Isogeometric analysis of plane-curved beams

Abstract

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

Designing a light fabric metamaterial being highly macroscopically tough under directional extension: first experimental evidence

“…In this respect, we underline that the so-called GBTs (Generalized Beam Theories) may be of use (see e.g., [39,[51][52][53]) also for starting the study of dynamical behavior of pantographic sheets. Furthermore, these meso-models can be developed on the framework of the isogeometric analysis as in [11,12,29,30,82].…”

“Fast” and “slow” pressure waves electrically induced by nonlinear coupling in Biot-type porous medium saturated by a nematic liquid crystal

“…From this point of view, an investigation on proper finite element (FE) simulation [21][22][23][24][25][26][27][28][29] or regularized FE [30][31][32][33][34][35][36][37] will be welcome in order to avoid, e.g., the unpleasant occurrence of instability [38][39][40][41][42][43][44][45][46][47][48][49]. Due to the high porosity, the Biot model should probably be modified, see e.g.…”

Linear pantographic sheets: Asymptotic micro-macro models identification

“…The homogenized energy introduced in this paper (56) is minimized by using the package "Weak Form PDE" and by introducing standard third-order Hermite finite elements. While the used code is surely not optimized for the introduced problem (we believe that the recently developed numerical methods would be more efficient, see, e.g., [Cazzani et al 2016a;Greco and Cuomo 2013;2014;2015;Turco and Aristodemo 1998;Beirão da Veiga et al 2008;), its rate of convergence seems satisfactory for getting preliminary results concerning the behavior of the simplest structures; actually, it is based on the introduction of an auxiliary tensor field which appears in the deformation energy and is equated to the displacement gradient by means of suitable fields of Lagrange multipliers. Remark also that all presented numerical simulations are really and intrinsically mesh-independent, because of the properties of the introduced continuum model, where the second gradient of displacement is at the same time modeling the relevant physical properties and supplies a regularizing effect on equilibrium equations.…”