In-Plane Elastic Stability of Arches under a Radial Concentrated Load

This paper is concerned with the in-plane elastic stability of arches subjected to a radial concentrated load. The equilibrium equation for pin-ended circular arches is established by using energy method, and it is proved that the axial force is nearly a constant along the circumference of the circular arches. Based on force method, the equation for the primary eigen function is derived and solved, and the approximate analytical solution of critical instability load is obtained. Numerical examples are given and discussed.

Research on the flow stability and noise reduction characteristics of quasi-periodic elastic support skin

To enhance flow stability and reduce hydrodynamic noise caused by fluctuating pressure,a quasiperiodic elastic support skin composed of flexible walls and elastic support elements is proposed for fluid noise reduction.The arrangement of the elastic support element is determined by the equivalent periodic distance and quasi-periodic coefficient.In this paper,a dynamic model of skin in a fluid environment is established.The influence of equivalent periodic distance and quasi-periodic coefficient on flow stability is investigated.The results suggest that arranging the elastic support elements in accordance with the quasi-periodic law can effectively enhance flow stability.Meanwhile,the hydrodynamic noise calculation results demonstrate that the skin exhibits excellent noise reduction performance,with reductions of 10 dB in the streamwise direction,11 dB in the spanwise direction,and 10 dB in the normal direction.The results also demonstrate that the stability analysis method can serve as a diagnostic tool for flow fields and guide the design of noise reduction structures.

In-plane elastic stability of fixed parabolic shallow arches

The nonlinear behavior of fixed parabolic shallow arches subjected to a vertical uniform load is inves- tigated to evaluate the in-plane buckling load. The virtual work principle method is used to establish the non-linear equilibrium and buckling equations. Analytical solutions for the non-linear in-plane sym- metric snap-through and antisymmetric bifurcation buckling loads are obtained. Based on the least square method, an approximation for the symmetric buckling load of fixed parabolic arch is proposed to simplify the solution process. And the relation between modified slenderness and buckling modes are discussed. Comparisons with the results of finite element analysis demonstrate that the solutions are accurate. A cable-arch structure is presented to improve the in-plane stability of parabolic arches. The comparison of buckling loads between cable-arch systems and arches only show that the effect of cables becomes more evident with the increase of arch’s modified slenderness.

A first-principles study on elastic properties and stability of Ti_xV_(1-x)C multiple carbide

The structure,stability and elastic properties of di-transition-metal carbides TixV1-xC were investigated by using the first-principles with a pseudopotential plane-waves method.The results show that the equilibrium lattice constants of TixV1-xC show a nearly linear reduction with increasing addition of V.The elastic properties of TixV1-xC are varied by doping with V.The bulk modulus of Ti0.5V0.5C is larger than that of pure TiC,as well as Ti0.5V0.5C has the largest C44 among TixV1-xC（0≤x≤1）,indicating that Ti0.5V0.5C has higher hardness than pure TiC.However,Ti0.5V0.5C presents brittleness based on the analysis of ductile/brittle behavior.The Ti0.5V0.5C carbide has the lowest formation energy,indicating that Ti0.5V0.5C is more stable than all other alloys.

Study on structural stability,elastic and electronic properties for β-Ti under pressure based on first principles

The structural stability, elastic and electronic properties under pressure at 0 K for β-Ti have been investigated by per-forming first-principles calculations. With the increase of pressure, the structure of β-Ti becomes stabler, which is further con-firmed by the calculation for density of state （DOS）. The phase transition pressure of is about 64. 3 GPa, which is consist-ent with other theoretical predictions （63. 7 GPa） and the experimental result （50 GPa）. The pressure dependence of elastic constants shows that the low-pressure limit for a mechanically stable β-Ti is about 50 GPa with low Young？s modulus value of about 30. 01 GPa, which approaches the value of a human bone （30 GPa）. In addition, the pressure dependence of bulk modu-lus B, shear modulus G, Young’s modulus E,Poisson’s ratio σ,aggregate sound velocities,and ductility/brittleness under different pressures were also discussed. B, G and E ascend monotonously with increasing pressure, while a descends. β-Ti re-mains ductile by analysis of B/G under considered pressures.

Phase stability,elastic properties and electronic structures of Mg-Y intermetallics from first-principles calculations

The phase stability,elastic properties and electronic structures of three typical Mg-Y intermetallics including Mg_(24)Y_(5),Mg_(2)Y and MgY are systematically investigated using first-principles calculations based on density functional theory.The optimized structural parameters including lattice constants and atomic coordinates are in good agreement with experimental values.The calculated cohesive energies and formation enthalpies show that either phase stability or alloying ability of the three intermetallics is gradually enhanced with increasing Y content.The single-crystal elastic constants C_(ij) of Mg-Y intermetallics are also calculated,and the bulk modulus B,shear modulus G,Young's modulus E,Poisson ratio v and anisotropy factor A of polycrystalline materials are derived.It is suggested that the resistances to volume and shear deformation as well as the stiffness of the three intermetallics are raised with increasing Y content.Besides,these intermetallics all exhibit ductile characteristics,and they are isotropic in compression but anisotropic to a certain degree in shear and stiffness.Comparatively,Mg_(24)Y_(5) presents a relatively higher ductility,while MgY has a relatively stronger anisotropy in shear and stiffness.Further analysis of electronic structures indicates that the phase stability of Mg-Y intermetallics is closely related with their bonding electrons numbers below Fermi level.Namely,the more bonding electrons number below Fermi level corresponds to the higher structural stability of Mg-Y intermetallics.

Phase stability,electronic,elastic and thermodynamic properties of Al-RE intermetallics in Mg-Al-RE alloy:A first principles study

Electronic structure and elastic properties of Al_(2)Y,Al_(3)Y,Al_(2)Gd and Al_(3)Gd phases were investigated by means of first-principles calculations from CASTEP program based on density functional theory(DFT).The ground state energy and elastic constants of each phase were calculated,the formation enthalpy(ΔH),bulk modulus(B),shear modulus(G),Young's modulus(E),Poisson's ratio(ν)and anisotropic coefficient(A)were derived.The formation enthalpy shows that Al_(2)RE is more stable than Al_(3)RE,and Al-Y intermetallics have stronger phase stability than Al-Gd intermetallics.The calculated mechanical properties indicate that all these four intermetallics are strong and hard brittle phases,it may lead to the similar performance when deforming due to their similar elastic constants.The total and partial electron density of states(DOS),Mulliken population and metallicity were calculated to analyze the electron structure and bonding characteristics of the phases.Finally,phonon calculation was conducted,and the thermodynamic properties were obtained and further discussed.

Effects of size-dependent elasticity on stability of nanotweezers

It is well-recognized that the electromechanical response of a nanostructure is affected by its element size. In the present article, the size dependent stability behavior and nanotweezers fabricated from nanowires are investigated by modified couple stress elasticity （MCSE）. The governing equation of the nanotweezers is obtained by taking into account the presence of Coulomb and intermolecular attractions. To solve the equation, four techniques, i.e., the modified variational iteration method （MVIM）, the monotonic iteration method （MIM）, the MAPLE numerical solver, and a lumped model, are used. The variations of the arm displacement of the tweezers versus direct current （DC） voltage are obtained. The instability parameters, i.e., pull-in voltage and deflection of the system, are computed. The results show that size-dependency will affect the stability of the nanotweezers significantly if the diameter of the nanowire is of the order of the length scale. The impact of intermolecular attraction on the size-dependent stability of the system is discussed.

First-principles study of structural stability and elastic properties of MgPd_(3) and its hydride

Theoretical study of structural stability and elastic properties ofα-andβ-MgPd_(3)intermetallic compounds as well as their hydrides have been carried out based on density functional theory.The results indicateα-MgPd_(3)is more stable thanβphase with increased stability in their hydrides.The calculated elastic constants ofα-MgPd_(3)are overall larger thanβphase.After hydrogenation,the elastic constants are enlarged.And the elastic moduli exhibit similar tendency.The anisotropy ofα-MgPd_(3)is larger thanβphase,and the hydrides demonstrate larger anisotropy.Their ductility follows the order ofα-MgPd_(3)H_(0.5)<α-MgPd_(3)<β-MgPd_(3)H<β-MgPd_(3).Compared withβphase,higher Debye temperature ofα-MgPd_(3)implies stronger covalent interaction,and the Debye temperature of hydrides increases slightly.The electronic structures demonstrate that the Pd-Pd interaction is stronger than Pd-Mg,and Pd-H bonds play a significant role in the phase stability and elastic properties of hydrides.

Determine Stability Wellbore Utilizing by Artificial Intelligence Systems and Estimation of Elastic Coefficients of Reservoir Rock

Rock elastic properties such as Young’s modulus, Poisson?s ratio, plays an important role in various stages upstream of such as borehole stability, hydraulic fracturing in laboratory scale for observing mechanical properties of the reservoir rock usually using conventional cores sample that obtained from underground in reservoir condition. This method is the most common and most reliable way to get the reservoir rock properties, but it has some weaknesses. Currently, neural network techniques have replaced usual laboratory methods because they can do a similar operation faster and more accurately. To obtain the elastic coefficient, we should have compressional wave velocity (VP), shear wave (Vs) and density bulk due to high cost of (Vs) measurement and low real ability of estimation through the (Vp) and porosity. Therefore in this study, neural networks were used as a suitable method for estimating shear wave, and then elastic coefficients of reservoir rock using different relationships were predicted. Neural network used in this study was not like a black box because we used the results of multiple regression that could easily modify prediction of (Vs) through appropriate combination of data. The same information that were intended for multiple regression were used as input in neural networks, and shear wave velocity was obtained using (Vp) and well logging data in carbonate rocks. The results showed that methods applied in this carbonate reservoir was successful, so that shear wave velocity was predicted with about 92% and 95% correlation coefficient in multiple regression and neural network method, respectively.

On stability of elastic domain during isothermal solid-solid phase transformationin a tube configuration

Under isothermal quasi-static stretching the phase transition of a superelastic NiTi tube involves the formation （during loading） and vanishing （in unloading） of a high strain （martensite） domain. The two events are accompanied by a rapid stress drop/rise due to the formation/vanishing of do- main fronts. From a thermodynamic point of view, both are instability phenomena that occur once the system reaches its critical state. This paper investigates the stability of a shrink- ing cylindrical domain in a tube configuration during unload- ing. The energetics and thermodynamic driving force of the cylindrical domain are quantified by using an elastic inclu- sion model. It is demonstrated that the two domain fronts ex- hibit strong interaction when they come close to each other, which brings a peak in the total energy and a sign change in the thermodynamic driving force. It is proved that such domain front interaction plays an important role in control- ling the stability of the domain and in the occurrence of stress jumps during domain vanishing. It is also shown that the pro- cess is governed by two nondimensional length scales （the normalized tube length and normalized wall-thickness） and that the length scale dependence of the critical domain length and stress jump for the domain vanishing can be quantified by the elastic inclusion model.

Influence of Nb and Mo contents on phase stability and elastic property of β-type Ti-X alloys

The energetic, electronic structure and elastic property of β-type Ti1-xXx (X=Nb and Mo, x=0.041 7, 0.062 5, 0.125 0, 0.187 5, 0.250 0, 0.312 5 and 0.375) binary alloys were calculated by the method of supercell and augmented plane waves plus local orbitals within generalized gradient approximation. The elastic moduli of the polycrystals for these Ti1-xXx alloys were calculated from the elastic constants of the single crystal by the Voigt-Reuss-Hill averaging method. Based on the calculated results, the influence of X content on the phase stability and elastic property of β-type Ti1-xXx alloys was investigated. The results show that the phase stability, tetragonal shear constant C′, bulk modulus, elastic modulus and shear modulus of β-type Ti1-xXx alloys increase with an increase of X content monotonously. When the valence electron number of β-type Ti1-xXx alloys is around 4.10, i.e. the content of Nb is 9.87% (molar fraction) in the Ti-Nb alloy and Mo is 4.77% (molar fraction) in Ti-Mo alloy, the tetragonal shear constant is nearly zero. The Ti1-xXx alloys achieve low phase stability and low elastic modulus when the tetragonal shear constant reaches nearly zero. In addition, the phase stability of β-type Ti1-xXx alloys was discussed together with the calculated electronic structure.

A simple criterion for finite time stability with application to impacted buckling of elastic columns

The existing theories of finite-time stability depend on a prescribed bound on initial disturbances and a prescribed threshold for allowable responses. It remains a challenge to identify the critical value of loading parameter for finite time instability observed in experiments without the need of specifying any prescribed threshold for al- lowable responses. Based on an energy balance analysis of a simple dynamic system, this paper proposes a general criterion for finite time stability which indicates that finite time stability of a linear dynamic system with constant coefficients during a given time interval [0, tf] is guaranteed provided the product of its maximum growth rate （determined by the maximum eigen-root pl 〉0） and the duration tf does not exceed 2, i.e., pltf 〈2. The proposed criterion （pltf=2） is applied to several problems of impacted buckling of elastic columns： （i） an elastic column impacted by a striking mass, （ii） longitudinal impact of an elastic column on a rigid wall, and （iii） an elastic column compressed at a constant speed （＂Hoff problem＂）, in which the time-varying axial force is replaced approximately by its average value over the time duration. Comparison of critical parameters predicted by the proposed criterion with available experimental and simulation data shows that the proposed criterion is in robust reasonable agreement with the known data, which suggests that the proposed simple criterion （pltf---2） can be used to estimate critical parameters for finite time stability of dynamic systems governed by linear equations with constant coefficients.

Elastic Dynamic Stability of Big-Span Power Transmission Tower Subjected to Seismic Excitations

By combining the time-history response analysis and the eigenvalue buckling analysis, this paper developed a computational procedure to study the elastic dynamic stability of a transmission tower by APDL language in ANSYS. The influences of different input directions of seismic excitations and damping ratio on the elastic dynamic stability of tower were discussed. The following conclusions were obtained： （ 1 ） Longitudinal direction of the transmission lines is the worst input direction of seismic excitation for the transmission tower. （2） Dead load has no significant effect on the critical load and the occurrence time of buckling. （3） Vertical input of seismic excitations has no great effect on the dynamic stability of the transmission tower. （4） Damping effect has an influence on the dynamic stability of the transmission tower; however, the inherent characteristics of dynamic buckling is not changed.

Stability of High-Order Staggered-Grid Schemes for 3D Elastic Wave Equation in Heterogeneous Media

In this paper, we firstly derive the stability conditions of high-order staggered-grid schemes for the three-dimensional (3D) elastic wave equation in heterogeneous media based on the energy method. Moreover, the plane wave analysis yields a sufficient and necessary stability condition by the von Neumann criterion in homogeneous case. Numerical computations for 3D wave simulation with point source excitation are given.

Thermal buckling and postbuckling of FGM circular plates with in-plane elastic restraints

Based on von Karman＇s plate theory, the axisymmetric thermal buckling and post-buckling of the functionally graded material （FGM） circular plates with in- plane elastic restraints under transversely non-uniform temperature rise are studied. The properties of the FGM media are varied through the thickness based on a simple power law. The governing equations are numerically solved by a shooting method. The results of the critical buckling temperature, post-buckling equilibrium paths, and configurations for the in-plane elastically restrained plates are presented. The effects of the in-plane elastic restraints, material property gradient, and temperature variation on the responses of thermal buckling and post-buckling are examined in detail.

A Critical Study of the Elastic Properties and Stability of Heusler Compounds: Phase Change and Tetragonal <i>X₂YZ</i>Compounds

In the present work, the elastic constants and derived properties of tetragonal Heusler compounds were calculated using the high accuracy of the full-potential linearized augmented plane wave (FPLAPW) method. To find the criteria required for an accurate calculation, the consequences of increasing the numbers of k-points and plane waves on the convergence of the calculated elastic constants were explored. Once accurate elastic constants were calculated, elastic anisotropies, sound velocities, Debye temperatures, malleability, and other measurable physical properties were determined for the studied systems. The elastic properties suggested metallic bonding with intermediate malleability, between brittle and ductile, for the studied Heusler compounds. To address the effect of off-stoichiometry on the mechanical properties, the virtual crystal approximation (VCA) was used to calculate the elastic constants. The results indicated that an extreme correlation exists between the anisotropy ratio and the stoichiometry of the Heusler compounds, especially in the case of Ni2MnGa. Metastable cubic Ni2MnGa exhibits a very high anisotropy (≈28) and hypothetical cubic Rh2FeSn violates the Born-Huang stability criteria in the L21 structure. The bulk moduli of the investigated tetragonal compounds do not vary much (&asymp;130 ...190 GPa). The averaged values of the other elastic moduli are also rather similar, however, rather large differences are found for the elastic anisotropies of the compounds. These are reflected in very different spatial distributions of Young’s moduli when comparing the different compounds. The slowness surfaces of the compounds also differ considerably even though the average sound velocities are in the same order of magnitude (3.2 ... 3.6 km/s). The results demonstrate the importance of the elastic properties not only for purely tetragonal Heusler compounds but also for phase change materials that exhibit magnetic shape memory or magnetocaloric effects.

Thermoelastic Stability of Closed Cylindrical Shell in Supersonic Gas Flow

In a linear framework,the problem of stability of closed cylindrical shell is briefly discussed.The cylindrical shell is immersed in a supersonic gas flow and under the influence of temperature field varying along the thickness.An unperturbed uniform velocity flow field,directed along the short edges of the shell,is applied.Due to the inhomogeneity of the temperature field distribution across the thickness shell buckling instability occurs.This instability accounts for the deformed shape of the shell,to be referred as the unperturbed state.Stability conditions and boundary for the unperturbed state of the system under consideration are presented following the basic theory of aero-thermo-elasticity.The stability boundary depends on the variables characterizing the flow speed,the temperature at the middle plane of the shell and the temperature gradient in the direction normal to that plane.It is shown that the combined effect of the temperature field and flowing stream regulates the process of stability,and the temperature field can significantly change the flutter critical speed.

Numerical Analysis on the Magneto-Elastic Stability of Current-Carrying Conductors: Aiming at Applications for the Tokamak System

A novel method for calculating the magnetic stiffness matrix was proposed for the numerical analysis of the magneto-elastic stability of complicated current-carrying structures aim- ing for application in the magneto-elastic behavior of the tokamak system. A code based on the proposed method was developed and applied to the numerical analysis of two typical current- carrying structures. The good consistency of the numerical and analytical results validated the proposed method and the related numerical code.

Non-uniqueness and stability of two-family fiber-reinforced incompressible hyper-elastic sheet under equibiaxial loading

The problems on the non-uniqueness and stability of a two-family fiber- reinforced anisotropic incompressible hyper-elastic square sheet under equibiaxial tensile dead loading are examined within the framework of finite elasticity. For a two-family fiber-reinforced square sheet, which is in-plane symmetric and subjected to the in-plane symmetric tension in dead loading on the edges, three symmetrically deformed configu- rations and six asymmetrically deformed configurations are possible for any values of the loading. Moreover, another four bifurcated asymmetrically deformed configurations are possible for the loading beyond a certain criticM value. The stability of all the solutions is discussed in comparison with the energy of the sheet. It is shown that only one of the symmetric solutions is stable when the loading is less than the critical value. However, this symmetric solution will become unstable when the loading is larger than the critical value, while one of the four bifurcated asymmetric solutions will be stable.