Principle Of Stationarity Research Articles

Strengthening of the railroad track for high-speed traffic on the Bukhara-Misken section

In the article the work of ballast prism and subgrade is considered, on the basis of analysis two-layer reinforcement from geotextile is offered, also strengthening by water-soluble polymer in conditions of sandy zone on high-speed sections of railroads is suggested. The principle of stationarity of the total potential energy of deformable Lagrangian systems is used to determine the stress-strain state of the earth bed. The dependences between the components of stress and strain tensors characterizing specific models of the medium have been established, and an elastic ground medium with no residual deformation from external load has been considered. And also offer designs of sleepers with concave surface, which will increase the service life and ensure the reliability of its operation on horizontal and vertical curves of railroads. A new fluoroplastic under-rail gasket, which does not change its characteristics during 5 years, contacting with the base of the rail, flat inner support surface, contacting with the sleeper, reduces load vibration from the rolling stock on the sections of high-speed traffic is offered.

Symmetry Properties of Models for Reversible and Irreversible Thermodynamic Processes

The problem of formulating variational models for irreversible processes of media deformation is considered in this paper. For reversible processes, the introduction of variational models actually comes down to defining functionals with a given list of arguments of various tensor dimensions. For irreversible processes, an algorithm based on the principle of stationarity of the functional is incorrect. In this paper, to formulate a variational model of irreversible deformation processes with an expanded range of coupled effects, an approach is developed based on the idea of the introduction of the non-integrable variational forms that clearly separate dissipative processes from reversible deformation processes. The fundamental nature of the properties of symmetry and anti-symmetry of tensors of physical properties in relation to multi-indices characterizing independent arguments of bilinear forms in the variational formulation of models of thermomechanical processes has been established. For reversible processes, physical property tensors must necessarily be symmetric with respect to multi-indices. On the contrary, for irreversible thermomechanical processes, the tensors of physical properties that determine non-integrable variational forms must be antisymmetric with respect to the permutation of multi-indices. As a result, an algorithm for obtaining variational models of dissipative irreversible processes is proposed. This algorithm is based on determining the required number of dissipative channels and adding them to the known model of a reversible process. Dissipation channels are introduced as non-integrable variational forms that are linear in the variations of the arguments. The hydrodynamic models of Darcy, Navier–Stokes, and Brinkman are considered, each of which is determined by a different set of dissipation channels. As another example, a variational model of heat transfer processes is presented. The equations of heat conduction laws are obtained as compatibility equations by excluding the introduced thermal potential from the constitutive equations for temperature and heat flux. The Fourier and Maxwell–Cattaneo equations and the generalized heat conduction laws of Gaer–Krumhansl and Jeffrey are formulated.

The stress-strain curve model in the form of an extremal of a non-integrable linear variation form

The article develops an idea that the stress-strain curve for an arbitrary material is the extremum of some functional. However, for irreversible processes, the using of the principle of stationarity of some functional is incorrect, because due to the dissipation of the deformation process, the possible work of internal forces is non-integrable. Therefore, it is proposed to use the generalized variational principle of L. I. Sedov for modeling the stress-strain curve of elastoplastic materials. A concept of sequential inclusion of certain deformation mechanisms on different segment of the stress-strain curve is proposed. According to this concept, each section of the stress-strain curve must correspond either to the stationary value of the corresponding functional, or to the stationary value of the non-integrated form of variations of the corresponding stress derivatives. The combination of naturally obtained spectra of boundary conditions at the ends of each segment leads to a variation-consistent formulation of the system of boundary and contact conditions of solutions of different differential equations on each segment of stress-strain curve. As a result, it is possible to construct a differentiable stress-strain curve over the entire area of the stress-strain curve definition. The resulting solution, in contrast to the Ramberg - Osgood empirical law, has a strictly liner segment. The obtained mathematical model was tested on experimental data of materials for various industrial purposes. The achieved accuracy of the mathematical model is sufficient for engineering applications.

ОЦЕНКА ВЕРОЯТНОСТИ ОБРАЗОВАНИЯ ЗАПРЕДЕЛЬНЫХ ПРОГИБОВ ПОСЛЕ ОБРАЗОВАНИЯ ТРЕЩИН В ЖЕЛЕЗОБЕТОННОЙ БАЛКЕ НА СТОХАСТИЧЕСКОМ ОСНОВАНИИ

The results of calculating a reinforced concrete beam on an elastic statistically inhomogeneous foundation after the formation of cracks in concrete are presented. The compliance coefficients of the base are considered as random stationary functions, and the load is assumed to be a random non-stationary function of the x coordinate. Strength parameters of concrete are taken as random Gaussian values. The distribution parameters are given for both the initial bending stiffness of a reinforced concrete beam and the stiffness of the beam after cracking, as a function of the random cube strength of concrete. The parameters of the distribution densities of the deflections of the beam before the formation of cracks in it, as well as after the formation of cracks, are determined. For an approximate solution of the differential equation for the bending of a reinforced concrete beam after the formation of cracks, the variational principle of stationarity of additional energy (the Castigliano functional) is used. This makes it possible to determine the probabilistic characteristics of the distribution of the equivalent constant stiffness of the beam, the probabilistic parameters of the distribution of beam deflections after cracking, as well as the total differential law of the distribution of deflections in a beam on an elastic foundation in an arbitrary section of the beam. The probability of occurrence of the limiting state in the form of exceeding the value of the deflections of the beam, the limiting standard value of the deflections, taking into account the possible formation of cracks in the beam, has been determined.

Elucidating Relaxation Phenomena in Lithium Metal Batteries with Odd-Random Phase Electrochemical Impedance Spectroscopy

The high reactivity of lithium metal is central to the challenges posed in lithium batteries with solid electrolyte interphase (SEI) and dendrite formation playing a major role in the performance and lifetime of batteries [1]. A wide variety of surface analysis, spectrometric, and spectroscopic techniques have already been deployed to investigate the deposition characteristics and time evolution, but it still remains a big challenge to access the interface region from an in-situ and operando perspective, not to mention the transparency of lithium metal to X-rays which excludes the effective use of many X-ray based techniques.Odd-Random Phase Electrochemical Impedance Spectroscopy (ORP-EIS) is a non-invasive, in-situ and operando technique developed at the Electrochemistry and Surface Engineering (SURF) research group at the Vrije Universiteit Brussel [2].ORP-EIS is a multisine technique which is able to produce instantaneous EIS spectra and also quantifies the noise level, non-linearities and non-stationarities through a selective frequency excitation mechanism. This is especially important in lithium metal systems in which the high reactivity means that the system is continuously evolving after deposition and where if conventional single-sine EIS were to be used, the principle of stationarity would not be respected due to the measurement time being considerably slower than the evolution of the system itself [3].In this presentation we discuss the findings of the first ever ORP-EIS analysis of lithium metal batteries and the behavior observed in the short timespan immediately after lithium deposition onto a copper current collector and how this technique can help to elucidate more of the dynamics with a much greater accuracy and confidence than conventional single-sine EIS measurements.

VIBRATIONS OF A LONGITUDINALLY STIFFENED, LIQUID-FILLED CYLINDRICAL SHELL IN LIQUID

In the paper we study free vibrations of a longitudinally stiffened, viscous liquid-filled orthotropic cylindrical shell in ideal liquid. The Navier – Stokеs linearized equation is used to describe the motion of the internal viscous liquid, the motion of the external liquid is described by a wave equation written in the potential by perturbed velocity. Frequency equation of a longitudinally stiffened orthotropic, viscous liquid-contacting cylindrical shell is obtained on the basis of the Hamilton – Ostrogradsky principle of stationarity of action. Characteristic curves of dependence are constructed.

Mixed Finite Element Matrix for Plate Bending Analysis Using Weighted-Residual Integral and Weak Formulation

The Conventional Finite Element Method for the analysis of plate bending based on a the principle of stationarity of total potential energy which is well known as Stiffness Formulation , using a variety of conformal and no-conformal elements was widely applicable in early of numerical solutions for such problems , later in order to improve the efficiency of such solutions , a more general and flexible formulation called Mixed Formulation based on variational principles which can be regarded as an extension of the Stiffness principle become important alternative. The explicit stiffness matrix for plate bending was given in the most if it`s not in all literatures so the reader can easy follow the solving procedure for such problems and verifying any published results , however such like-matrix (Augmented Matrix) in case of mixed formulation not given , at least for simple elements in the literatures as well as concerned researches . This quietly leads to some difficulties concerning the verification as well as understanding the published results. The main objective of this paper is to introduce this matrix in abbreviated size followed by a applicability through a some detailed examples for some bending models. The derived matrix will be helpful subject of research work in addition to , reveals a very good feeling with understanding and verification the published results in plus to comparing with the analytical solutions of different plate bending problems as the reader can do that.

Mixed Finite Element Matrix for Plate Bending Analysis Using Weighted-Residual Integral and Weak Formulation

The Conventional Finite Element Method for the analysis of plate bending based on a the principle of stationarity of total potential energy which is well known as Stiffness Formulation , using a variety of conformal and no-conformal elements was widely applicable in early of numerical solutions for such problems , later in order to improve the efficiency of such solutions , a more general and flexible formulation called Mixed Formulation based on variational principles which can be regarded as an extension of the Stiffness principle become important alternative. The explicit stiffness matrix for plate bending was given in the most if it`s not in all literatures so the reader can easy follow the solving procedure for such problems and verifying any published results , however such like-matrix (Augmented Matrix) in case of mixed formulation not given , at least for simple elements in the literatures as well as concerned researches . This quietly leads to some difficulties concerning the verification as well as understanding the published results. The main objective of this paper is to introduce this matrix in abbreviated size followed by a applicability through a some detailed examples for some bending models. The derived matrix will be helpful subject of research work in addition to , reveals a very good feeling with understanding and verification the published results in plus to comparing with the analytical solutions of different plate bending problems as the reader can do that.

Postbuckling of a uniformly compressed simply supported plate with free in-plane translating edges

The postbuckling of a Kirchhoff isotropic simply supported plate is considered in detail. The in-plane displacements on the edges of the plate are not constrained. The solution is obtained using the principle of the total potential energy stationarity. The expression for energy is written in the three versions: in terms of the Biot strains, the Cauchy-Green strains, and the strains corresponding to Fuppl-von Karman plate theory. Some approximate solution is constructed by the classical Ritz method. The basis functions are taken in the form of Legendre polynomials and their linear combinations. The obtained diagram of equilibrium states is rather similar to the classical diagrams of compressed shells. We show the failure of Foppl-von Karman theory under large deflections. Using the Biot strains and the Cauchy-Green strains leads to the discrepancy between the results of at most 5 %. We demonstrate the high accuracy and convergence of the approximate solution.

Buckling analysis of rod structure of the two-tier dome

The paper deals with the problem of calculating the rod structure of a two-tier dome for stability. Such structures consisting of straight rod elements are widely used in practice and have a number of significant advantages. First of all, it is a high rigidity with a low mass. Also, this type of construction is well resistant to dynamic loads. At the same time, the dome model allows for the bifurcation of points on the equilibrium state curve of the system. The problem of the dynamic stability of double dome is solved by the principle of stationarity of total potential energy of the system. The analysis of the obtained solution is carried out, and the equilibrium state diagram for a two-tier core dome is constructed.

Three-point bending of a short beam with symmetrically varying mechanical properties

The subject of the paper is a short beam with symmetrically varying mechanical properties. The values of elastic modules vary in the depth direction of the beam. The nonlinear shear deformation theory is assumed i.e. the hypothesis for plane cross section. Based on the principle of stationarity of total potential energy three differential equations of equilibrium are obtained. The system of equations is solved for three-point bending of the beam with the use the trigonometric series. The shear stresses distribution in the cross section of the beam and the deflections are determined. Moreover, numerical – FEM model of the beam is developed and the shear stresses distribution and the deflections of the beam are calculated. The results of these two methods are compared.

Why not energy conservation?

Energy conservation is a deep principle that is obeyed by all of the fundamental forces of nature. It puts stringent constraints on all systems, particularly systems that are ‘isolated,’ meaning that no energy can enter or escape. Notwithstanding the success of the principle of stationary action, it is fair to wonder to what extent physics can be formulated from the principle of stationary energy. We show that if one interprets mechanical energy as a state function, then its stationarity leads to a novel formulation of classical mechanics. However, unlike Lagrangian and Hamiltonian mechanics, which deliver their state functions via algebraic proscriptions (i.e., the Lagrangian is always the difference between a system’s kinetic and potential energies), this new formalism identifies its state functions as the solutions to a differential equation. This is an important difference because differential equations can generate more general solutions than algebraic recipes. When applied to Newtonian systems for which the energy function is separable, these state functions are always the mechanical energy. However, while the stationary state function for a charged particle moving in an electromagnetic field proves not to be energy, the function nevertheless correctly encodes the dynamics of the system. Moreover, the stationary state function for a free relativistic particle proves not to be the energy either. Rather, our differential equation yields the relativistic free-particle Lagrangian (plus a non-dynamical constant) in its correct dynamical context. To explain how this new formalism can consistently deliver stationary state functions that give the correct dynamics but that are not always the mechanical energy, we propose that energy conservation is a specific realization of a deeper principle of stationarity that governs both relativistic and non-relativistic mechanics.

A unifying variational framework for stress gradient and strain gradient elasticity theories

Abstract Stress gradient elasticity and strain gradient elasticity do constitute distinct continuum theories exhibiting mutual complementary features. This is probed by a few variational principles herein presented and discussed, which include: i) For stress gradient elasticity, a (novel) principle of minimum complementary energy and an (improved-form) principle of stationarity of the Hellinger–Reissner type; ii) For strain gradient elasticity, a (known) principle of minimum total potential energy and a (novel) principle of stationarity of the Hu–Washizu type. Additionally, the higher order boundary conditions for stress gradient elasticity, previously derived by the author (Polizzotto, Int. J. Solids Struct. 51, 1809–1818, (2014)) in the form of higher order boundary compatibility equations, are here revisited and reinterpreted with the aid of a discrete model of the body's boundary layer. The reasons why the latter conditions need to be relaxed for beam and plate structural models are explained.

Nonstationarities in the occurrence rates of flood events in Portuguese watersheds

Abstract. An exploratory analysis on the variability of flood occurrence rates in 10 Portuguese watersheds is made, to ascertain if that variability is concurrent with the principle of stationarity. A peaks-over-threshold (POT) sampling technique is applied to 10 long series of mean daily streamflows and to 4 long series of daily rainfall in order to sample the times of occurrence (POT time data) of the peak values of those series. The kernel occurrence rate estimator, coupled with a bootstrap approach, was applied to the POT time data to obtain the time dependent estimated occurrence rate curves, λˆ(t), of floods and extreme rainfall events. The results of the analysis show that the occurrence of those events constitutes an inhomogeneous Poisson process, hence the occurrence rates are nonstationary. An attempt was made to assess whether the North Atlantic Oscillation (NAO) casted any influence on the occurrence rate of floods in the study area. Although further research is warranted, it was found that years with a less-than-average occurrence of floods tend to occur when the winter NAO is in the positive phase, and years with a higher occurrence of floods (more than twice the average) tend to occur when the winter NAO is in the negative phase. Although the number of analyzed watersheds and their uneven spatial distribution hinders the generalization of the findings to the country scale, the authors conclude that the mathematical formulation of the flood frequency models relying on stationarity commonly employed in Portugal should be revised in order to account for possible nonstationarities in the occurrence rates of such events.

An analysis method for magnetotelluric data based on the Hilbert–Huang Transform

Prevailing methods of magnetotelluric (MT) data analysis determine the spectra using variations of the Fourier Transform (FT), which is based on the principle of signal stationarity. However, MT data series are non-stationary random signals that do not meet the basic requirements of conventional methods based on the FT. In recent years, the Hilbert–Huang Transform (HHT) has been regarded as a powerful tool for adaptive analysis of non-linear and non-stationary signals. This paper proposes for the first time the adoption of a new method of analysis for MT data, and focuses on two aspects that are facilitated by applying the HHT. The first aspect is the pretreatment of the MT time series data through selecting MT data subsets, and noise suppression; the other concerns the determination of the impedance and apparent resistivity using the HHT instantaneous spectrum. The conclusion reached through discussion of the first aspect is that the proposed methods can greatly improve the quality of MT data. The conclusion drawn from the second aspect is that the HHT instantaneous spectrum method can overcome the problems described above, and obtain stable and reliable estimation of the impedance tensor, and thus naturally minimise the estimation bias brought about by the non-stationary characteristics of MT data. Therefore, the HHT method is effective in analysing MT data and is able to generate meaningful geological information.

Axi-symmetrical deflection and buckling of circular porous-cellular plate

The main goal of this paper is a solution of the problem of buckling and deflection. A circular porous plate with simply supported edge under radial uniform compression and uniformly distributed load (pressure) is considered. Mechanical properties of the isotropic porous material vary across the thickness of the plate. Middle plane of the plate is its symmetry plane. A field of displacements (geometric model of nonlinear hypothesis) is described. The principle of stationarity of the total potential energy allowed to get a system of differential equations that govern the plate stability. A critical load and a deflection are determined. The results obtained for porous plates are compared to homogeneous circular plates.

Regions where transient signals are influenced between a source and receiver

At infinite frequency, a medium only influences the waveform of a received signal emitted from a source along one or more infinitesimally thin rays. For transient signals at finite frequencies, an exact method is developed to compute the regions in a medium that significantly influence the received signal for any specified window of signal travel time. Results are (1) in homogeneous media, a significant portion of the signal originates from waves that traverse paths that are approximately integer and half-integer numbers of cycles greater than the straight path between source and receiver. Called ‘‘constructive and destructive paths of influence,’’ they do not obey Fermat’s principle of path stationarity. (2) For reflection from a flat interface in a homogeneous medium, the received signal is significantly influenced by constructive and destructive paths of influence whose angles of incidence and reflection differ. (3) Near 100 Hz in an oceanic waveguide, the region of influence markedly departs from a ray. Near upper turning points, the influential region is flat for O(10) km instead of O(1) km for a ray. (4) The first Fresnel zone is an inappropriate scale to characterize the region of influence for transient signals near a steep ray in inhomogeneous media.

The breakdown of microscopic reversibility in a chiral ensemble in a time varying enantiomorphous influence: A computer simulation.

A computer simulation is used to investigate whether breakdown at microscopic reversibility occurs in an ensemble of (S)-CHBrClF molecules subjected to a time varying enantiomorphous external influence. Time correlation functions of the chiral ensemble in the field applied steady state are shown to obey the principle of stationarity to within 0.1%. Assuming that there is a link between stationarity and microscopic reversibility, it appears on this evidence that the latter is too small to appear above the noise of the simulation, even in a very strong enantiomorphic field.

Mean field method in the theory of quadrupolar glass with axial interaction of infinite range

The principle of stationarity of the free energy in a model with axial interaction of quadrupole systems of infinite range is used to calculate the mean number of metastable states as a function of the temperature. A self-consistent system of equations is obtained for the order parameters, and its solution near the temperatures of the transition to the quadrupolar glass phase and the orientationally ordered phase, and also at low temperatures, indicates that the existence of a gradient of the external electric field can lead not only to the formation of the quadrupolar glass phase but also to the formation of mixed ferro- and antiferroquadrupolar phases.

Theory of spin glasses based on the principle of stationarity of the free energy infinite-range model

Theory of spin glasses based on the principle of stationarity of the free energy infinite-range model