58 research outputs found
A targeted review on large deformations of planar elastic beams: extensibility, distributed loads, buckling and post-buckling
No full textIn this paper, we give a targeted review of the state of the art in the study of planar elastic beams in large deformations, also in the presence of geometric nonlinearities. The main scope of this work is to present the different methods of analysis available for describing the possible equilibrium forms and the motions of elastic beams. For the sake of completeness, we start by giving an overview of the nonlinear theories introduced for approaching this argument and then we account for the variational principles and deformation energies introduced for modelling beams undergoing large deformations and displacements. We then consider different kinds of loads treated in the literature and the corresponding induced beam deformations. We conclude by accounting for the available analysis for stability and some considerations about problems where live loads are applied, as well as by describing some relevant numerical methods of use in the applications we have in mind. The selection criterion for the reviewed papers is dictated by the need to study large deformations and the dynamics of pantographic sheets. (Large deformations of planar extensible beams and pantographic lattices: heuristic homogenization, experimental and numerical examples of equilibrium. Proc R Soc A 2016; 472(2185): 20150790), dell’Isola et al. (Designing a light fabric metamaterial being highly macroscopically tough under directional extension: first experimental evidence. Z Angew Math Phys 2015; 66(6): 3473–3498), Turco et al. (Hencky-type discrete model for pantographic structures: numerical comparison with second gradient continuum models. Z Angew Math Phys 2016; 67(4): 1–28)]
Influence of the characteristics of isolation and mitigation devices on the response of single-degree-of-freedom vibro-impact systems with two-sided bumpers and gaps via shaking table tests
No full textDuring strong earthquakes, structural pounding may occur between structures (buildings, bridges, strategic facilities, critical equipment, etc.) and the surrounding moat wall because of the limited separation distance and the deformations of the isolator. An arrangement that favors the solution of this problem is the interposition of shock absorbers. Thus, the influence of geometrical and mechanical characteristics of isolation and mitigation devices on nonlinear, nonsmooth response of vibro-impact systems is experimentally investigated in this paper on the basis of a laboratory campaign of experimental tests. Shaking table tests were carried out under a harmonic excitation in order to investigate two different configurations: the absence and the presence of bumpers. Three different values of the table acceleration peak were applied, four different amplitude values of the total gap between mass and bumpers were considered, and also four different types of bumpers were employed; moreover, two problems were addressed, namely, control of excessive displacements and control of excessive accelerations, and hence, two types of normalization were adopted in order to better interpret experimental results. Suitable choices of pairs of bumpers and gaps were suggested as a trade-off between conflicting objectives. Furthermore, a numerical model was proposed, and its governing parameters identified in order to simulate the experimental results
Scenarios in the experimental response of a vibro-impact single-degree-of-freedom system and numerical simulations
No full textIn this paper, possible scenarios within the experimental dynamic response of a vibro-impact single-degree-of-freedom system, symmetrically constrained by deformable and dissipative bumpers, were identified and described. The different scenarios were obtained varying selected parameters, namely peak table acceleration A , amplitude of the total gap between mass and bumpers G and bumper’s stiffness B. Subsequently, using a Simplified Nonlinear Model results in good agreement with the experimental outcomes were obtained, although the model includes only the nonlinearities due to clearance existence and impact occurrence. Further numerical analysis highlighted other scenarios that can be obtained for values of the parameters not considered in the experimental laboratory campaign. Finally, to attempt a generalization of the results, suitable dimensionless parameters were introduced
Soft impact dynamics of deformable bodies
No full textSystems constituted by impacting beams and rods of non-negligible mass are often encountered in many applications of engineering practice. The impact between two rigid bodies is an intrinsically indetermi- nate problem due to the arbitrariness of the velocities after the instantaneous impact and implicates an infinite value of the contact force. The arbitrariness of after-impact velocities is solved by releasing the impenetrability condition as an internal constraint of the bodies and by allowing for elastic deformations at contact during an impact of finite duration. In this paper, the latter goal is achieved by interposing a concentrate spring between a beam and a rod at their contact point, simulating the deformability of impacting bodies at the interaction zones. A reliable and convenient method for determining impact forces is also presented. An example of engineering interest is carried out: a flexible beam that impacts on an axially deformable strut. The solution of motion under a harmonic excitation of the beam built-in base is found in terms of transverse and axial displacements of the beam and rod, respectively, by superimposition of a finite number of modal contributions. Numerical investigations are performed in order to examine the influence of the rigidity of the contact spring and of the ratio between the first natural frequencies of the beam and the rod, respectively, on the system response, namely impact velocity, maximum displacement, spring stretching and contact force. Impact velocity diagrams, non- linear resonance curves and phase portraits are presented to determine regions of periodic motion with impacts and the appearance of chaotic solutions, and parameter ranges where the functionality of the non-structural element is at ris
Biaxial bias extension test for pantographic sheets
No full textPantographic fabrics are emerging in the literature as promising metamaterials. They are made up of two orthogonal families of fibers connected at their intersection points by pivots. Fibers are supposed to be straight in the reference configuration and to store energy while undergoing extension and bending deformations only. Pivots, which oppose to relative rotations of fibers, are supposed to store energy when undergoing torsion, thus to confer shear stiffness at macro level. In the paper we present some new numerical simulations in which a 2D planar non linear second gradient continuum model is employed, derived by a heuristic homogenization procedure (dell’Isola et al. 2016) and aimed at describing the mechanical behaviour inherited by its micro-structure. A bi-axial extension test has been studied. We show that, similarly to the uni-axial bias extension test, the internal stored energy is localized at the corners of the clamping areas, whereas in the central area the internal stored energy distributes almost uniformly. Unlike to the uni-axial test, due to symmetry reasons, shear deformation in the central area of the domain vanishes
Introductory remarks about the Volume II of the complete works of Gabrio Piola
No full textIn this Volume II of the translations into English of the works by Gabrio Piola, we begin from the true first work written by the young Gabrio before 1824, when he was less than 30 years old. The content of the work Sull’applicazione de’ principj della meccanica analitica del Lagrange ai principali problemi. Memoria di Gabrio Piola presentata al concorso del premio e coronata dall’I.R. Istituto di Scienze, ecc. nella solennità del giorno 4 ottobre 1824, Milano, Imp. Regia stamperia, 1825, submitted to respond to a research program proposed by the I.R. Istituto on 4th October 1822, is in some aspects very modern and astonishingly topical
Prediction of micromotion initiation of an implanted femur under physiological loads and constraints using the finite element method
No full textIn cementless total hip replacement surgery the conditions for micromotion initiation at the bone–stem interface and the role of stair climbing versus gait in promoting incipient slipping deserve attention. The goal of the present paper was to propose a finite element approach for analysing the structural behaviour of hip joint prostheses under physiological loadings and boundary conditions, which allows the prediction of micromotion initiation with low computational effort. In this paper, three-dimensional (3D) finite element analyses were performed of intact and implanted human femurs in order to address the above-mentioned problems. Accurate finite element models based on computed tomography images of a human femur were employed; tetrahedral elements were used to construct the models and the contact options of a full bond between the femoral bone and stem were also used. The shear strains at the contact between femoral bone and stem were evaluated. Two loading cases, namely walking and stair climbing, were applied to investigate the effect of different loading conditions on the shear strain patterns. Shear strains in the z direction can be reasonably considered a significant stimulus of slip initiation or fibrous tissue formation or both at the bone–stem interface, whereas shear strains in the x–y plane can be assumed to be a sensible measurement of the tendency to implant–bone micromotion under torsional loads. Comparisons with other studies are complicated by the difference in the methods and testing conditions used. If mobilization is to be initiated, rotational displacements at the interface should be sensible and significant parameters, i.e. the material, should be distorted to some extent. Thus, for a particular point on the bone–metal interface, the maximum shear strain in any direction within the interface plane will indicate the likelihood of slippage initiation at that point. The different femur states (intact and implanted) and loading conditions (walking and stair climbing) are compared. The stair-climbing loads resulted in the highest strains observed under any conditions, either intact or implanted
The influence of different geometries of matrix/scaffold on the remodeling process of a bone and bioresorbable material mixture with voids
No full textSince internal architecture greatly influences crucial factors for tissue regeneration, such as nutrient diffusion, cell adhesion and matrix deposition, scaffolds have to be carefully designed, keeping in mind case-specific mechanical, mass transport and biological requirements. However, customizing scaffold architecture to better suit conflicting requirements, such as biological and mechanical ones, remains a challenging issue. Recent advances in printing technologies, together with the synthesis of novel composite biomaterials, have enabled the fabrication of various scaffolds with defined shape and controlled in vitro behavior. Thus, the influence of different geometries of the assemblage of the matrix and scaffold on the remodeling processes of living bone and artificial material should be investigated. To this end, two implant shapes are considered in this paper, namely a circular inclusion and a rectangular groove of different aspect ratios. A model of a mixture of bone tissue and bioresorbable material with voids was used to numerically analyze the physiological balance between the processes of bone growth and resorption and artificial material resorption in a plate-like sample. The adopted model was derived from a theory for the behavior of porous solids in which the matrix material is elastic and the interstices are void of material
A Ritz approach for the static analysis of planar pantographic structures modeled with nonlinear Euler–Bernoulli beams
No full textWe present a finite element discrete model for pantographic lattices, based on a continuous Euler–Bernoulli beam for modeling the fibers composing the pantographic sheet. This model takes into account large displacements, rotations and deformations; the Euler–Bernoulli beam is described by using nonlinear interpolation functions, a Green–Lagrange strain for elongation and a curvature depending on elongation. On the basis of the introduced discrete model of a pantographic lattice, we perform some numerical simulations. We then compare the obtained results to an experimental BIAS extension test on a pantograph printed with polyamide PA2200. The pantographic structures involved in the numerical as well as in the experimental investigations are not proper fabrics: They are composed by just a few fibers for theoretically allowing the use of the Euler–Bernoulli beam theory in the description of the fibers. We compare the experiments to numerical simulations in which we allow the fibers to elastically slide one with respect to the other in correspondence of the interconnecting pivot. We present as result a very good agreement between the numerical simulation, based on the introduced model, and the experimental measures
Gedanken experiments for the determination of two-dimensional linear second gradient elasticity coefficients
No full textIn the present paper, a two-dimensional solid consisting of a linear elastic isotropic material, for which the deformation energy depends on the second gradient of the displacement, is considered. The strain energy is demonstrated to depend on 6 constitutive parameters: the 2 Lamé constants (λ and μ) and 4 more parameters (instead of 5 as it is in the 3D-case). Analytical solutions for classical problems such as heavy sheet, bending and flexure are provided. The idea is very simple: The solutions of the corresponding problem of first gradient classical case are imposed, and the corresponding forces, double forces and wedge forces are found. On the basis of such solutions, a method is outlined, which is able to identify the six constitutive parameters. Ideal (or Gedanken) experiments are designed in order to write equations having as unknowns the six constants and as known terms the values of suitable experimental measurements
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