Use Of Energy Method Research Articles

Degenerate lake equations: classical solutions and vanishing viscosity limit

The objective of this paper is twofold. First, we show the existence of global classical solutions to the degenerate inviscid lake equations. This result is achieved after revising the elliptic regularity for a degenerate equation on the associated stream-function, and adapting the method used for construction of classical solutions to the incompressible Euler equations. Second, we show that the weak solutions of the viscous lake equations converge to classical solutions of the inviscid lake equations when the viscosity coefficient goes to zero, which constitutes an important physical validation of these models. The later result is achieved by the use of energy method as in the proofs of Kato-type theorems. This method also allows us to expose a convergence rate.

An Analytical Solution for Lateral-Torsional Buckling Resistance of Perforated Cold-Formed Steel Channel Beams with Circular Holes in Web

Perforated cold-formed steel (PCFS) beams are regarded as an economical option for steel construction industry owing to its various advantages. They can provide access for the facilities like electric wires and pipelines to penetrate the web so that extra building space could be saved. However, the web openings might change the web stress distribution as well as reduce the cross-sectional properties, which make the PCFS beams more susceptible to buckling and may have effect on their load-bearing capacity. In this paper, a simplified spring model was proposed based on the use of energy method, to predict the critical moment of lateral-torsional buckling of PCFS channel beams with circular holes in web subject to pure bending. The effect of hole sizes and lateral restraint at the tension flange was examined by using the derived analytical solution. In addition, eigenvalue buckling analysis was conducted by using finite-element package ANSYS to validate the accuracy of the proposed analytical model. The results demonstrated that the proposed analytical solution was reliable and the critical moment predicted can be used for the extension of DSM formulae for the design of PCFS beams when considering the failure caused by lateral-torsional buckling of the beams.

РЕГУЛЮВАННЯ ЕНЕРГЕТИЧНОЇ СФЕРИ УКРАЇНИ В ПЕРІОД ЄВРОПЕЙСЬКОЇ ІНТЕГРАЦІЇ: НОРМАТИВНО-ПРАВОВІ ЗАСАДИ

The article defines the aspects of the regulatory foundations of the regulation of the energy sector of Ukraine, which are possible conditions for the European integration of the state. Investigating the issue of regulation of the energy security system of the state, it is worth noting the complete lack of systematicity, as well as the lack of orderliness of regulatory and legal documents that ensure regulation of the energy sector. Regulatory and legal acts of the specified industry function under conditions of lobbying by individual subjects, under conditions of inconsistency in the priority directions of their development; the existence of regional energy markets, isolation of security positions of energy enterprises, ecological and technological requirements, standardization, licensing, etc. An essential aspect of forming physical protection of energy facilities is relying on business entities. The costs of ensuring the appropriate security are included in the gross costs upon prior agreement with the Regulator of Energy Markets. However, the Regulator currently does not have the legal authority to take into account such categories of expenses, which makes it impossible to legitimize the source of defense funding. It is worth noting that the energy infrastructure is not protected at the departmental level beforehand without appropriate coordination and coordination with other priority strategies and measures to ensure national security. The mentioned circumstances testify to threats to the energy security system due to the non-regulation of the legislative basis and foresee the need for significant improvement of mechanisms and tools of protection from the side of regulatory and legal support. The current circumstances of the economic system of Ukraine have caused changes in the energy legislation. At the moment, a new energy environment is being formed, which cannot be clarified by rigid regulatory documents. The implemented changes affect not only the peculiarities of the relationship between energy market subjects (producers, consumers, and the state) but also put pressure on the principles of regulation of the latter's activities; it refers to the application of EU approaches, the rejection of administrative levers for regulating the activity of markets and state paternalism, etc. The result is the emergence of new threats to the uninterrupted functioning of the country's energy sector due to the use of energy methods as an analog of "energy weapons." In turn, the previously accepted mechanisms and tools of management activity in the energy security system should be reviewed.

REGULATORY AND LEGAL FOUNDATIONS OF THE REGULATION OF THE ENERGY SPHERE OF UKRAINE IN THE CONDITIONS OF EUROPEAN INTEGRATION

Investigating the issue of regulation of the energy security system of the state, it is worth noting the complete lack of systematicity, as well as the lack of orderliness of regulatory and legal documents that ensure regulation of the energy sector. Regulatory and legal acts of the specified industry function under conditions of lobbying by individual subjects, under conditions of inconsistency in the priority directions of their development; the existence of regional energy markets, isolation of security positions of energy enterprises, ecological and technological requirements, standardization, licensing, etc. The essential aspect of forming physical protection of energy facilities is relying on business entities. The costs of ensuring the appropriate security are included in the gross costs upon prior agreement with the Regulator of Energy Markets. However, the Regulator currently does not have the legal authority to take into account such categories of expenses, which makes it impossible to legitimize the source of defense funding. It is worth noting that the energy infrastructure is not protected at the departmental level beforehand without appropriate coordination and coordination with other priority strategies and measures to ensure national security. The mentioned circumstances testify to threats to the energy security system due to the non-regulation of the legislative basis and foresee the need for significant improvement of mechanisms and tools of protection from the side of regulatory and legal support. The current circumstances of the economic system of Ukraine have caused changes in the energy legislation. Now, the new energy environment is being formed, which cannot be clarified by rigid regulatory documents. The implemented changes affect not only the peculiarities of the relationship between energy market subjects (producers, consumers, and the state) but also put pressure on the principles of regulation of the latter's activities; it refers to the application of EU approaches, the rejection of administrative levers for regulating the activity of markets and state paternalism, etc. The result is the emergence of new threats to the uninterrupted functioning of the country's energy sector due to the use of energy methods as an analog of "energy weapons." In turn, the previously accepted mechanisms and tools of management activity in the energy security system should be reviewed. The purpose of this article is a multifaceted study, as well as the determination of aspects, normative and legal foundations of the regulation of the energy sector of Ukraine, which are possible conditions for the European integration of the state. Keywords: energy sphere, European integration, national security, regulatory and legal foundations, energy security.

SPATIAL BEHAVIOR OF SOLUTIONS FOR A CLASS OF HYPERBOLIC EQUATIONS WITH NONLINEAR DISSIPATIVE TERMS

This paper deals with the spatial behavior of solutions for aviscoelastic wave equations with nonlinear dissipative terms in asemi-infinite $n$-dimensional cylindrical domain. An alternativeof Phragm\'{e}n-Lindel\{o}f type theorems is obtained in theresult. In the case of decay, an upper bound will be derived forthe total energy by means of the boundary data. The main point ofthe contribution is the use of energy method.

Energy methods for fractional Navier–Stokes equations

In this paper we make use of energy methods to study the Navier–Stokes equations with time-fractional derivative. Such equations can be used to simulate anomalous diffusion in fractal media. In the first step, we construct a regularized equation by using a smoothing process to transform unbounded differential operators into bounded operators and then obtain the approximate solutions. The second part describes a procedure to take a limit in the approximation program to present a global solution to the objective equation.

On the use of energy method with element splitting to determine the stability of a constrained elastica

A constrained elastica under edge thrust may have multiple static equilibrium positions. It is in general difficult to determine the stability of these equilibrium positions due to the presence of unilateral constraints. In this paper we propose an energy method for this purpose. The beam is decretized into a series of rigid links connected at the joints by torsional springs. To deal with the unilateral constraints in question, we allow the contact point on the elastica to be slightly different before and after superposing virtual displacements. In order to accommodate this change of contact point we split the link near the boundary point of the contact region into two sub-links. It is noted that certain restrictions must be imposed on the contact point change in order for the total potential to be stationary if the equilibrium position is symmetric. After linearizing the constraint equations, the matrix associated with the second variation of the total potential before and after superposing virtual displacement can be established. From the eigenvalues of this matrix, the stability of the constrained elastica can be determined. One-point-contact and one-line-contact deformations are discussed in detail. Other deformation patterns can be analyzed in a similar manner. This energy method supplements the vibration method proposed earlier by the first author, in which the contact point is allowed to change during vibration.

Stiffness properties of certain oscillatory systems: quantification and possibilities for corrections

This study is concerned with the use of energy methods to find the equivalent stiffness properties of certain vibration models. The first class of models are one-degree-of-freedom oscillatory systems that include several combinations of a main spring and an additional spring. The stiffness properties of the equivalent system as well as the condition for different types of the resulting oscillatory motion are determined. Then, two-degree-of-freedom systems comprising two pairs of mutually orthogonal or symmetrically attached springs are examined. The corresponding equivalent stiffness properties are obtained and the possibilities for corrections are also discussed.

A Technique for TEV-Based Detection and Location of Partial Discharges on MV Metal-Clad Switchgears

The principle of detection of partial discharge in MV Metal-Clad Switchgears utilizing Transient Earth Voltage (TEV) method is introduced and some problems in application of the traditional PD detection systems are summarized and analyzed. After that, an improved PD detection system is proposed and established with an advanced technique. The technique involves use of energy method to determine time difference among multiple signals and external trigger method to realize phase integrity during data acquisition process. Laboratory experiment and site tests are conducted and it is proved that the improved detection system is of great effectiveness in PD location and interference identification.

Deflection Analysis of Woven Composite Planes under In-Plane Loading

Deflection analysis of yarns of a bi-axial woven composite plate under tensional loading is investigated in this article. A unit part of the warp yarn which is limited by two adjacent weft yarns is modeled by a curved beam. Using the Winkler theory of curved beams, the strain energy under the tensile loading is derived. Initial shape of yarns is chosen to be arc shaped. The deflection analysis is accomplished by making use of energy method. First, the external work of the horizontal (or tensile) force and also the vertical contacting force is evaluated. Second, using the variational method the governing equations and boundary conditions are derived and then solved to find out the displacement fields exactly. Finally, making use of the continuity of the deflection of two contacting yarns at the contacting point the vertical contacting force is obtained. It must be mentioned that shear forces and slipping of contacting yarns are disregarded here. The validation of the work is performed by comparison of results with the semi circle beam (yarn) which is found in some usual text books.

A Generalized Constraint Model for Two-Dimensional Beam Flexures: Nonlinear Strain Energy Formulation

Abstract The beam constraint model (BCM), presented previously, captures pertinent nonlinearities to predict the constraint characteristics of a generalized beam flexure in terms of its stiffness and error motions. In this paper, a nonlinear strain energy formulation for the beam flexure, consistent with the transverse-direction load-displacement and axial-direction geometric constraint relations in the BCM, is presented. An explicit strain energy expression, in terms of beam end displacements, that accommodates generalized loading conditions, boundary conditions, initial curvature, and beam shape, is derived. Using energy-based arguments, new insight into the BCM is elucidated by fundamental relations among its stiffness, constraint, and energy coefficients. The presence of axial load in the geometric constraint and strain energy expressions—a unique attribute of distributed compliance flexures that leads to the elastokinematic effect—is highlighted. Using the principle of virtual work, this strain energy expression for a generalized beam is employed in determining the load-displacement relations, and therefore constraint characteristics, of a flexure mechanism comprising multiple beams. The benefit of this approach is evident in its mathematical efficiency and succinctness, which is to be expected with the use of energy methods. All analytical results are validated to a high degree of accuracy via nonlinear finite element analysis.

Determining Functionals for the Strongly Damped Nonlinear Wave Equation

We consider the existence of a wide collection of finite sets of functionals on the phase space that completely determines asymptotic behavior of solutions to the strongly damped nonlinear wave equation. The proof makes use of energy methods and the concept of the completeness defect. We also show that the number of determining nodes is two, that is, the asymptotic behavior of solutions is determined by the values of two sufficiently close points in the interval [0, 1].

An upper bound for the waiting time for doubly nonlinear parabolic equations

the local waiting time for u at x0. Our aim is to achieve a quantitative upper bound for the local waiting time at x0 depending on the growth of the initial value u0 near x0. In many cases it is possible to obtain a quantitative lower bound for this waiting time as one can see in Giacomelli–Grun [4]. The recent monograph of Antontsev–Diaz–Shmarev [1] provides conditions for the appearance of waiting time by the use of energy methods, and Shishkov– Shchelkov [9] showed that the supports of solutions for the doubly nonlinear parabolic equation spread slowly for small initial data. But not much is known about quantitative upper bounds for the waiting time. Only for the porous medium equation (e.g. Chipot–Sideris [2]) an upper bound has been obtained, and very recently Choi–Kim [3] found conditions describing waiting time phenomena for the Hele–Shaw and Stefan problems.

The Buckling of Spherical Liposomes

In the classical "first approximation" theory of thin-shell structures, the constitutive relations for a generic shell element--i.e. the elastic relations between the bending moments and membrane stresses and the corresponding changes in curvature and strain, respectively-are written as if an element of the shell is flat, although in reality it is curved. In this theory it is believed that discrepancies on account of the use of "flat" constitutive relations will be negligible provided the ratio shell-radius/thickness is of sufficiently large order. In the study of drawing of narrow, cylindrical "tethers" from liposomes it has been known for many years that it is necessary to use instead a constitutive law which explicitly describes a curved element in order to make sense of the mechanics; and indeed such tethers are generally of "thick-walled" proportions. In this paper we show that the proper constitutive relations for a curved element must also be used in the study, by means of shell equations, of the buckling of initially spherical thin-walled giant liposomes under exterior pressure: these involve the inclusion of what we call the "Mkappa" terms, which are not present in the standard "first-approximation" theory. We obtain analytical expressions for both the bifurcation buckling pressure and the slope of the post-buckling path, in terms of the dimensions and elastic constants of the lipid bi-layer, and also the initial state of bending moment in the vesicle. We explain physically how the initial bending moment can affect the bifurcation pressure, whereas it cannot in "first-approximation" theory. We use these results to map the conditions under which the vesicle buckles into an oblate, as distinct from a prolate ("rugby-ball") shape. Some of our results were obtained long ago by the use of energy methods; but our aim here has been to identify precisely what is lacking in "first-approximation" theory in relation to liposomes, and so to put the "shell equations" approach onto a firm footing in mechanics.

Model-Based Simulation of Durability of Materials and Structures

Insufficient long-term durability of civil engineering infrastructure, especially concrete structures, has been a major problem causing enormous economic loss to many countries. Concrete structures are plagued by reinforcement corrosion, cracking due to drying shrinkage and nonuniform creep, alkali-silica reaction, sulfate attack, carbonation, leaching, freeze-thaw, etc. Short-term resistance of concrete structures exposed to fire has become a major question for high-strength concrete in recent years. At the same time, it would be highly beneficial to devise ways of incorporating into concrete certain industrial wastes, such as blast furnace slag and crushed bottle glass from curbside recycling. A rational approach to all these problems requires realistic mathematical models and computer simulations of chemical reactions, diffusion processes for heat and transport of various chemical agents, expansive processes in the microstructure, and fracture and long-term deformations of the material. Since durability problems generally involve large uncertainties, stochastic modeling and predictions of statistical scatter are very important. The durability problems represent a major challenge for mathematical modeling. The diffusion processes involved are generally nonlinear and coupled. Along with the diffusion process, complex chemical reactions take place at reaction fronts as well as in the bulk. Characterization of reaction rates as functions of pressure, temperature, and concentrations can be accomplished only by comprehensive models, which must capture capillarity as well as adsorption phenomena on the surfaces of nanopores, calling for the use of surface thermodynamics aside from bulk thermodynamics. In addition, volume changes caused by chemical reactions, surface adsorption, etc., are sensitive to pressure, and the volumetric changes result in damage in the form of distributed microcracking. In the case of chemical reactions on surfaces, the reaction rates depend not only on pressure but also on such surface stress components as crystal growth pressure, which gives rise to reaction anisotropy. Ion transport gives rise to electric current and electrochemical cells. The damage localizes into macrocracks. This causes interaction of the diffusion-chemical reaction problem and ion transport with structural stress analysis, and calls for the use of energy methods of fracture mechanics. In fact, fracture mechanics is generally coupled with the diffusion and chemical reaction problems. Furthermore, all these phenomena exhibit considerable randomness, which makes it necessary to approach the problem probabilistically and take into account both the randomness of the process and the uncertainty in the properties of the material and the reacting chemical involved.

On the Original Publication of the General Canonical Functional of Linear Elasticity

The general canonical functional of linear elastostatics is associated with the names of Hu and Washizu, who published it independently in 1955. This note discusses how that functional, in a generalized four-field form, had been derived by B. M. Fraeijs de Veubeke in a 1951 technical report. This report presents five of the seven canonical functionals of elasticity. In addition to the general functional, it exhibits what is likely the first derivation of the strain-displacement dual of the Hellinger-Reissner functional. The tour of five variational principles takes only a relatively small portion of the report: 8 pages out of 56. The bulk is devoted to the use of energy methods for analysis of wing structures. The title, technology focus, and limited dissemination may account for the subsequent neglect of this original contribution to variational mechanics. [S0021-8936(00)00401-3]

Discrete Hamilton's equations for viscous compressible fluid dynamics

Lagrange’s and Hamilton’s equations are used extensively in numerical modeling of rigid body dynamics and continuum solid dynamics problems. The use of energy methods in viscous compressible flow problems has been by contrast rather limited, largely confined to the development of basic balance laws in partial differential equation form. However, finite element interpolation of the modeled flow field allows for the direct application of the discrete form of Hamilton’s equations to viscous compressible fluid dynamics in Eulerian frames. The resulting model is a true energy formulation, developed without reference to the partial differential balance equations which underlie conventional finite difference, weighted residual finite element, and finite volume methods.

On the use of energy methods for interpretation of results of single-fiber fragmentation experiments

_We consider fragmentation experiments as a set of experimental results for fiber break density as a function of applied strain. This paper explores the potential for using fracture mechanics or energy methods in interpreting fragmentation experiments. We found that energy does not control fiber fracture; instead, fiber fracture releases much more energy than required to fracture the fiber. The excess released energy can lead to other damage mechanisms such as interfacial debonding. By assuming that all the excess released energy causes interfacial debonding and balancing energy using the energy release rate for debonding, we were able to determine interfacial toughness from fragmentation experiments. A reliable determination of interfacial toughness requires prior knowledge of interphase stress-transfer properties, fiber failure properties, actual damage mechanisms, and the coefficient of friction at the interface.

Study on Vibration Characteristics of Stiffened Plates in Contact with Water by Use of Energy Method (1st Report)

The dynamic characteristics of stiffened rectangular plates in contact with water are studied. Numerical analysis is performed by use of an energy method where vibration modes of the stiffened plate and fluid velocity potential are developed using harmonic wave series. Interaction of added mass of water adjoining stiffened plates are investigated.

Energy methods for stability of bilinear systems with oscillatory inputs

AbstractA large body of recent literature has been devoted to the topic of motions of mechanical systems forced by oscillatory inputs (see, for example, References 7, 12, 15, 17 and 29). A common feature in most of this work (with Reference 7 being the exception) is that the results apply principally to kinematic problems, and the equations of motion do not involve drift terms. The main object of study in this paper is the class of bilinear control systems with oscillatory (periodic) inputs. We shall show that included in this class are models of mechanical system dynamics which are obtained through a process of reduction and linearization about operating points. In particular, we study the stability of such systems under high‐frequency, periodic forcing. The averaged potential is defined for linearizations of the systems on the (reduced) configuration space, and it is shown that stable motions of the forced system are associated with minimum values of this quantity. We use both classical averaging theory as well as a novel geometric argument to provide parallel but independent assessments of the use of the averaged potential in carrying out a stability analysis. A salient feature of the geometric approach is that we are able to justify the use of an energy‐like quantity to determine Lyapunov stability in conservative mechanical systems. This makes contact with a growing body of literature on the use of energy methods for stability and control design (e.g. References 7, 8, 18, 24, 26 and 27). We briefly describe the connection with previous work on the averaged potential.