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## ‣ Buckling and post-buckling of extensible rods revisited: A multiple-scale solution

Mazzilli, Carlos Eduardo Nigro
Fonte: PERGAMON-ELSEVIER SCIENCE LTD Publicador: PERGAMON-ELSEVIER SCIENCE LTD
Tipo: Artigo de Revista Científica
Português
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An exact non-linear formulation of the equilibrium of elastic prismatic rods subjected to compression and planar bending is presented, electing as primary displacement variable the cross-section rotations and taking into account the axis extensibility. Such a formulation proves to be sufficiently general to encompass any boundary condition. The evaluation of critical loads for the five classical Euler buckling cases is pursued, allowing for the assessment of the axis extensibility effect. From the quantitative viewpoint, it is seen that such an influence is negligible for very slender bars, but it dramatically increases as the slenderness ratio decreases. From the qualitative viewpoint, its effect is that there are not infinite critical loads, as foreseen by the classical inextensible theory. The method of multiple (spatial) scales is used to survey the post-buckling regime for the five classical Euler buckling cases, with remarkable success, since very small deviations were observed with respect to results obtained via numerical integration of the exact equation of equilibrium, even when loads much higher than the critical ones were considered. Although known beforehand that such classical Euler buckling cases are imperfection insensitive...

## ‣ Numerical simulation of drop impact and jet buckling problems using the eXtended Pom-Pom model

Oishi, C. M.; Martins, F. P.; Tome, M. F.; Alves, M. A.
Fonte: ELSEVIER SCIENCE BV; AMSTERDAM Publicador: ELSEVIER SCIENCE BV; AMSTERDAM
Tipo: Artigo de Revista Científica
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This work presents numerical simulations of two fluid flow problems involving moving free surfaces: the impacting drop and fluid jet buckling. The viscoelastic model used in these simulations is the eXtended Pom-Pom (XPP) model. To validate the code, numerical predictions of the drop impact problem for Newtonian and Oldroyd-B fluids are presented and compared with other methods. In particular, a benchmark on numerical simulations for a XPP drop impacting on a rigid plate is performed for a wide range of the relevant parameters. Finally, to provide an additional application of free surface flows of XPP fluids, the viscous jet buckling problem is simulated and discussed. (C) 2011 Elsevier B.V. All rights reserved.; CNPq (Conselho Nacional de Desenvolvimento Cientifico e Tecnologico) [477858/2009-0, 305447/2010-6, 302631/2010-0, 471793/2010-8]; Conselho Nacional de Desenvolvimento Cientifico e Tecnologico (CNPq); Fundacao de Amparo a Pesquisa do Estado de Sao Paulo (FAPESP); FAPESP (Fundacao de Amparo a pesquisa do Estado de Sao Paulo) [2009/15892-9]; CAPES; CAPES [BEX 2844/10-9]; FCT; FCT; FEDER [PTDC/EME-MFE/114322/2009]; FEDER

## ‣ Avaliação crítica de engenharia em dutos submersos sujeitos a flambagem lateral controlada.; Engineering critical assessment of submarine pipelines subjected to controlled lateral buckling.

Garmbis, Alexandre Galiani
Fonte: Biblioteca Digitais de Teses e Dissertações da USP Publicador: Biblioteca Digitais de Teses e Dissertações da USP
Tipo: Dissertação de Mestrado Formato: application/pdf
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## ‣ Structural stability concepts in medieval and renaissance mechanics

Godoy,Luis A.
Fonte: Associação Brasileira de Ciências Mecânicas Publicador: Associação Brasileira de Ciências Mecânicas
Tipo: Artigo de Revista Científica Formato: text/html
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The identification of the origins of what we now call the theory of elastic stability is not an easy task. Most authors trace the origins to the pioneering work of Leonhard Euler in 1744, and some shift this origin to the experimental works of Petrus van Musschenbroek in 1729. However, other contemporary authors interested in the history of the discipline postulate that the works of Medieval and Renaissance scholars should be considered as the true sources of the buckling studies performed in the XVIII Century. This paper reports a historical research based on the original works of Al-Khazini, Jordanus de Nemore, Leonardo da Vinci, and Marini Merssene, in order to discuss what kind of Aknowledge they had about the topics of stability and lateral deflections of columns under axial loads. Our investigation shows that there were observations of the phenomenon considered, but those observations were not translated into a deeper understanding of the phenomenon, so that the causes of this efect or the role of strength on the response were not considered. Leonardo was closer than others in his understanding of the nature of the problem and produced some tentative rules of behavior; however, those were only documented in private writings and did not make an impact in his contemporaries or even 100 years later. We postulate that there was a continuity of problems between medieval authors and those who lived in the XVIII Century...

## ‣ Thermal effects on the stability of circular graphene sheets via nonlocal continuum mechanics

Asemi,Saeid Reza; Farajpour,Ali; Borghei,Mehdi; Hassani,Amir Hessam
Fonte: Associação Brasileira de Ciências Mecânicas Publicador: Associação Brasileira de Ciências Mecânicas
Tipo: Artigo de Revista Científica Formato: text/html
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Recently, graphene sheets have shown significant potential for environmental engineering applications such as wastewater treatment. Different non-classical theories have been used for modeling of such nano-sized systems to take account of the effect of small length scale. Among all size-dependent theories, the nonlocal elasticity theory has been commonly used to examine the stability of nano-sized structures. Some research works have been reported about the mechanical behavior of rectangular nanoplates with the consideration of thermal effects. However, in comparison with the rectangular graphene sheets, research works about the nanoplates of circular shape are very limited, especially for the buckling properties with thermal effects. Hence, in this paper, an axisymmetric buckling analysis of circular single-layered graphene sheets (SLGS) is presented by decoupling the nonlocal equations of Eringen theory. Constitutive relations are modified to describe the nonlocal effects. The governing equations are derived using equilibrium equations of the circular plate in polar coordinates. Numerical solutions for buckling loads are computed using Galerkin method. It is shown that nonlocal effects play an important role in the buckling of circular nanoplates. The effects of the small scale on the buckling loads considering various parameters such as the radius of the plate...

## ‣ Creep buckling of spherical shells.

Xirouchakis, Paul Christos
Fonte: Massachusetts Institute of Technology Publicador: Massachusetts Institute of Technology
Tipo: Tese de Doutorado Formato: 391 leaves; 13961993 bytes; 13961752 bytes; application/pdf; application/pdf
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Thesis. 1978. Ph.D.--Massachusetts Institute of Technology. Dept. of Ocean Engineering.; MICROFICHE COPY AVAILABLE IN ARCHIVES AND ENGINEERING.; Includes bibliographical references.

## ‣ Buckling distortion of thin aluminum plates during welding.

Pattee, Frank Michael
Fonte: Massachusetts Institute of Technology Publicador: Massachusetts Institute of Technology
Tipo: Tese de Doutorado Formato: 214 leaves; 15266040 bytes; 15265797 bytes; application/pdf; application/pdf
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Thesis. 1975. M.S.--Massachusetts Institute of Technology. Dept. of Ocean Engineering.; Includes bibliographical references.

## ‣ 13.10J Structural Mechanics, Fall 2002; Structural Mechanics

Patrikalakis, N. M. (Nicholas M.); Connor, J. J. (Jerome J.)
Fonte: MIT - Massachusetts Institute of Technology Publicador: MIT - Massachusetts Institute of Technology
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Fundamental concepts of structural mechanics with applications to marine, civil, and mechanical structures. Residual stresses. Thermal effects. Analysis of beams, columns, tensioned beams, trusses, frames, arches, cables, and shafts of general shape and material, including composites. Elastic buckling of columns. Exact and approximate methods, energy methods, principle of virtual work, introduction to computational structural mechanics. Examples from civil, mechanical, offshore, and ship structures.

## ‣ Geometric optimization based on the constructal design of perforated thin plates subject to buckling

Rocha, Luiz Alberto Oliveira; Real, Mauro de Vasconcellos; Correia, Anderson Luis Garcia; Vaz, Joaquim; Santos, Elizaldo Domingues dos; Isoldi, Liércio André
Tipo: Artigo de Revista Científica
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Elastic buckling is an instability phenomenon that can occur if a slender and thin-walled plate is subjected to axial compressive load. It is well known that the presence of holes in structural plate elements is almost inevitable in inspection, maintenance, and service purposes, or to reduce the structural weight. In this paper constructal design was employed to optimize the geometry of thin perforated plates submitted to elastic buckling. Simply supported rectangular perforated plates were analyzed with three different shapes of centered holes: elliptical, rectangular, and diamond. The purpose was to obtain the optimal geometry that maximizes the critical buckling load. The ratio between the height and length of the plate was kept constant, while the ratio between the characteristic dimensions of the holes was optimized for several hole volume fractions (φ). A finite-element model was used to assess the plate buckling load, and the Lanczos method was applied to the solution of the corresponding eigenvalue problem. When φ ≤ 0.20 the optimum geometry is the diamond hole, reaching maximum buckling loads around 80.0,21.5, and 17.4% higher than a plate without perforation and plates with elliptical and rectangular holes, respectively. For intermediate and higher values of φ...

## ‣ Numerical simulation and constructal theory applied for geometric optimization of thin perforated plates subject to elastic buckling

Correia, Anderson Luis Garcia; Helbig, Daniel; Real, Mauro de Vasconcellos; Santos, Elizaldo Domingues dos; Isoldi, Liércio André
Tipo: Conferência ou Objeto de Conferência
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Many elements in engineering are formed by thin plates. Hulls and decks of ships are examples of application. These elements can have holes that serve as inspection port, access or even to weight reduction. The presence of holes causes a redistribution of the membrane stresses in the plate, significantly altering their stability. In this paper the Bejan’s Constructal Theory was employed to discover the best geometry of thin perforated plates submitted to elastic buckling phenomenon. To study this behavior simply supported rectangular plates with a centered elliptical perforation were analyzed. The purpose was to obtain the optimal geometry which maximizes the critical buckling load. For this, the degrees of freedom H/L (ratio between width and length of the plate) and H0/L0 (ratio between the characteristic dimensions of the hole) were varied. Moreover, different values of hole volume fraction ϕ (ratio between the perforation volume and the massive plate volume) were also investigated. A computational modeling, based on the Finite Element Method (FEM), was used for assessing the plate buckling load. The results showed that Constructal Design can be employed not only in the heat transfer and fluid flow problems, but also to define the best shapes in solid mechanics problems.

## ‣ Buckling and deformation of heated conical shells.

Chang, Lu-Kang, 1938-
Tipo: Artigo de Revista Científica Formato: viii, 151 leaves ill. : ; 28 cm.
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(Thesis) Thesis--University of Florida.; (Bibliography) Bibliography: leaves 148-150.; Manuscript copy.; Vita.; (Statement of Responsibility) Lu-Kang Chang.

## ‣ Projeto mecânico de biela automotiva baseado em otimização estrutural; Automotive connecting rod mechanical design based on structural optimization

Rafael Augusto de Lima e Silva
Fonte: Biblioteca Digital da Unicamp Publicador: Biblioteca Digital da Unicamp
Tipo: Dissertação de Mestrado Formato: application/pdf
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## ‣ New approach to Monte Carlo calculation of buckling of supercoiled DNA loops

Yang, Zhang
Tipo: Artigo de Revista Científica
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The short supercoiled circular DNA molecules are shown to be glassy systems and canonical Metropolis Monte Carlo simulations of the systems tend to get stuck in local metastable energy basins. A novel Monte Carlo algorithm is developed to alleviate the problem of ergodicity breaking'' of the glassy systems, in which the Markov process is driven by an explicitly analytic weight factor with enhanced probability in both low- and high-energy regions. To characterize the degree of puckering of the supercoiled DNA loops, a new quantity of aplanarity is introduced as the shortest principal axis of configurational ellipsoid of DNA. With the suggested Monte Carlo method, the quantitative correlation between supercoiling degree and buckling of DNA is attained. With supercoiling stress increasing, the conformational transition from a circle to mono-, diplo- or triple interwound superhelical structure will take place in a successive but decreasingly abrupt mode.; Comment: 4 pages, 3 PS figures, to appear at Phys. Rev. E as a Rapid Communication

## ‣ Bifurcations in the optimal elastic foundation for a buckling column

Rayneau-Kirkhope, Daniel; Farr, Robert; Ding, K.; Mao, Yong
Tipo: Artigo de Revista Científica
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We investigate the buckling under compression of a slender beam with a distributed lateral elastic support, for which there is an associated cost. For a given cost, we study the optimal choice of support to protect against Euler buckling. We show that with only weak lateral support, the optimum distribution is a delta-function at the centre of the beam. When more support is allowed, we find numerically that the optimal distribution undergoes a series of bifurcations. We obtain analytical expressions for the buckling load around the first bifurcation point and corresponding expansions for the optimal position of support. Our theoretical predictions, including the critical exponent of the bifurcation, are confirmed by computer simulations.; Comment: 7 pages, 8 figures. Accepted by Physics Letters A

## ‣ Controlled Buckling and Crumpling of Nanoparticle-Coated Droplets

Datta, Sujit S.; Shum, Ho Cheung; Weitz, David A.
Tipo: Artigo de Revista Científica
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We introduce a new experimental approach to study the structural transitions of large numbers of nanoparticle-coated droplets as their volume is reduced. We use an emulsion system where the dispersed phase is slightly soluble in the continuous phase. By adding a fixed amount of unsaturated continuous phase, the volume of the droplets can be controllably reduced, causing them to buckle or crumple, thereby becoming nonspherical. The resultant morphologies depend both on the extent of volume reduction and the average droplet size. The buckling and crumpling behavior implies that the droplet surfaces are solid.; Comment: Supporting information (pictures, text, movie) available free of charge online at http://pubs.acs.org/doi/abs/10.1021/la103874z

## ‣ Finite-temperature buckling of an extensible rod

Bedi, Deshpreet Singh; Mao, Xiaoming
Tipo: Artigo de Revista Científica
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Thermal fluctuations can play an important role in the buckling of elastic objects at small scales, such as polymers or nanotubes. In this paper, we study the finite-temperature buckling transition of an extensible rod by analyzing fluctuation corrections to the elasticity of the rod. We find that, in both two and three dimensions, thermal fluctuations delay the buckling transition, and near the transition, there is a critical regime in which fluctuations are prominent and make a contribution to the effective force that is of order $\sqrt{T}$. We verify our theoretical prediction of the phase diagram with Monte Carlo simulations.; Comment: 14 pages, 5 figures

## ‣ Buckling, Fluctuations and Collapse in Semiflexible Polyelectrolytes

Hansen, Per Lyngs; Podgornik, Rudi; Svenšek, Daniel; Parsegian, V. Adrian
Tipo: Artigo de Revista Científica
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We present a systematic statistical mechanical analysis of the conformational properties of a stiff polyelectrolyte chain with intrachain attractions that are due to counterion correlations. We show that the mean-field solution corresponds to an Euler-like buckling instability. The effect of the conformational fluctuations on the buckling instability is investigated, first, qualitatively, within the harmonic (semiclassical'') theory, then, systematically, within a 1/d-expansion, where d denotes the dimension of embedding space. Within the semiclassical'' approximation, we predict that the effect of fluctuations is to renormalize the effective persistence length to smaller values, but not to change the nature of the mean-field (i.e., buckling) behavior. Based on the 1/d-expansion we are, however, led to conclude that thermal fluctuations are responsible for a change of the buckling behavior which is turned into a polymer collapse. A phase diagram is constructed in which a sequence of collapse transitions terminates at a buckling instability that occurs at a place that varies with the magnitude of the bare persistence length of the polymer chain, as well as with the strength and range of the attractive potential.; Comment: 30 pages + 4 eps figures

## ‣ Intercalation and buckling instability of DNA linker within locked chromatin fiber

Victor, Jean-Marc; Ben-Haïm, Eli; Lesne, Annick
Tipo: Artigo de Revista Científica
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The chromatin fiber is a complex of DNA and specific proteins called histones forming the first structural level of organization of eukaryotic chromosomes. In tightly organized chromatin fibers, the short segments of naked DNA linking the nucleosomes are strongly end constrained. Longitudinal thermal fluctuations in these linkers allow intercalative mode of protein binding. We show that mechanical constraints generated in the first stage of the binding process induce linker DNA buckling; buckling in turn modifies the binding energies and activation barriers and creates a force of decondensation at the chromatin fiber level. The unique structure and properties of DNA thus yield a novel physical mechanism of buckling instability that might play a key role in the regulation of gene expression.; Comment: 5 pages, 4 figures. To appear in Physical Review E (Rapid Communication)

## ‣ Anomalous Buckling of Charged Rods

Zandi, Roya; Golestanian, Ramin; Rudnick, Joseph
Tipo: Artigo de Revista Científica
Unscreened electrostatic interactions exert a profound effect on the onset of the buckling instability of a charged rod. When this interaction is unscreened, the threshold value of the compressional force needed to induce buckling is independent of rod length for sufficiently long rods. In the case of rods of intermediate length, the critical buckling force crosses over from the classic inverse-square length dependence to asymptotic length-independent form with increasing rod length. It is suggested that this effect might lead to the possibility of the electromechanical'' stiffening of nanotubes, which would allow relatively long segments of them to be used as atomic force probes.; Comment: 4 pages, 4 figures