Stress–strain analysisStress–strain analysis (or stress analysis) is an engineering discipline that uses many methods to determine the stresses and strains in materials and structures subjected to forces. In continuum mechanics, stress is a physical quantity that expresses the internal forces that neighboring particles of a continuous material exert on each other, while strain is the measure of the deformation of the material. In simple terms we can define stress as the force of resistance per unit area, offered by a body against deformation.
Stress–strain curveIn engineering and materials science, a stress–strain curve for a material gives the relationship between stress and strain. It is obtained by gradually applying load to a test coupon and measuring the deformation, from which the stress and strain can be determined (see tensile testing). These curves reveal many of the properties of a material, such as the Young's modulus, the yield strength and the ultimate tensile strength. Generally speaking, curves representing the relationship between stress and strain in any form of deformation can be regarded as stress–strain curves.
Infinitesimal strain theoryIn continuum mechanics, the infinitesimal strain theory is a mathematical approach to the description of the deformation of a solid body in which the displacements of the material particles are assumed to be much smaller (indeed, infinitesimally smaller) than any relevant dimension of the body; so that its geometry and the constitutive properties of the material (such as density and stiffness) at each point of space can be assumed to be unchanged by the deformation.
Economic equilibriumIn economics, economic equilibrium is a situation in which economic forces such as supply and demand are balanced and in the absence of external influences the (equilibrium) values of economic variables will not change. For example, in the standard text perfect competition, equilibrium occurs at the point at which quantity demanded and quantity supplied are equal. Market equilibrium in this case is a condition where a market price is established through competition such that the amount of goods or services sought by buyers is equal to the amount of goods or services produced by sellers.
Stress (mechanics)In continuum mechanics, stress is a physical quantity that describes forces present during deformation. An object being pulled apart, such as a stretched elastic band, is subject to tensile stress and may undergo elongation. An object being pushed together, such as a crumpled sponge, is subject to compressive stress and may undergo shortening. The greater the force and the smaller the cross-sectional area of the body on which it acts, the greater the stress. Stress has units of force per area, such as newtons per square meter (N/m2) or pascal (Pa).
General equilibrium theoryIn economics, general equilibrium theory attempts to explain the behavior of supply, demand, and prices in a whole economy with several or many interacting markets, by seeking to prove that the interaction of demand and supply will result in an overall general equilibrium. General equilibrium theory contrasts with the theory of partial equilibrium, which analyzes a specific part of an economy while its other factors are held constant.
Mechanical equilibriumIn classical mechanics, a particle is in mechanical equilibrium if the net force on that particle is zero. By extension, a physical system made up of many parts is in mechanical equilibrium if the net force on each of its individual parts is zero. In addition to defining mechanical equilibrium in terms of force, there are many alternative definitions for mechanical equilibrium which are all mathematically equivalent. In terms of momentum, a system is in equilibrium if the momentum of its parts is all constant.
Competitive equilibriumCompetitive equilibrium (also called: Walrasian equilibrium) is a concept of economic equilibrium, introduced by Kenneth Arrow and Gérard Debreu in 1951, appropriate for the analysis of commodity markets with flexible prices and many traders, and serving as the benchmark of efficiency in economic analysis. It relies crucially on the assumption of a competitive environment where each trader decides upon a quantity that is so small compared to the total quantity traded in the market that their individual transactions have no influence on the prices.
Earth ellipsoidAn Earth ellipsoid or Earth spheroid is a mathematical figure approximating the Earth's form, used as a reference frame for computations in geodesy, astronomy, and the geosciences. Various different ellipsoids have been used as approximations. It is a spheroid (an ellipsoid of revolution) whose minor axis (shorter diameter), which connects the geographical North Pole and South Pole, is approximately aligned with the Earth's axis of rotation.
Planetary coordinate systemA planetary coordinate system (also referred to as planetographic, planetodetic, or planetocentric) is a generalization of the geographic, geodetic, and the geocentric coordinate systems for planets other than Earth. Similar coordinate systems are defined for other solid celestial bodies, such as in the selenographic coordinates for the Moon. The coordinate systems for almost all of the solid bodies in the Solar System were established by Merton E.
Chemical equilibriumIn a chemical reaction, chemical equilibrium is the state in which both the reactants and products are present in concentrations which have no further tendency to change with time, so that there is no observable change in the properties of the system. This state results when the forward reaction proceeds at the same rate as the reverse reaction. The reaction rates of the forward and backward reactions are generally not zero, but they are equal. Thus, there are no net changes in the concentrations of the reactants and products.
Equilibrium constantThe equilibrium constant of a chemical reaction is the value of its reaction quotient at chemical equilibrium, a state approached by a dynamic chemical system after sufficient time has elapsed at which its composition has no measurable tendency towards further change. For a given set of reaction conditions, the equilibrium constant is independent of the initial analytical concentrations of the reactant and product species in the mixture.
SizeSize in general is the magnitude or dimensions of a thing. More specifically, geometrical size (or spatial size) can refer to linear dimensions (length, width, height, diameter, perimeter), area, or volume. Size can also be measured in terms of mass, especially when assuming a density range. In mathematical terms, "size is a concept abstracted from the process of measuring by comparing a longer to a shorter". Size is determined by the process of comparing or measuring objects, which results in the determination of the magnitude of a quantity, such as length or mass, relative to a unit of measurement.
Opacity (optics)Opacity is the measure of impenetrability to electromagnetic or other kinds of radiation, especially visible light. In radiative transfer, it describes the absorption and scattering of radiation in a medium, such as a plasma, dielectric, shielding material, glass, etc. An opaque object is neither transparent (allowing all light to pass through) nor translucent (allowing some light to pass through). When light strikes an interface between two substances, in general some may be reflected, some absorbed, some scattered, and the rest transmitted (also see refraction).
Advanced PlacementAdvanced Placement (AP) is a program in the United States and Canada created by the College Board. AP offers undergraduate university-level curricula and examinations to high school students. Colleges and universities in the US and elsewhere may grant placement and course credit to students who obtain qualifying scores on the examinations. The AP curriculum for each of the various subjects is created for the College Board by a panel of experts and college-level educators in that academic discipline.
Brain sizeThe 'size of the brain' is a frequent topic of study within the fields of anatomy, biological anthropology, animal science and evolution. Brain size is sometimes measured by weight and sometimes by volume (via MRI scans or by skull volume). Neuroimaging intelligence testing can be used to study the volumetric measurements of the brain. Regarding "intelligence testing", a question that has been frequently investigated is the relation of brain size to intelligence.
Rank–size distributionRank–size distribution is the distribution of size by rank, in decreasing order of size. For example, if a data set consists of items of sizes 5, 100, 5, and 8, the rank-size distribution is 100, 8, 5, 5 (ranks 1 through 4). This is also known as the rank–frequency distribution, when the source data are from a frequency distribution. These are particularly of interest when the data vary significantly in scales, such as city size or word frequency.
Particle sizeParticle size is a notion introduced for comparing dimensions of solid particles (flecks), liquid particles (droplets), or gaseous particles (bubbles). The notion of particle size applies to particles in colloids, in ecology, in granular material (whether airborne or not), and to particles that form a granular material (see also grain size). Particle size measurement There are several methods for measuring particle size and particle size distribution. Some of them are based on light, other on ultrasound, or electric field, or gravity, or centrifugation.
Sample size determinationSample size determination is the act of choosing the number of observations or replicates to include in a statistical sample. The sample size is an important feature of any empirical study in which the goal is to make inferences about a population from a sample. In practice, the sample size used in a study is usually determined based on the cost, time, or convenience of collecting the data, and the need for it to offer sufficient statistical power.
N-sphereIn mathematics, an n-sphere or a hypersphere is a topological space that is homeomorphic to a standard n-sphere, which is the set of points in (n + 1)-dimensional Euclidean space that are situated at a constant distance r from a fixed point, called the center. It is the generalization of an ordinary sphere in the ordinary three-dimensional space. The "radius" of a sphere is the constant distance of its points to the center. When the sphere has unit radius, it is usual to call it the unit n-sphere or simply the n-sphere for brevity.
