Power Theory of Exchange and Money

Modern exchange theories model a large market, but do not explain single exchanges. This paper considers the phenomenon of single exchange and formulates the general exchange problem in the form of a system of two equations, subjective and objective. Subjective equilibrium is given by the Walras–Jevons marginal utility equation. Objective equilibrium equations by Walras and Jevons are averaged over all transactions in the market and can only give a rough general picture without explaining the specific price of an individual exchange. An exchange micro-condition must be found that, when averaged, will give the Walras market equilibrium macro-condition. The study of the internal structure of exchange leads to the need to consider power. The concept of generalized power is introduced. It is generalized power that serves as the primary comparable and measurable objective basis of exchange. The power theory of exchange provides the objective price-equation. It is demonstrated that money is a measure of generalized power in exchange and a certification of generalized power in subsequent exchanges. This methodology is based on an interdisciplinary analysis of an abstract exchange model in the form of a system of equations. The proposed theory is able to uniformly explain any exchange, including a single one, which is impossible with the existing theories of exchange.

3D Stress Analysis of Multilayered Functionally Graded Plates and Shells under Moisture Conditions

This paper presents the steady-state stress analysis of single-layered and multilayered plates and shells embedding Functionally Graded Material (FGM) layers under moisture conditions. This solution relies on an exact layer-wise approach; the formulation is unique despite the geometry. It studies spherical and cylindrical shells, cylinders, and plates in an orthogonal mixed curvilinear coordinate system (α, β, z). The moisture conditions are defined at the external surfaces and evaluated in the thickness direction under steady-state conditions following three procedures. This solution handles the 3D Fick diffusion equation, the 1D Fick diffusion equation, and the a priori assumed linear profile. The paper discusses their assumptions and the different results they deliver. Once defined, the moisture content acts as an external load; this leads to a system of three non-homogeneous second-order differential equilibrium equations. The 3D problem is reduced to a system of partial differential equations in the thickness coordinate, solved via the exponential matrix method. It returns the displacements and their z-derivatives as a direct result. The paper validates the model by comparing the results with 3D analytical models proposed in the literature and numerical models. Then, new results are presented for one-layered and multilayered FGM plates, cylinders, and cylindrical and spherical shells, considering different moisture contents, thickness ratios, and material laws.

Improving the technology for manufacturing hollow cylindrical parts for vehicles by refining technological estimation dependences

This paper shows that the technological preparation of production accounts for 20‒70 % of the total labor intensity of technical preparation. An important role belongs to the applied programs of finite-element modeling. However, such software packages often cannot be purchased by small-scale industrial enterprises for various reasons. Therefore, special empirical and analytical calculation models are used, which have proved to be quite effective in typical metal processing processes. Drawing a cylindrical hollow part was used as an example of the improved analytical dependence to calculate meridional tensile stresses. Existing analytical models of the process accounted for the bending moment through additional stresses. However, this approach only roughly described the deformation process. It was possible to refine the existing analytical dependences by introducing a term into the differential equilibrium equations that takes into consideration the bending moment that acts in the meridional direction when a workpiece passes the rounding on the matrix edge. Analysis of the obtained expression revealed that the bending of a workpiece gives rise to the stretching meridional stresses, which depend on the ratio of the squares of the thickness of the workpiece and the radius of the matrix rounding. The results of the estimation data from the numerical and theoretical models coincided for small values of the radius of the matrix rounding of 1‒2 mm, which confirms the adequacy of the analytical solution. In the numerical model, there is an extreme point where the tensile stresses have a minimum and, after it, begin to increase; this corresponds to the matrix rounding radius of 5 mm

Inter-Element Crack Propagation with High-Order Stress Equilibrium Element

The present contribution proposes a formulation based on the use of hybrid equilibrium elements (HEEs), for the analysis of inter-element delamination and fracture propagation problems. HEEs are defined in terms of quadratic stress fields, which strongly verify both the homogeneous and inter-element equilibrium equations and they are employed with interfaces, initially exhibiting rigid behavior, embedded at the elements’ sides. The interface model is formulated in terms of the same degrees of freedom of the HEE, without any additional burden. The cohesive zone model (CZM) of the extrinsic interface is rigorously developed in the damage mechanics framework, with perfect adhesion at the pre-failure condition and with linear softening at the post-failure regime. After a brief review, the formulation is computationally tested by simulating the behavior of a double-cantilever-beam with diagonal loads; the obtained numerical results confirm the accuracy and potential of the method.

DETAILS OF NORMAL SECTIONS STRENGTH CALCULATION OF FLEXIBLE REINFORCED CONCRETE STRUCTURES BY THE WOOD’S METHOD IN PC "LIRA SAPR"

Problem statement. The problem of realization of the calculation method of normal cross-sections strength of reinforced concrete constructions under flat bending, which is established in the current building codes of Ukraine, is considered. The main attention is paid to atypical and practically not considered calculation cases, typical for automated algorithms in the environment of SP "LIRA SAPR". The purpose of the article. Analysis of the feasibility of using the calculation method of current building codes with further development of recommendations, based on the specifics of computerized calculations. Methodology. Within the framework of the performed research, rectangular cross-sections of reinforced concrete structures with single and double reinforcement (provided a significant increase in the area of reinforcement of the compressed cross-sectional area) with variation of concrete classes, reinforcement coefficient and ratio of reinforcement areas were considered. The stress-strain diagrams of concrete and reinforcement are bilinear with characteristic values set for the first group of limit states. The character of change of cross-sections’ status diagrams "M - εc(1) " is investigated. Research results. It is found that for single-reinforced sections with decreasing reinforcement area there is a decrease of the value of deformation of the compressed fiber of concrete, which is used to find solutions for systems of nonlinear equilibrium equations of the deformation method. This leads to an increase of the execution time of calculations of the flat elements’ reinforcement by the Wood method. It is established that for sections with double reinforcement at relatively large values of the ratios of the reinforcement areas, the equilibrium of the section is at the maximum deformations of the compressed concrete fiber. Conclusions. An approach aimed at accelerating the calculation of sections with single reinforcement, which is based on the use of the relationship between the percentage (area) of reinforcement and the deformation of the most compressed fiber of the reinforced concrete element. Features of analytical algorithms for calculating the selected sections are taken into account by implementing this technique in the PC "LIRA SAPR", optimization and acceleration of automated algorithms for calculating reinforced concrete structures.

Treatise on Sustainable Infrastructure Construction: Green Composites, Cross Laminated/Mass Timber, Wood Truss Connectors, Nondestructive Technologies, Health Assessment and Monitoring: Utility Poles and Geofoam

The understanding of the engineering performance of green laminated composites is necessary to the design of load bearing components in building and infrastructure construction, and packaging applications. These components are made of outer thin laminae called skins or faces and a thick inner layer called core. The use of bonding is unavoidable in the assembling of these composite products. Like all materials, the bonding materials have finite mechanical properties, e.g. stiffness, but when used in the literature, they are assumed perfectly rigid. That is an unrealistic assumption. Our analytical solutions change this assumption by using the real properties of bonding. In general, the analytical formulations are based on the equilibrium equations of forces, the compatibility of interlaminar stresses and deformation, and the geometrical conditions of the panels. Once solutions are obtained, the next step is to evaluate them. The numerical evaluations proved that perfect rigid bonding in laminated composites greatly underestimates the true performance. At low values of adhesive stiffness, the serviceability is multiple orders of magnitude of that at high values. The logical question is thus: what constitutes perfect bonding? The answer to this question lies in the core-to-adhesive stiffness. The lower the ration is the higher the error in using the rigid-bond theories. It is worth noting that green-composites in this chapter refer to components made of traditional materials such as wood, in addition to newly developed bio-based and bio-degradable and bio-based composites, made of renewable resources. In addition, bonding and adhesive are used interchangeably.

Behavior of solution of the elasticity problem for a radial inhomogeneous cylinder with small thickness

A non-axisymmetric problem of the theory of elasticity for a radial inhomogeneous cylinder of small thickness is studied. It is assumed that the elastic moduli are arbitrary positive piecewise continuous functions of a variable along the radius. Using the method of asymptotic integration of the equations of the theory of elasticity, based on three iterative processes, a qualitative analysis of the stress-strain state of a radial inhomogeneous cylinder is carried out. On the basis of the first iterative process of the method of asymptotic integration of the equations of the theory of elasticity, particular solutions of the equilibrium equations are constructed in the case when a smooth load is specified on the lateral surface of the cylinder. An algorithm for constructing partial solutions of the equilibrium equations for special types of loads, the lateral surface of which is loaded by forces polynomially dependent on the axial coordinate, is carried out. Homogeneous solutions are constructed, i.e., any solutions of the equilibrium equations that satisfy the condition of the absence of stresses on the lateral surfaces. It is shown that homogeneous solutions are composed of three types: penetrating solutions, solutions of the simple edge effect type, and boundary layer solutions. The nature of the stress-strain state is established. It is found that the penetrating solution and solutions having the character of the edge effect determine the internal stress-strain state of a radial inhomogeneous cylinder. Solutions that have the character of a boundary layer are localized at the ends of the cylinder and exponentially decrease with distance from the ends. These solutions are absent in applied shell theories. Based on the obtained asymptotic expansions of homogeneous solutions, it is possible to carry out estimates to determine the range of applicability of existing applied theories for cylindrical shells. Based on the constructed solutions, it is possible to propose a new refined applied theory.

Free Vibration of Annular Circular Plates Based on Higher-Order Shear Deformation Theory: A Spline Approximation Technique

This research is based on higher-order shear deformation theory to analyse the free vibration of composite annular circular plates using the spline approximation technique. Equilibrium equations are derived, and differential equations in terms of displacement and rotational functions are obtained. Cubic or quantic spline is used to approximate the displacement and rotational functions depending upon the order of these functions. A generalized eigenvalue problem is obtained and solved numerically for eigenfrequency parameter and associated eigenvector of spline coefficients. Frequency of annular circular plates with different numbers of layers with each layer consisting of different materials is analysed. The effect of geometric and material parameters on frequency value is investigated for simply supported condition. A comparative study with existing results narrates the validity of the present results. Graphs and tables depict the obtained results. Some figures and graphs are drawn by using Autodesk Maya and Matlab software.

Theoretical background for simulation of physical processes in the interfacial layer “solid-liquid”

The paper shows a modification of the quasi-thermodynamic approach to simulation of the interfacial layer from conditions of its mechanical equilibrium. The anisotropy of the interfacial stress tensor is represented as the sum of the ball and deviator parts, where the ball part defines the pressure in the medium and the deviator part forms the components responsible for the liquid surface tension. Obtaining a closed system of equilibrium equations was possible taking into account evaporation from free surface of liquid. The result is a simple expression for determining the thickness of the interfacial layer.

Power Theory of Exchange and Money

Modern exchange theories model a large market, but do not explain single exchange. The paper considers the phenomenon of single exchange and formulates the general exchange problem in the form of a system of two equations, subjective and objective. Subjective equilibrium is given by the Walras-Jevons marginal utility equation. Objective equilibrium equations by Walras and Jevons are averaged over all transactions in the market and can only give a rough general picture without explaining the specific price of an individual exchange. An exchange micro-condition must be found that, when averaged, will give the Walras market equilibrium macro-condition. The study of the internal structure of exchange leads to the need to consider power. The concept of generalized power is introduced. It is generalized power that serves as the primary comparable and measurable objective basis of exchange. The power theory of exchange provides the objective price-equation. It is demonstrated that money is a measure of generalized power in exchange and a certification of generalized power in subsequent exchanges. The proposed theory is able to uniformly explain any exchange, including a single one, which is impossible with the existing theories of exchange.