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General-Purpose Finite Element-Based Path Following of Nonlinear Dynamical Systems
No full textThis paper summarizes ongoing efforts toward an advanced integration of algorithmsfrom the finite-element and bifurcation domains, thus enabling an accurate and effective unfoldingof the bifurcation and post-bifurcation scenarios of nonautonomous PDEs typical of nonlinearstructural dynamics including multi-physics applications. The developed tools rely on a nonlinearfinite-element (FE) formulation coupled with a MATLAB-based platform for continuation of periodicorbits called COCO.The paper demonstrates the versatility of the approach through a comparison between the predictionsof the frequency-response curves for a hinged-hinged nonlinear beam subject to a primaryresonanceharmonic transverse load using an in-house FE discretization of the approximate Mettlermodel and using a FE discretization of the special Cosserat model of rods implemented in COMSOLMultiphysics. As the latter accounts for the full nonlinearities and extensional/flexural/shearing deformations,it is expected to yield physically more realistic results. As demonstrated in this paper, italso allows for a straightforward analysis of different sets of boundary conditions without the needfor further simplifications or model reductions
Nonlinear finite element-based path following of periodic solutions
No full textA computational framework is proposed to path follow the periodic solutions of nonlinear spatially continuous systems and more general coupled multiphysics problems represented by systems of partial differential equations with time-dependent excitations. The set of PDEs is cast in first order differential form (in time) ?u = f(u; s; t; c) where u(s; t) is the vector collecting all state variables including the velocities/time rates, s is a space co-ordinate (here, one-dimensional systems are considered without lack of generality for the space dependence) and t denotes time. The vector field f depends, in general, not only on the classical state variables (such as positions and velocities) but also on the space gradients of the leading unknowns. The space gradients are introduced as part of the state variables. This is justified by the mathematical and computational requirements on the continuity in space up to the proper differential order of the space gradients associated with the unknown position vector field. The path following procedure employs, for the computation of the periodic solutions, only the evaluation of the vector field f. This part of the path following procedure within the proposed combined scheme was formerly implemented by Dankowicz and co-workers in a MATLAB software package called COCO. The here proposed procedure seeks to discretize the space dependence of the variables using finite elements based on Lagrangian polynomials which leads to a discrete form of the vector field f: A concurrent bifurcation analysis is carried out by calculating the eigenvalues of the monodromy matrix. A hinged-hinged nonlinear beam subject to a primary-resonance harmonic transverse load or to a parametric-resonance horizontal end displacement is considered as a case study. Some primary-resonance frequency-response curves are calculated along with their stability to assess the convergence of the discretization scheme. The frequency-response curves are shown to be in close agreement with those calculated by direct integration of the PDEs through the FE software called COMSOL Multiphysics. Besides primary-resonance direct forcing conditions, also parametric forcing causing the principal parametric resonance of the lowest two bending modes is considered through construction of the associated transition curves. The proposed approach integrates algorithms from the finite element and bifurcation domains thus enabling an accurate and effective unfolding of the bifurcation and post-bifurcation scenarios of nonautonomous PDEs with the underlying structures. Copyright © 2011 by ASME
Coupling FEM With Parameter Continuation for Analysis of Bifurcations of Periodic Responses in Nonlinear Structures
No full textA computational framework is proposed to perform parameter continuation of periodic solutions of nonlinear, distributed-parameter systems represented by partial differential equations with time-dependent coefficients and excitations. The path-following procedure, encoded in the general-purpose MATLAB-based computational continuation core (referred to below as COCO), employs only the evaluation of the vector field of an appropriate spatial discretization; for example as formulated through an explicit finite-element discretization or through reliance on a black-box discretization. An original contribution of this paper is a systematic treatment of the coupling of COCO with COMSOL MULTIPHYSICS, demonstrating the great flexibility afforded by this computational framework. COMSOL MULTIPHYSICS provides embedded discretization algorithms capable of accommodating a great variety of mechanical/physical assumptions and MULTIPHYSICS interactions. Within this framework, it is shown that a concurrent bifurcation analysis may be carried out together with parameter continuation of the corresponding monodromy matrices. As a case study, we consider a nonlinear beam, subject to a harmonic, transverse direct excitation for two different sets of boundary conditions and demonstrate how the proposed approach may be able to generate results for a variety of structural models with great ease. The numerical results include primary-resonance, frequency-response curves together with their stability and two-parameter analysis of multistability regions bounded by the loci of fold bifurcations that occur along the resonance curves. In addition, the results of COMSOL are validated for the Mettler model of slender beams against an in-house constructed finite-element discretization scheme, the convergence of which is assessed for increasing number of finite elements
Damage model of carbon nanotubes debonding in nanocomposites
No full textThe progressive interfacial debonding between aligned carbon nanotubes and the hosting matrix of a nanocomposite in the direction normal to the CNTs axis is described by means of an equivalent constitutive model with evolutionary damage. The Eshelby-Mori-Tanaka theory is used to describe the macroscopic mechanical response of the nanocomposite for a given volume fraction of the different phases (i.e., perfectly bonded and fully debonded CNTs). The novelty of this work is the proposition of a new thermodynamically consistent phase flow law that describes the cumulative progression of debonding derived from the Weibull statistics. Monotonic and cyclic uniform strain histories are considered to investigate the nanocomposite response features such as the stress-strain softening hysteretic cycles, the progressive degradation of the elastic moduli, and the dissipated energy
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Variations on the Author
Full text link“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
Appropriate Similarity Measures for Author Cocitation Analysis
Full text linkWe provide a number of new insights into the methodological discussion about author cocitation analysis. We first argue that the use of the Pearson correlation for measuring the similarity between authors’ cocitation profiles is not very satisfactory. We then discuss what kind of similarity measures may be used as an alternative to the Pearson correlation. We consider three similarity measures in particular. One is the well-known cosine. The other two similarity measures have not been used before in the bibliometric literature. Finally, we show by means of an example that our findings have a high practical relevance.information science;Pearson correlation;cosine;similarity measure;author cocitation analysis
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