scholarly journals Mechanical Instabilities in Perfect Crystals: From Dislocation Nucleation to Bucklinglike Modes

2016 ◽  
Vol 83 (12) ◽  
Author(s):  
Akanksha Garg ◽  
Craig E. Maloney
Keyword(s):  
Pitchfork Bifurcation ◽  
Dislocation Nucleation ◽  
Radius Of Curvature ◽  
Geometrical Parameters ◽  
Free Standing ◽  
Buckling Mode ◽  
Euler Buckling ◽  
Dislocation Type ◽  
Spatially Extended ◽  
The Stability

We perform atomistic simulations of nanoindentation on Lennard–Jones 2D hexagonal crystals. In this work, we find a new spatially extended buckling-like mode of instability, which competes with the previously known instability governed by dislocation-dipole nucleation. The geometrical parameters governing these instabilities are the lattice constant, a, the radius of curvature of the indenter, R, and the thickness of the indenter layer, Ly. Whereas dislocation nucleation is a saddle-node bifurcation governed by R/a, the buckling-like instability is a pitchfork bifurcation (like classical Euler buckling) governed by R/Ly. The two modes of instability exhibit strikingly different behaviors after the onset of instability. The dislocation nucleation mode results in a stable final configuration containing a surface step and a stable dislocation at some depth beneath the surface, while the buckling modes are always followed immediately by subsequent nucleation of many dislocation dipoles. We show that this subsequent dislocation nucleation is also observed immediately after buckling in free standing rods, but only for rods which are of sufficiently wide aspect ratio, while thinner rods exhibit stable buckling followed only later by dislocation nucleation in the buckled state. Finally, we study the utility of several recently proposed local and quasi-local stability criteria in detecting the buckling mode. We find that the so-called Λ criterion, based on the stability of a representative homogeneously deformed lattice, is surprisingly useful in detecting the transition from dislocation-type instability to buckling-type instability.

Parametric Optimization of Dental Implants

2020 ◽  
Vol 22 (4) ◽  
pp. 1061-1076
Author(s):  
Wafa Bensmain ◽  
Mohammed Benlebna ◽  
Boualem Serier ◽  
Bel Abbes ◽  
Bachir Bouiadjra
Keyword(s):  
Dental Implants ◽  
Clinical Success ◽  
Equivalent Stress ◽  
Radius Of Curvature ◽  
Geometrical Parameters ◽  
Neck Size ◽  
Biomechanical Behavior ◽  
Dynamic Charging ◽  
The Stability ◽  
Masticatory Process

AbstractOsseointegration is a fundamental phenomenon of dental implantology. It ensures the stability, the safety and the durability of dental implants and predictable clinical success in long-term. The geometric form of the implant is a defining parameter of osseointegration and implant-bone charge transfer. This is the essential constitutes of this study. In fact, we demonstrate using the finite elements method with tridimensional numerical computations, that the geometrical parameters of the implant conditionate the level and the repartition of the stresses, induced in the cortical bone and the spongy bone during the masticatory process, simulated here by dynamic charging. The effect of several parameters [size and conicity of the implant neck, size and radius of curvature of the implant apex] and the shape of the implant corps on the biomechanical behavior of the bone. The latest was analyzed in terms of variation of the equivalent stress induced in the bone. The purpose of this analysis was the developing of an implant form allowing stress relaxation, during the mastication process, in the living tissue.

scholarly journals sp2 Carbon Stable Radicals

2021 ◽  
Vol 7 (2) ◽  
pp. 31
Author(s):  
Elena F. Sheka
Keyword(s):  
Carbon Nanotubes ◽  
Carbon Black ◽  
Intermolecular Interaction ◽  
Open Shell ◽  
Size And Shape ◽  
Spatially Extended ◽  
Stable Radicals ◽  
The Stability ◽  
Shungite Carbon ◽  
Technological Products

sp2 Nanocarbons such as fullerenes, carbon nanotubes, and graphene molecules are not only open-shell species, but spatially extended, due to which their chemistry is quite specific. Cogently revealed dependence of the final products composition on size and shape of the carbons in use as well as on the chemical prehistory is accumulated in a particular property—the stabilization of the species’ radical efficiency, thus providing the matter of stable radicals. If the feature is highly restricted and rarely available in ordinary chemistry, in the case of sp2 nanocarbons it is just an ordinary event providing, say, tons-in-mass stable radicals when either producing such widely used technological products as carbon black or dealing with deposits of natural sp2 carbons such as anthracite, shungite carbon, and other. Suggested in the paper is the consideration of stable radicals of sp2 nanocarbons from the standpoint of spin-delocalized topochemistry. Characterized in terms of the total and atomically partitioned number of effectively unpaired electrons as well as of the distribution of the latter over carbon atoms and described by selectively determined barriers of different reactions exhibiting topological essence of intermolecular interaction, sp2 nanocarbons reveal a peculiar topokinetics that lays the foundation of the stability of their radical properties.

scholarly journals Postbuckling Analysis Of A Rectangular Plate Loaded In Compression

2015 ◽  
Vol 15 (2) ◽  
Author(s):  
Jozef Havran ◽  
Martin Psotný
Keyword(s):  
Rectangular Plate ◽  
User Program ◽  
Nonlinear Fem ◽  
Buckling Mode ◽  
Energy Principle ◽  
Initial Imperfections ◽  
Potential Energy Principle ◽  
Total Potential ◽  
The Stability ◽  
Minimum Total Potential Energy

Abstract The stability analysis of a thin rectangular plate loaded in compression is presented. The nonlinear FEM equations are derived from the minimum total potential energy principle. The peculiarities of the effects of the initial imperfections are investigated using the user program. Special attention is paid to the influence of imperfections on the post-critical buckling mode. The FEM computer program using a 48 DOF element has been used for analysis. Full Newton-Raphson procedure has been applied.

Effect of Geometric Parameters of New Semisubmersible Platform on Stability and Hydrodynamic Performance

2021 ◽  
Author(s):  
Tianying Wang ◽  
Yanjun Zhou ◽  
Honglin Tang ◽  
Shihua Zhang ◽  
Haiqing Tian
Keyword(s):  
Geometric Parameters ◽  
Hydrodynamic Performance ◽  
Geometrical Parameters ◽  
Main Body ◽  
Floating Bodies ◽  
Full Picture ◽  
New Type ◽  
Design Plan ◽  
The Stability ◽  
Shape Characteristics

Abstract The JCSM concept (short for Jackup Combined Semisubmersible Multifunction Platform) is a new type of semisubmersible platform presented by the first author, which overcomes the shortcomings of the available semisubmersible platforms, and combines the advantages of the traditional semisubmersible platform, the Jackup platform and the new FPSO concept - IQFP. Due to the complicated interaction between stability and hydrodynamic performance, it is necessary to explore the effect of geometrical parameters of the main body on the stability and hydrodynamic performance in order to obtain the optimal design plan of a JCSM platform. Firstly, the structure components and innovations of the JCSM were briefly reviewed in order to facilitate readers to understand its full picture. Then, six independent geometric parameters were selected by carefully studying the shape characteristics of the initial design plan of a JCSM study case. Furthermore, the stability heights and motion responses of various floating bodies of the JCSM case with different geometric parameters in wave were calculated using boundary element method based on potential flow theory. Lastly, effect of the shape parameters on stability and hydrodynamic performance of the JCSM was qualitatively evaluated. The research would shed lights on the shape design of the JCSM main body.

scholarly journals Effects of plies orientations and initial geometric imperfections on buckling strength of a composite stiffened panel

2018 ◽  
Vol 191 ◽  
pp. 00008
Author(s):  
Ikram Feddal ◽  
Abdellatif Khamlichi ◽  
Koutaiba Ameziane
Keyword(s):  
Stiffened Panel ◽  
Buckling Mode ◽  
Element Analysis ◽  
Geometric Imperfections ◽  
Stiffened Panels ◽  
Specific Strength ◽  
Euler Buckling ◽  
Buckling Behavior ◽  
Composite Stiffened Panel ◽  
Strength And Stiffness

The use of composite stiffened panels is common in several activities such as aerospace, marine and civil engineering. The biggest advantage of the composite materials is their high specific strength and stiffness ratios, coupled with weight reduction compared to conventional materials. However, any structural system may reach its limit and buckle under extreme circumstances by a progressive local failure of components. Moreover, stiffened panels are usually assembled from elementary parts. This affects the geometric as well as the material properties resulting in a considerable sensitivity to buckling phenomenon. In this work, the buckling behavior of a composite stiffened panel made from carbon Epoxy Prepregs is studied by using the finite element analysis under Abaqus software package. Different plies orientations sets were considered. The initial distributed geometric imperfections were modeled by means of the first Euler buckling mode. The nonlinear Riks method of analysis provided by Abaqus was applied. This method enables to predict more consistently unstable geometrically nonlinear induced collapse of a structure by detecting potential limit points during the loading history. It was found that plies orientations of the composite and the presence of geometric imperfections have huge influence on the strength resistance.

Analysis of Nonlinear Buckling of a Long-Span Elliptic Paraboloid Suspended Dome Structure

2013 ◽  
Vol 639-640 ◽  
pp. 191-197 ◽  
Author(s):  
Zheng Rong Jiang ◽  
Kai Rong Shi ◽  
Xiao Nan Gao ◽  
Qing Jun Chen
Keyword(s):  
Single Layer ◽  
Buckling Mode ◽  
Nonlinear Buckling ◽  
Elliptic Paraboloid ◽  
Geometric Imperfection ◽  
Long Span ◽  
Initial Geometric Imperfection ◽  
Dome Structure ◽  
Unsymmetrical Loading ◽  
The Stability

The suspended dome structure, which is a new kind of hybrid spatial one composed of the upper single layer latticed shell and the lower cable-strut system, generally has smaller rise-to-span ratio, thus the overall stability is one of the key factors to the design of the structure. The nonlinear buckling behavior of an elliptic paraboloid suspended dome structure of span 110m80m is investigated by introducing geometric nonlinearity, initial geometric imperfection, material elastic-plasticity and half-span distribution of live loads. The study shows that the coefficient of stable bearing capacity usually is not minimal when the initial geometric imperfection configuration is taken as the first order buckling mode. The unsymmetrical loading distribution and the material nonlinearity might have significant effects on the coefficient. The structure is sensitive to the changes of initial geometric imperfection, and the consistent mode imperfection method is not fully applicable to the stability analysis of suspended dome structure.

Stability of the neutral equilibrium of columns with a rotational end restraint by the generalized Fourier series

2019 ◽  
Vol 25 (4) ◽  
pp. 961-967
Author(s):  
Yan-Ping Zhao ◽  
Lin Li ◽  
Ming Jin
Keyword(s):  
Fourier Series ◽  
Potential Energy ◽  
Energy Functional ◽  
Buckling Mode ◽  
Generalized Fourier Series ◽  
Order Variation ◽  
Neutral Equilibrium ◽  
Post Buckling ◽  
The Stability ◽  
End Restraint

In this paper, stability of the neutral equilibrium and initial post-buckling of a column with a rotational end restraint is analyzed based on Koiter initial post-buckling theory. The potential energy functional is written in terms of the angle. By the generalized Fourier series of the disturbance angle, it is proved that the second-order variation of the potential energy is semi-positive definite at the neutral equilibrium. The stability of the neutral equilibrium is determined by the sign of the fourth-order variation for the buckling mode. For all values of the stiffness of the rotational end restraint, the neutral equilibrium is stable and the bifurcation equilibrium is upward in the initial post-buckling.

Dielectric Elastomer as a New Material for Electrostatically Actuated Microbeams: Stability Analysis

2019 ◽  
Vol 11 (10) ◽  
pp. 1950098
Author(s):  
Mohammad Fathalilou ◽  
Pegah Rezaei-Abajelou ◽  
Afsoon Vefaghi ◽  
Ghader Rezazadeh
Keyword(s):  
Pitchfork Bifurcation ◽  
Dielectric Elastomer ◽  
Micro Electro Mechanical Systems ◽  
High Deformation ◽  
Electrostatically Actuated ◽  
Eigen Value ◽  
Deformation Ability ◽  
New Material ◽  
The Stability ◽  
Stability Regime

Due to the interesting properties such as light weight and high deformation ability, dielectric elastomer (DE) resonators can be good alternatives for conventional silicon resonant beams used in micro-electro-mechanical systems (MEMS). This paper proposes a modeling in which a pre-stretched clamped-clamped DE-based microbeam oscillating above the ground substrate is subjected to an external electrostatic pressure. Using a DE-based beam affects the total rigidity of the system, which may lead to an anticipated saddle-node or pitchfork bifurcation. Hence, the present study tries to analyze the effects of DE properties on changing the stability regime of DE-based microbeams under electrostatic actuation. The stability of the system has been investigated using an eigen-value form of the problem. The effects of DE properties including pre-stress, relative permittivity and voltage value across the electrodes on pull-in or divergence instability as well as the frequency response of the system have been investigated. Moreover, the critical values of the DE voltage as a booster of instability occurrence have been obtained in either the presence or absence of the direct current (DC) voltage. It has been found that the pre-stress and appropriate DE permittivity can provide a needed magnitude of the DE actuating voltage to alter the resonance frequency and stability positions of the structure.

Sensitivity enhancement of a folded beam MEMS capacitive accelerometer-based microphone for fully implantable hearing application

2018 ◽  
Vol 63 (6) ◽  
pp. 699-708 ◽  
Author(s):  
Apoorva Dwivedi ◽  
Gargi Khanna
Keyword(s):  
Microelectromechanical Systems ◽  
Bone Structure ◽  
Design Parameters ◽  
Comsol Multiphysics ◽  
Geometrical Parameters ◽  
Efficient Design ◽  
Capacitive Accelerometer ◽  
Biomedical Device ◽  
Device Geometry ◽  
The Stability

Abstract The present work attempts to enhance the sensitivity of a folded beam microelectromechanical systems (MEMS) capacitive accelerometer by optimising the device geometry. The accelerometer is intended to serve as a microphone in the fully implantable hearing application which can be surgically implanted in the middle ear bone structure. For the efficient design of the accelerometer as a fully implantable biomedical device, the design parameters such as size, weight and resonant frequency have been considered. The geometrical parameters are varied to obtain the optimum sensitivity considering the design constraints and the stability of the structure. The optimised design is simulated and verified using COMSOL MULTIPHYSICS 4.2. The stability of the device is ensured using eigenfrequency analysis. Optimised results of the device geometry are presented and discussed. The accelerometer has a sensing area of 1 mm2 and attains a nominal capacitance of 5.3 pF and an optimum sensitivity of 6.89 fF.

On Post-Critical Behavior of a Beam on an Elastic Foundation

2018 ◽  
Vol 18 (06) ◽  
pp. 1850082 ◽  
Author(s):  
Lidija Z. Rehlicki ◽  
Marko B. Janev ◽  
Branislava N. Novaković ◽  
Teodor M. Atanacković
Keyword(s):  
Total Energy ◽  
Elastic Foundation ◽  
Nonlinear Problem ◽  
Bifurcation Analysis ◽  
Nontrivial Solutions ◽  
Buckling Mode ◽  
Nonlinear Equilibrium ◽  
The Stability ◽  
The One ◽  
Two Parameter

In this paper, we analyze the nonlinear equilibrium equation corresponding to the two-parameter bifurcation problem arising in the stability analysis of an elastic simply supported beam on the Winkler type elastic foundation for the case when bimodal buckling occurs. We perform the bifurcation analysis of the nonlinear problem, by using Lyapunov–Schmidt reduction, thus obtaining the number of the nontrivial solutions to the nonlinear problem and qualitatively characterizing the solution patterns. We also give the formulation of the problem and bifurcation analysis from the total energy viewpoint and determine the energy of each bifurcating solution. We assert that the solution with the smallest energy is the one that will be observed in the post-critical state. For specific choice of parameters, the bifurcating solution in the form of the second buckling mode has the smallest total energy. The numerical results illustrating the theory are also provided.

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