Effect of geometrical imperfections on swelling-induced buckling patterns in gel films with a square lattice of holes

In this study, we investigate the effect of geometrical imperfections on swelling-induced buckling patterns in gel films with a square lattice of holes. Finite element analysis is performed using the inhomogeneous field theory of polymeric gels in equilibrium proposed by Hong et al. (2009). Periodic units consisting of 2 × 2 and 10 × 10 unit cells are analyzed under a generalized plane strain assumption. Geometrical imperfections are introduced using randomly oriented elliptical holes. The 2 × 2 unit cells show that the resulting buckling patterns are sensitive to imperfections; three different buckling patterns are obtained, and the most dominant one is the diamond plate pattern observed in experiments, which cannot be described using the model without imperfections. The 10 × 10 unit cells reveal that random imperfections are responsible for inducing homogeneous transformation into the diamond plate pattern. Furthermore, domain wall formation is simulated using a 10 × 10 unit cell model containing two elliptic holes.     

Thermal behavior of elastic columns with second-mode imperfections

Pin-ended columns having an initial imperfection in a second buckling mode and subjected to thermal loading have been studied in this paper. Based on a nonlinear relationship between strains and displacements, the buckling equilibrium equations are given with the energy method. Then the formulae for the axial compression and transversal displacement are presented. The relationship between the anti-symmetric imperfection and the axial compression has been studied along with the effect of elevated temperature on the initial imperfection. The response of the column in fire to the modified slenderness ratio is investigated. The proposed method has the potential to provide more detailed information for column designs and thus be deployed in future research to minimize the need for expensive laboratory testing.     

Dispositif optique pour implantation et micro-usinage par projection d'images ioniques Ion imaging for ion implantation and for micromachining

It is well known that more and more precise doping is needed for producing high performance's electronic components and circuits of increasingly enhanced complexity. An ion optic can be used to directly produce a localised implantation allowing to free one self from all masking techniques. The experimental set up mainly consist in a projecting lens which focuses the reduced image of a “model”, structure partially transparent to the ion beam, on the crystal to be implanted. One of the difficult points is connected with the tine control of the focusing of the ion image on the surface of the target. In order to check this focusing an “Ion Image Converter” is used as the projection lens. On the one hand the 10 keV energy positive ion beam is post accelerated to a hundred keV as it is focused on the target; on the other hand, the secondary electrons ejected from the target are accelerated and focused backwards permitting the formation of an electron image which is an enlargement of the ion figure projected on the target; this auxiliary image after further magnification is observed on a fluorescent screen allowing to adjust and to control the focusing and the illumination of the ion image.     

Elastic wave and vibration bandgaps in two-dimensional acoustic metamaterials with resonators and disorders

The vibration properties of two-dimensional (2D) finite acoustic metamaterials (AMs) consisting of discrete masses and springs are investigated in this paper. In order to clarify the mechanisms of the bandgaps in AMs, the infinite symmetrical systems are also studied, especially the impact of the physical asymmetry caused by the discrepant stiffness coefficients of the springs connecting the unit-cells. Although the asymmetry cannot change the bandgap width, the change of the phase velocity and the generation of the shear mode have been proven analytically. To study the vibration properties of the finite AM model, the effective mass of each unit-cell is used. The effective mass properties of the unit-cell with single resonator and multi-resonators in 2D AMs subjected to a time-harmonic excitation are discussed. The effects of the number of the unit-cells, multi-resonators in each unit-cell, graded resonators in the finite AM model on the vibration suppression are thoroughly examined by the frequency response analysis. Numerical results show that the degree of the vibration attenuation is related to the size of the model and the number of the bandgaps changes corresponding to the disorders of the local resonators. Furthermore, imperfections or defects are introduced into the finite AM system. Wave propagation and guiding in a finite model for straight waveguide are investigated and discussed. The defect states induced by changing the central resonator of a supercell are demonstrated. Defect bands are obtained and their location is illustrated.     

Dynamic buckling of partially-sway frames with varying stiffness using catastrophe theory

This work deals with the static and dynamic stability analysis of imperfect partially-sway frames with non-uniform columns. The examined two-bar frames are elastically supported and subjected to an eccentrically vertical load at their joint. Through a linear stability analysis, the effect of the taper ratio of the column cross-section on the buckling capacity of the partially-sway frame is thoroughly discussed. Using a non-linear method an accurate formula has been established for determining the exact asymmetric bifurcation point associated with the maximum load carrying capacity. These findings have been re-derived more readily using Catastrophe Theory (CT) and considering the frame as a one degree-of-freedom (1-DOF) system through an efficient technique. A local analysis allows us to classify, after reduction, the total potential energy (TPE) function of the system to one of the seven elementary Thom׳s catastrophes (with known properties) and to obtain static and dynamic singularity as well as bifurcational sets. It has been found that geometrical and loading imperfections, which are always present in structural engineering problems, have a significant effect on the dynamic buckling loads. The efficiency of the present approach is illustrated via several examples, while results from finite element analyses are in good agreement with the analytical solution presented herein.