1,721,100 research outputs found
Coactive stresses in MEMS and NEMS based on periodically bent crystals
No full textA variety of MEMS and NEMS are base on chemical film deposition onto a ceramic substrate. Generally, the substrate consists of a Si (silicon) or Ge (germanium) plate. One of the most used chemical processes is low-pressure chemical vapor deposition (LPCVD). Through such a technology a wide class of MEMS/NEMS can be realized, with particular reference to crystalline undulators (CU)s [1]. CUs (Figure 1) are devices to generate intense coherent and collimated electromagnetic radiation across the UV and X-ray ranges. Electrical charges are forced to oscillate in the electromagnetic field of the crystalline lattice thus emitting electromagnetic radiation.The present study concerns the effects induced by coactive stresses on displacement and stress fields induced in the system by thermal loading due to the LPCVD process. The aim of the study is to find the optimum geometrical parameters (a, p, hf) suitable to obtain a CU. By imposing equilibrium conditions and perfect adhesion between the thin films and the substrate, a singular integral equation is derived. A closed-form solution is achieved by expanding the unknown interfacial shear stress fields in Chebyshev series. This leads to an algebraic system which solution allows assessing the stress, strain and displacement fields in the CU.
REFERENCES:
[1] Guidi V, Lanzoni L, Mazzolari A, et al. Design of a crystalline undulator based on patterning by tensile Si3N4 strips on a Si crystal. Appl Phys Lett 2007; 90(11): 11410
Resistivity contribution tensor for nonconductive sphere doublets
Full text linkThe distribution of the temperature and heat flux fields around a couple of unequal nonconductive tangent spherical inhomogeneities (or pores) embedded in an infinite medium under a steady-state and remotely applied heat flux is addressed in the present work. Owing to the 3D geometrical layout of the inhomogeneity, use is made of the tangent sphere coordinate system. A corrective temperature field expressed in terms of convergent integrals is superposed to the fundamental one to fulfill the BCs at the surfaces of the spheres. When the heat flux is aligned to the symmetry axis (axisymmetric problem), the solution can be found straightforwardly by introducing a stream function, which allows for transforming the Neumann BCs into a Dirichlet boundary value problem. Conversely, for the transversal heat flux (non-axisymmetric problem), the problem is formulated in terms of temperature, thus leading to a system of two ODEs which is handled numerically through a Euler shooting method, after preliminary asymptotic expansions.
Once the temperature fields are known, the components of the resistivity contribution tensor are assessed varying the aspect ratio of the two spheres. It is found that the extrema of the thermal resistivity are achieved for spheres of equal size. The study allows assessing the effective thermal conductivity of a wide range of smart composites involving insulating inhomogeneities resembling sphere doublets
Elastic solution for a circular disk with a central crack under compressive diametrical load
No full textThe splitting tensile strength test (Brazilian test) is widely used because of its simplicity to assess the ultimate tensile strength and fracture behaviour of a variety of brittle materials, with specific reference to ceramics, concrete, and cementitious composites. Indeed, from the linear theory of elasticity, the distribution of the normal stress along any diameter of an uncracked disk subjected to a pair of concentrated diametrical compressive forces is known in closed form. Conversely, a Brazilian disk with a pre-existing central crack of a given length turns out to be a much more challenging problem owing to the mixed boundary conditions to be imposed inside and outside the crack along the crack direction, together with the condition about the stress field along the outer curved boundary of the disk.
Few studies deal with such a demanding layout. Among these, based on the weight function method, Dong et al. (2004) evaluated the SIFs varying the angle of the external load with respect the crack plane and the crack length as well. Critical conditions for the achievement of pure mode I and mode II loading have been found also. However, that study is restricted to the neighbouring of the crack tips.
In the present study, the full field solution of the Brazilian disk is provided analytically in terms of Airy stress function in bipolar coordinates. The study is handled by examining separately a skew-symmetric and a symmetric loading condition, representative for the mode II and mode I loadings, respectively. Both the situations lead to a Fredholm hypersingular integral equation, whose solution is found through a collocation method by expanding the unknown in series of Chebyshev polynomials. It is pointed out that for mode I loading, a closing or an opening crack may arise. Both these circumstances have been analysed in detail. Conversely to the existing studies, the proposed formulation allows assessing both the displacement and stress fields along the entire diameter of the disk in the direction of the crack for any loading angle
The formation and growth of a cross kink in a rope under torsion: An interpretation based on structural mechanics
Full text linkThe application of large twistings to a thin rope is known to cause the occurrence and evolution of an intermediate cross kink. Using classical linear elastic structural mechanics, the branched equilibrium path, which characterizes the kink formation, has been obtained. This path is characterized by increasing torsional stiffness. Some energy considerations have been formulated to motivate why the rope moves along the branched path generating the cross kink
The Bending of Beams in Finite Elasticity
No full textIn this paper the analysis for the anticlastic bending under constant curvature of nonlinear solids and beams, presented by Lanzoni, Tarantino (J. Elast. 131:137–170,2018), is extended and further developed for the class of slender beams. Following a semi-inverse
approach, the problem is studied by a three-dimensional kinematic model for the longitudinal inflexion, which is based on the hypothesis that cross sections deform preserving their planarity. A compressible Mooney-Rivlin law is assumed for the stored energy function and from the equilibrium equations, the free parameter of the kinematic model is computed. Thus, taking into account the three-dimensionality of the beam, explicit formulae for the displacement field, the stretches and stresses in every point of the body, following both Lagrangian and Eulerian description, are derived. Subsequently, slender beams under variable curvature were examined, focusing on the local determination of the curvature and bending moment along the deformed beam axis. The governing equations take the form of a coupled system of three equations in integral form, which is solved numerically. The proposed analysis allows to study a very wide class of equilibrium problems for nonlinear beams under different restraint conditions and subject to generic external load systems. By way of example, the Euler beam and a cantilever beam loaded by a dead or live (follower) concentrated force applied at the free end have been considered, showing the shape assumed by the beam as the load multiplier increases
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
Shear deformable beams in contact with an elastic half-plane
Full text linkThe 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
On the seismic response of a flexible wall retaining a viscous poroelastic soil
No full textA simple and reliable method is presented for the seismic analysis of a flexible wall retaining a layer of fluid-saturated viscous and poroelastic soil. A viscous version of the linear poroelastic Biot model is adopted for the description of the soil dissipative behavior. The effects of the wall flexibility and the mechanical properties of the soil on the amplitude and distribution of the pressures and the associated forces acting on the wall under harmonic loadings are firstly analyzed. The pseudostatic response is then recovered as a particular case for a vanishing small frequency of excitation. Finally, the response of the soil-wall system to generic seismic excitation is obtained using the Discrete Fourier Transform (FFT) method through the superposition of the contribution of each harmonic component of the ground acceleration spectrum. The analysis of the dynamic response obtained for different geometries of the wall and mechanical soil behavior allowed the relative importance of the various parameters involved in the seismic response of the system to be assessed. (c) 2007 Elsevier Ltd. All rights reserved
On the anticlastic bending of solids at finite strains
No full textThe present work deals with the problem of compressible isotropic hyperelastic solids under finite bending. The problem is fully nonlinear and, conversely to the classical Rivlin solution [1], it is formulated in the framework of three-dimensional kinematics involving both large displacements and strains according to the context of finite elasticity. The model entails three kinematic assumptions, which stand for the planarity of the cross sections (Bernoulli-Navier hypothesis), the invariance of the curvature along the longitudinal direction of the solid (uniform bending) and the curvature of the cross sections (anticlastic curvature), that is assumed constant along the width of the solid [2]. Based on the semi-inverse approach and according to the kinematic assumptions, the 3D displacement field is found, and, in turn, the deformation gradient is assessed. Then, the equilibrium conditions, specialized for a compressible Mooney-Rivlin material, provide proper relations among the unknown kinematic parameters, thus leading to the closure of the problem. Emphasis in placed on the “moment-curvature relation”, which is found to be governed by two independent dimensionless parameters: the Eulerian slenderness and the compactness index of the solid cross sections [3]. Similarity is observed with respect the previous works of Lamb (1890) regarding the mechanical response of bent plates and the experiments performed by Searle (1933) as well. Moreover, such an analysis allows broadening the “Elastica” to the more general context of finite elasticity.
In this work, the main results provided by the theoretical model are compared with those obtained by FE simulations and an experimental investigation based on a specifically designed mechanical apparatus, founding good agreement also for the case of extremely inflexed solids
Modeling and simulation of trapping mechanisms of granular media in space
No full textThis paper describes the modeling and simulation of trapped granular media, within the context of the Granular Imager project. We describe the physics of trapped granular media in space, and the methodologies used to stably confine and shape such a medium using electromagnetic fields. The numerical models have also been validated with results in the literature, obtaining excellent agreement. The results of the numerical tests indicate that it is possible, with structural arrangements of rings and plates at different levels of electrostatic potential, to stably confine one or more charged particles, when driven by voltages that can be modulated in time and space
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