonstrated that nonlocal effects can also originate and localize at the meso-and macro scales. These studies reinforced the realization that nonlocal effects can exist and, more importantly, can interact across scales.…”

“…This complex multi-level nonlocal phenomenon was the focus of a recent study [33] in which the phenomenon was denominated "multiscale nonlocal elasticity". Real-world applications that exemplify the characteristics and the importance of multiscale nonlocal elasticity include, for example, layered and woven composites [2,34], 3D printed solids [2,35], functionally graded solids [6,7], solids with graded porosity [36][37][38], and semiconductors fabricated by atomic layer deposition [9]. In order to support the discovery, the understanding, and the performance assessment of these material systems, it is essential to develop computationally efficient multiscale models that offer two fundamental characteristics [39,40]: C1) the ability to simultaneously capture nonlocal effects across scales within a physically consistent and mathematically well-posed framework, and C2) the ability to naturally interconnect scales and exchange information without resorting to artificial hand-shaking approaches.…”