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

The problem of free vibrations of the Timoshenko beam model is here addressed. A careful analysis of the governing equations allows identifying that the vibration spectrum consists of two parts, separated by a transition frequency, which, depending on the applied boundary conditions, might be itself part of the spectrum. For both parts of the spectrum, the values of natural frequencies are computed and the expressions of eigenmodes are provided. This allows to acknowledge that the nature of vibration modes changes when moving across the transition frequency. Among all possible combination of end constraints which can be applied to single-span beams, the case of a simply supported beam is considered. These theoretical results can be used as benchmarks for assessing the correctness of the numerical values provided by several numerical techniques, e.g. traditional Lagrangian-based finite element models or the newly developed isogeometric approach

The theoretical results relevant to the vibration modes of Timoshenko beams are here used as benchmarks for assessing the correctness of the numerical values provided by several finite element models, based on either the traditional Lagrangian interpolation or on the recently developed isogeometric approach. Comparison of results is performed on both spectrum error (in terms of the detected natural frequencies) and on the l2 relative error (in terms of the computed eigenmodes): this double check allows detecting for each finite element model, and for a discretization based on the same number of degrees‐of‐freedom, N, the frequency threshold above which some prescribed accuracy level is lost, and results become more and more unreliable. Hence a quantitative way of measuring the finite element performance in modeling a Timoshenko beam is proposed. The use of Fast Fourier Transform is finally employed, for a selected set of vibration modes, to explain the reasons of the accuracy decay, mostly linked to a poor separation of the natural frequencies in the spectrum, which is responsible of some aliasing of modes.

In order to assess decay in the mechanical characteristics of fire-exposed Reinforced Concrete (RC)

This paper presents two alternative approaches for the study of reinforced concrete beams under blast loads. In the first approach, the beam is modeled by means of Euler–Bernoulli’s theory and its elastic–plastic behavior is expressed through a new nonlinear relationship between bending moment and curvature. In the second approach, instead, the beam is idealized as a single degree of freedom system. The effects of strain rate, which are of paramount relevance in blast problems, are taken into consideration by introducing time-variable coefficients into the equations of motion derived from the two models. The latter are employed to assess the time-history of the maximum deflection of a simply supported beam subjected to a uniformly distributed blast load. By comparing the theoretical results with some experimental findings available in literature and with the solution obtained from a commercial finite element software, it is found that the first approach is capable of accurately evaluating the maximum deflection of the beam at failure; on the other hand, the second approach provides a less precise prediction, however it is simpler to implement in practice because it requires less computational effort

The problem of free vibrations of the Timoshenko beam model has been addressed in the first part of this paper. A careful analysis of the governing equations has shown that the vibration spectrum consists of two parts, separated by a transition frequency, which, depending on the applied boundary conditions, might be itself part of the spectrum. Here, as an extension, the case of a doubly clamped beam is considered. For both parts of the spectrum the values of natural frequencies are computed and the expressions of eigenmodes are provided: this allows to acknowledge that the nature of vibration modes changes when moving across the transition frequency. This case is a meaningful example of more general ones, where the wave-numbers equation cannot be written in a factorized form and hence must be solved by general root-finding methods for non-linear transcendental equations. These theoretical results can be used as further benchmarks for assessing the correctness of the numerical values provided by several numerical techniques, e.g. finite element models.

No abstract

Many of modern life activities involve the risk of fire, explosions, and impacts. In addition, natural extreme events are becoming more and more common. Thus, robustness, the ability to avoid disproportionate collapse due to an initial damage, and resilience, the ability to adapt to and recover from the effects of changing external conditions, represent two important characteristics of current structures and infrastructures. Their definitions are reviewed in this paper with the aim of sorting and describing the different approaches proposed in the literature and in the international standards. A simple example is also analysed in order to compare different methods.