A curved beam element based on the Timoshenko model and non-uniform rational B-splines (NURBS) interpolation\ud both for geometry and displacements is presented. Such an element can be used to suitably analyse plane-curved beams and arches. Some numerical results will explore the effectiveness and accuracy of this novel method by comparing its performance with those of some accurate finite elements proposed in the technical literature, and also with analytical\ud solutions: for the cases where such closed-form solutions were not available in the literature, they have been computed by exact integration of the governing differential equations. It is shown that the presented element is almost insensitive to both membrane- and shear-locking, and that such phenomena can be easily controlled by properly choosing the number\ud of elements or the NURBS degree

The current development of the isogeometric approach in various fields of mechanics is explained by the high-accuracy results which can be achieved at a reduced computational cost by codes based on non-uniform rational B-splines (NURBS). In the case of strongly curved beams the simple diagonal de Saint-Venant’s constitutive model can lead to significant errors as it has been reported in the classic literature. Other models such as Winkler’s have been proposed and seem more suitable for these kinds of structures. Unfortunately several numerical codes are based on a diagonal constitutive model which neglects the coupling effect of elongation and curvature even if a highly refined geometry description can be developed by means of NURBS. The results obtained by means of numerical codes based on isogeometrical analysis for curved beams are here reported and basic choices, computational costs and numerical accuracy of the above-mentioned constitutive models are discussed, from a qualitative and quantitative point of view. This comparison, in the authors’ opinion, is necessary to avoid an excessive gap between the computational efficiency of NURBS, which are capable of very accurate geometry description, and a simplistic representation of the constitutive relations that is efficient for straight beams but not so much for curved beams whose curvature is large. The results of some selected tests are presented and discussed to highlight differences between the two approaches, showing that the small increase of computational cost of Winkler’s model is well compensated by the accuracy gain

We illustrate a numerical tool for analyzing plane arches such as those frequently used in historical\ud masonry heritage. It is based on a refined elastic mechanical model derived from the isogeometric approach. In\ud particular, geometry and displacements are modeled by means of non-uniform rational B-splines. After a brief\ud introduction, outlining the basic assumptions of this approach and the corresponding modeling choices, several numerical applications to arches, which are typical of masonry structures, show the performance of this novel\ud technique. These are discussed in detail to emphasize the advantage and potential developments of isogeometric analysis in the field of structural analysis of historical masonry buildings with complex geometries

We propose a computational procedure to assess size effects in nonfunctionalized single-walled carbon nanotube (CNT)-polymer composites. The procedure upscales results obtained with atomistic simulations on a composite unit cell with one CNT to an equivalent continuum composite model with a large number of CNTs. Molecular dynamics simulations demonstrate the formation of an ordered layer of polymer matrix surrounding the nanotube. This layer, known as the interphase, plays a central role in the overall mechanical response of the composite. Due to poor load transfer from the matrix to the CNT, the reinforcement effect attributed to the CNT is negligible; hence the interphase is regarded as the only reinforcement phase in the composite. Consequently, the mechanical properties of the interface and the CNT are not derived since their contribution to the elastic response of the composite is negligible. To derive the elastic properties of the interphase, we employ an intermediate continuum micromechanical model consisting of only the polymer matrix and a three-dimensional fiber representing the interphase. The Young’s modulus and Poisson’s ratio of the equivalent fiber, and therefore of the interphase, are identified through an optimization procedure based on the comparison between results from atomistic simulations and those obtained from an isogeometric analysis of the intermediate micromechanical model. Finally, the embedded reinforcement method is employed to determine the macroscopic elastic properties of a representative volume element of a composite with various fiber volume fractions and distributions. We then investigate the role of the CNT diameter on the elastic response of a CNT polymer composite; our simulations predict a size effect on the composite elastic properties, clearly related to the interphase volume fraction