1,720,965 research outputs found
Shear deformable beams in contact with an elastic half-plane
Get PDFThe present work deals with the contact problem of a Timoshenko beam bonded to an elastic semi-infinite substrate under different loading conditions. The analysis allows investigating the effects induced by shear compliance of the beam, the stress intensity factors ad the beam edges as well as the singular nature of the interfacial stresses
Advancing contact between a rigid pin and a FGM circular beam with clearance
No full textThe progressive and frictionless contact problem between a rigid circular pin and a circular beam with a uniform cross-section made of elastic functionally graded material (FGM) is investigated under clearance-fit conditions. The stress and displacement fields in the FGM circular beam are taken from the general solution for plane elastic problems involving FGMs in polar coordinates, analogous to Mitchell’s solution for homogeneous isotropic materials. The frictionless contact conditions yield a set of dual series equations similar to those obtained for a homogeneous and isotropic elastic circular beam, then reduced to a linear system of infinite equations, which is solved by truncation. By assuming discrete values of the contact angle, the corresponding stress and displacement fields within the lug are derived and, in turn, the resultant load acting on the rigid pin is assessed. The new analytical results are then validated against finite element predictions and a satisfactory agreement is observed for typical geometries and various material grading parameters. The present findings can assist mechanical engineers in optimally designing innovative pinned connections and improving their load-bearing capacity by exploiting the advantages of FGMs
The Bending Theory of Fully Nonlinear Beams
No full textThis book presents the bending theory of hyperelastic beams in the context of finite elasticity. The main difficulties in addressing this issue are due to its fully nonlinear framework, which makes no assumptions regarding the size of the deformation and displacement fields. Despite the complexity of its mathematical formulation, the inflexion problem of nonlinear beams is frequently used in practice, and has numerous applications in the industrial, mechanical and civil sectors. Adopting a semi-inverse approach, the book formulates a three-dimensional kinematic model in which the longitudinal bending is accompanied by the transversal deformation of cross-sections. The results provided by the theoretical model are subsequently compared with those of numerical and experimental analyses. The numerical analysis is based on the finite element method (FEM), whereas a test equipment prototype was designed and fabricated for the experimental analysis. The experimental data was acquired using digital image correlation (DIC) instrumentation. These two further analyses serve to confirm the hypotheses underlying the theoretical model. In the book’s closing section, the analysis is generalized to the case of variable bending moment. The governing equations then take the form of a coupled system of three equations in integral form, which can be applied to a very wide class of equilibrium problems for nonlinear beams
Large Deformations and Stability of the Two-Bar Truss Under Vertical Loads
No full textAnalytical formulations for the static equilibrium of truss structures are often based on concepts of linear elasticity. Geometric nonlinearities are taken into account, but the nonlinear constitutive behavior of the material is not considered. However, the assumption of linear elastic material is not consistent with the response of solids subjected to large deformations. In light of this, accurate models must take into account both geometric and constitutive nonlinearities. In the present work, we investigate the problem of the von Mises (or two-bar) truss subjected to a vertical load. The bars of the truss are composed of rubber so as to observe large displacements and deformations. We propose a theoretical model that is entirely developed in three-dimensional nonlinear elasticity. A compressible Mooney-Rivlin law is employed for the constitutive behavior of the rubber. Experimental tests on the von Mises truss subjected to a vertical load are carried out. Snap-through is observed and good agreement is found with the analytical predictions. Finally, a simple formulation to predict the critical Euler buckling load is presented and validated through experimental observation
Snap-through and Eulerian buckling of the bi-stable von Mises truss in nonlinear elasticity: A theoretical, numerical and experimental investigation
No full textIn this paper, the equilibrium and stability of the von Mises truss subjected to a vertical load is analyzed from theoretical, numerical and experimental points of view. The bars of the truss are composed of a rubber material, so that large deformations can be observed. The analytical model of the truss is developed in the fully nonlinear context of finite elasticity and the constitutive behavior of the rubber is modeled using a Mooney–Rivlin law. The constitutive parameters are identified by means of a genetic algorithm that fits experimental data from uniaxial tests on rubber specimens. The numerical analysis is performed through a finite element (FE) model. Differently from the analytical and FE simulations that can be found in the literature, the models presented in this work are entirely developed in three-dimensional finite elasticity. Experiments are conducted with a device that allows the rubber specimens to undergo large axial deformations. For the first time, snap-through is observed experimentally on rubber materials, showing good agreement with both theoretical and numerical results. Further insights on Eulerian buckling of the rubber specimens and its interaction with the snap-through are given. A simple formulation to determine the critical load of the truss is presented and its accuracy is validated through experimental observation. Comparisons with a linear elasticity based approach demonstrate
that an accurate prediction of snap-through and Eulerian buckling requires nonlinear formulations, such as the ones proposed in this work
Finite Torsion of Compressible Circular Cylinders: An Approximate Solution
No full textThis paper deals with the equilibrium problem of circular cylinders under finite torsion. A three-dimensional kinematic model, where the large twisting of the cylinder is accompanied by transverse contraction and longitudinal extension, is formulated. Following a semi-inverse approach, the displacement field prescribed by the above kinematic model contains as unknowns the longitudinal displacement, the rigid rotation and the transverse stretch of cross sections. To simplify the mathematical formulation, the transverse stretch is assumed to be constant, as it radially undergoes very low variations. This hypothesis produces some approximations in the field equations, but the equilibrium solution obtained is however characterized by a satisfactory accuracy, as shown by the comparisons performed using the numerical techniques of the Finite Element Method (FEM). A Lagrangian analysis is performed and the compressible Mooney-Rivlin law is assumed for the stored energy function. Once evaluated the Piola-Kirchhoff stresses, the unknowns are determined by imposing the equilibrium conditions and the boundary conditions. For the end base of the cylinder two
different boundary conditions have been considered, according to which the longitudinal translation of this surface is allowed or prevented. Once the kinematic unknowns have been determined, explicit formulae for displacements, stretches and stresses are provided, which show the role of the geometric and constitutive parameters, as well as of the twisting angle. The results provided by the proposed solution are shown by a series of graphs. The same torsion problem has been addressed with FEM. A very good agreement was found between the results obtained with the two different analyses. Finally, the nonlinear torsion problem was linearized by introducing the hypothesis of smallness of the displacement and deformation fields. With this linearization, the classical solution for the infinitesimal torsion problem was fully retrieved
Bending device and anticlastic surface measurement of solids under large deformations and displacements
No full textLarge bending of elastic bodies gives rise to significant transverse effects. Based on a recent theoretical model in the context of finite elasticity, both the longitudinal and anticlastic curvatures in bent solids under large deformation and displacement can be accurately assessed. In order to experimentally investigate the anticlastic deformation induced by large inflexion and corroborate the theoretical predictions, a properly designed mechanical bending device is here proposed. By imposing a rotation at the ends of the sample, both the longitudinal and anticlastic curvatures are measured by DIC (digital image correlation) monitoring instrumentation and compared with the theoretical results, finding good agreement. Compact analytical formulae for assessing the radii of curvature within the thickness of the sample are provided. Conversely to existing studies of the anticlastic surface induced by infinitesimal bending, the present analysis takes into account large through-to-thickness curvature variations, whose knowledg can plays a key role for a wide class of mechanical applications
Going Beyond Counting First Authors in Author Co-citation Analysis
Get PDFThe 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
Get PDF“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
- …
