Solution Of Equilibrium Equations Research Articles

Retraction Note: New applications of the existence of solutions for equilibrium equations with Neumann type boundary condition

The Editors-in-Chief have retracted this article [1] because it shows evidence of both authorship and peer review manipulation. In addition, the identity of the corresponding author could not be verified: Universidad Austral confirmed that Tanriver Ülker was never affiliated to this institution.The authors have not responded to any correspondence regarding this retraction.

RETRACTED ARTICLE: New applications of the existence of solutions for equilibriumequations with Neumann type boundary condition

Using the existence of solutions for equilibrium equations with aNeumann type boundary condition as developed by Shi and Liao (J. Inequal. Appl.2015:363, 2015), we obtain the Rieszintegral representation for continuous linear maps associated with additiveset-valued maps with values in the set of all closed bounded convex non-emptysubsets of any Banach space, which are generalizations of integral representationsfor harmonic functions proved by Leng, Xu and Zhao (Comput. Math. Appl. 66:1-18,2013). We also deduce the Rieszintegral representation for set-valued maps, for the vector-valued maps ofDiestel-Uhl and for the scalar-valued maps of Dunford-Schwartz.

Tow Forces for Emergency Towing of Containerships

For a series of five containerships of differing capacities (707, 3400, 5300, 14,000, and 18,000 TEU), systematic computations were performed to estimate the tow force required in an emergency. Time-average ship positions with respect to the given waves, wind, and current directions and the corresponding time-average forces were considered. Current speed was considered to include also towing speed. Directionally aligned as well as not aligned wind and waves were investigated. Wave height, wind speed, and wave and wind direction relative to current direction were systematically varied. Wind speeds based on the Beaufort wind force scale corresponded to significant wave heights for a fully arisen sea. Waves were assumed to be irregular short-crested seaways described by a Joint North Sea Wave Observation Project (JONSWAP) spectrum with peak parameter 3.3 and cosine squared directional spreading. For each combination of current speed, wave direction, significant wave height, and peak wave period, the required tow force and the associated drift angle were calculated. Tow force calculations were based on the solution of equilibrium equations in the horizontal plane. A Reynolds-Averaged Navier–Stokes (RANS) solver obtained current and wind forces and moments; and a Rankine source-patch method, drift forces and moments in waves. Tow forces accounted for steady (calm-water) hydrodynamic forces and moments, constant wind forces and moments, and time-average wave drift forces and moments. Rudder and propeller forces and towline forces were neglected.

Apparatus and applications of a generalized Fourier method for transversally isotropic bodies bounded by a plane and a paraboloid of rotation

We construct new basic solutions of equilibrium equations of a transversally isotropic paraboloid of rotation and obtain summation theorems that express them in terms of cylindrical solutions for a half-space and vice versa. The problem of the action of an axial concentrated force on an elastic transversally isotropic half-space with a fixed inclusion in the form of a paraboloid of rotation is investigated. The problem is solved by a generalized Fourier method and is reduced to a system of integral equations with a Fredholm operator on the condition that intersections of the boundaries of the half-space and inclusion are absent. We consider dependences of stresses on the shape of the paraboloidal inclusion and on the distance between the boundary surfaces and analyze the results of the calculation.

Universal solutions for isotropic incompressible micropolar solids

The deformations that satisfy the equilibrium equations for an arbitrary material from a certain class in the absence of mass loadings are called the universal deformations (universal solutions) for this class of materials in continuum mechanics. The significance of universal solutions consists in the fact that they can be used efficiently for the experimental determination of equations of state of a material. In the nonlinear theory of elasticity of simple (nonpolar) materials [1– 5], five families of inhomogeneous deformations, which are the universal solutions of equilibrium equa� tions for homogeneous incompressible isotropic sol� ids, are known. In this work, we found the universal finite deforma� tions for incompressible isotropic micropolar materi� als, i.e., solids with moment stresses and rotation interaction of particles. The model of the micropolar medium (the Cosserat continuum) is applied to the description of composites, polymers, and also nano�

Gas geochemistry for the Los Azufres (Michoacán) geothermal reservoir, México

Gas data of the Los Azufres geothermal field were analyzed using a method based on equilibrium of the Fischer- Tropsch (FT) reaction: CH4 + 2H2O = 4H2 +CO2 and on the combined pyrite-hematite-magnetite (HSH2) reactions: 5/4 H2 +3/2 FeS2 +3/4 Fe2O3 + 7/4 H2O = 3 H2S +Fe3O4 in order to estimate reservoir temperature and excess steam. The solution of equilibrium equations produces a grid (FT-HSH2). This method is suitable for reservoirs with relatively high H2S but low H2 and NH3 concentrations in the fluid as is the case of the Los Azufres well discharges. Reservoir temperature and reservoir excess steam values were estimated for initial and present conditions in representative wells of the field to study the evolution of fluids, because of exploitation and waste fluids reinjection. This method was very useful in estimating reservoir temperatures in vapor wells, while in two-phase wells it was found that as the well produces a smaller fraction of water, the reservoir temperature estimation agrees qualitatively with results from cationic or silica geothermometers. For liquid-dominated wells the reservoir temperature estimations agree with temperatures obtained from the well simulator WELFLO. This indicates that FT-HSH2 results provide the temperature of the fluid entering the well where the last equilibrium occurs. Results show a decrease in reservoir temperatures in the southern zone of the field where intensive reinjection takes place. With exploitation, it was also noted that the deep liquid phase in the reservoir is changing to two-phase increasing the reservoir steam fraction and the non-condensable gases in well discharges.

Material forces and phase transitions in elasticity

A computational scheme for the determination of the interface in a strain-induced phase-transition problem for an elastic bar is proposed. The algorithm is based on the material force notion and more specifically on the simultaneous solution of equilibrium equations for the physical and material forces. The weak form of both equations is derived with the aid of a variational principle that accounts for the variations of the dependent and the independent variables. The whole scheme concludes in a nonlinear algebraic system which is numerically solved by the Newton method. The numerical results thus derived seem to be quite encouraging for further application of the concept of material forces in computations related to phase transition problems. The austenite–martensite transformation could be a possible application of the proposed model.

THERMAL STRESSES AROUND AN INSULATED BARRIER

The main interest in this study is to determine the thermal stresses around an insulated barrier due to constant heat flux in a homogeneous semi-infinite medium. Reducing the diffusion equation to a singular integral equation, the temperature distribution around the insulated barrier is obtained by defining an unknown function, the so-called density function, as a series expansion of orthogonal polynomials. After the temperature distribution is obtained then it can be used in equilibrium equations as an input function to find thermal stresses for different thickness parameters. Using the solution of equilibrium equations one can also obtain displacements around an insulated barrier as a secondary interest of the problem.

The vibrations of rectangular plates rib-reinforced in one direction

The exact solution of equilibrium equations is found on the assumption that ribs are symmetrical about the middle plane of a plate and work in bending from this plane. The necessary and sufficient conditions of the applicability of the theory of structurally orthotropic shells to the solution of the problem are formulated.

Incompatible mode method for finite deformation quasi-incompressible elasticity

In this work we develop a geometrically nonlinear version of the method of incompatible modes, suitable for quasi-incompressible finite deformation hyperelasticity. The proposed method is featuring the principal axis representation of the theory, facilitating the choice of the strain energy function (in terms of the principal stretches) and simplifying the stress computation. The choice of the spatial Cauchy-Green strain measure, leading to a very sparse structure of the strain-displacement operators, and the operator split solution of equilibrium equations, leading to reduced secondary storage requirements, further increase the computational efficiency. A set of numerical examples is used to illustrate a robust performance of the constructed plane strain element with a single incompatible mode in quasi-incompressible deformation patterns.

On accuracy, stability and efficiency of the Newmark method with incomplete solution by multilevel methods

The use of an incomplete iterative solver aimed at approximating solution of equilibrium equation resulting from the finite element semidiscretization in space is studied. Our approach is motivated by the fact that: (i) the effective stiffness matrix is well conditioned because of the stabilizing effect of the diagonally dominated mass matrix, (ii) the dominance of the temporal error in implicit computations with large step size, and (iii) the utilization of a class of iterative methods where the primary computational cost is associated with a construction of the preconditioner rather than with an iterative process. One of the primary goals of the present manuscript is to control the temporal and the equilibrium solution errors and to give their a posteriori estimates. Numerical experiments reveal that the computational cost of three cycles conducted with the Generalized Aggregation Multilevel solver [1–4] is comparable to a single back substitution on the source grid, while the resulting equilibrium solution error is negligible compared with the local temporal error. Copyright © 1999 John Wiley & Sons, Ltd.

The R- and H-Defects in a Cylindrical Capillary

Having based on well-known limiting cases, we constructed the approximate solutions of equilibrium equations for nematic liquid crystals for the radial (R) and hyperbolic (H) point defects in a capillary with normal boundary conditions. On the contrary to the point of view accepted before we have to claim that because of equivalence of both directions of “escaping” along the capillary axis the bound R- and H-defects occurred instead of non-singular disclination. The comparative analysis of elastic fields of free and bound R- and H-defects has been given. It has been shown that the boundaries do not influence on topology of the elastic fields and far from the singularities the structure coincides with the structure of a non-singular disclination. It has been obtained that the difference between the energies of the R- and H-defects in the bound state is half as much as the correspondent value for the free defects.

Modeling the nonlinear seismic behavior of cable-stayed bridges with passive control bearings

A three-dimensional nonlinear finite element model is developed for cable-stayed bridges under static and dynamic loadings based on the total Lagrangian formulation. The model can account for the large displacements that are usually associated with extended in plane contemporary cable-supported structures. A four-node isoparametric cable element is introduced and proposed for the idealization of cables. The element can predict both in-plane and out-of-plane responses. In addition, the cable element takes into consideration the effect of pretension which is one of the features of cable-stayed bridges. Four-node isoparametric beam elements are proposed to model the deck and towers. The element is formulated for general symmetric sections including multi-vent box sections, plate sections and cut-off corner tower sections. The introduced beam element handles large displacements, shear deformations and curved configurations. However, the main advantage of the proposed element is the reduction of degrees of freedom associated with some deck types such as the box sections where one beam element can represent the main girder. Moreover, the internal nodes for both beam and cable elements can be eliminated during the solution of equilibrium equations; however the response can be retrieved at their locations without approximations or loss of accuracy. Furthermore, the eccentric nature of cable-deck and cable-tower connections can be considered by a proper transformation. The control and improvement of the vibrations of cable-stayed bridges necessitates the inclusion of energy dissipation devices at certain locations. The problem becomes difficult to solve with the very large number of degrees of freedom associated with accurate modeling of the bearings and the bridge components. A simplified model is proposed for the dissipation devices in which a two-node element is introduced for a stiffness-type analysis approach. The element is capable of withstanding axial and shear forces. The parameters that control the hysteretic behavior of the element can be estimated out of sophisticated analytical models and/or experimental results. In addition, guidelines based on simplified assumptions are presented for approximating the force-displacement curve of some devices for preliminary analysis and design. The investigation of an appropriate passive control system started with exploring the ideology of seismic isolation by considering a two-dimensional model for a single-plane harp-type cable-stayed bridge. In order to have more realistic insight into the usefulness of passive energy dissipation devices, two different cable-stayed bridges models with double-plane harp and fan-type cables are presented for the numerical analysis. Significant reduction in earthquake induced forces along the bridge can be achieved with the energy dissipation devices as compared to the case of using conventional connections.

Brillouin limit in cylinders and torus with shaped cross sections

The Brillouin limit for non-neutral plasma is calculated in cylindrical and toroidal traps with shaped cross section. In particular, the effect of ellipticity and D-shaping is considered. Perturbative solutions of equilibrium equations are constructed in powers of inverse aspect ratio. It is found that ellipticity and D-shaping both enhance the storage efficiency and Brillouin limit of cylindrical traps. In case of toroidal traps it is found that the ellipticity enhances the storage efficiency. The D-shaping also enhances the storage efficiency provided the vertex of the D shape is toward the major axis.

Solution of equilibrium equations in the force method: A compact band scheme for underdetermined linear systems

This paper presents a compact storage scheme for the (rectangular) equilibrium matrix of a general structural assembly, and a simple yet efficient algorithm for solving the system of equilibrium equations without ever exceeding the number of coefficients stored at the beginning. An implementation of the algorithm, written in C, is given in the Appendix.

General solution of equilibrium equations for plates made of materials with a thin-layer structure

General solution of equilibrium equations for plates made of materials with a thin-layer structure

The Carbonate Chemistry of Green Lake, Jamesville, NYa

ABSTRACT The temporal and vertical distributions of inorganic carbon and related forms were assessed for the mixolimmion of Green Lake, Jamesville, NY, based on a biweekly monitoring program conducted for a 14 month period. The daily time structure of the distributions was delineated for a single diurnal cycle. Attendant [H2CO3*] ([H2CO3] + [CO2(aq)]) and calcite equilibrium conditions were determined through solution of equilibrium equations, adjusted for temperature and ionic-strength. Inorganic carbon equilibrium conditions within the ion-rich chemocline/monimollmnion were evaluated with the aid of a computer model, which incorporated ion-pair interactions, utilizing data obtained from a single sampling. A seasonal cycle was demonstrated for the inorganic carbon species within the lake's mixolimnion which was temporally consistent with the system's thermal and productivity transformations. Dramatic differences in carbonate chemistry developed between the epilmnion and hypolimnion during summer stratification. The epilimnion was highly supersaturated with respect to calcite throughout summer stratification. Minimum H2CO3* saturation was observed for the same period. These seasonal variations in equilibrium conditions, as well as diurnal variations, were mediated largely through temporal changes in pH. Factoral analysis of the temporal trends with respect to the influencing factors of temperature, ionic strength, and CO2 metabolism, indicates they were largely a result of photosynthetic consumption of CO2. Precipitation of calcite within the upper 5 m during summer was implied by the continuing decrease in [Ca+2] during the calcite supersaturation period. Seventy-five percent of the calcite formed is estimated to reach either the mixolimnic sediments or the monimolimnion. Most of the calcite entering the monimolimnion would probably reach the sediments, since the layer is nearly saturated or supersaturated with the mineral.

General solution of equilibrium equations of plate flexure in steady temperature field

General solution of equilibrium equations of plate flexure in steady temperature field