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Clapeyron's Theorem (elasticity)
In the linear theory of elasticity Clapeyron's theorem states that the potential energy of deformation of a body, which is in equilibrium under a given load, is equal to half the work done by the external forces computed assuming these forces had remained constant from the initial state to the final state.Love, A.E.H., "A Treatise on the Mathematical Theory of Elasticity", 4th ed. Cambridge, 1927, p. 173 It is named after the French scientist Émile Clapeyron Benoît Paul Émile Clapeyron (; 26 January 1799 – 28 January 1864) was a French engineer and physicist, one of the founders of thermodynamics. Life Born in Paris, Clapeyron studied at the École polytechnique, graduating in 1818. He also studi .... For example, consider a linear spring with initial length ''L''0 and gradually pull on the spring until it reaches equilibrium at a length ''L''1 when the pulling force is ''F''. By the theorem, the potential energy of deformation in the spring is given by: :\fracF (L ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Elasticity (physics)
In physics and materials science, elasticity is the ability of a body to resist a distorting influence and to return to its original size and shape when that influence or force is removed. Solid objects will deform when adequate loads are applied to them; if the material is elastic, the object will return to its initial shape and size after removal. This is in contrast to ''plasticity'', in which the object fails to do so and instead remains in its deformed state. The physical reasons for elastic behavior can be quite different for different materials. In metals, the Crystal structure, atomic lattice changes size and shape when forces are applied (energy is added to the system). When forces are removed, the lattice goes back to the original lower energy state. For rubber elasticity, rubbers and other polymers, elasticity is caused by the stretching of polymer chains when forces are applied. Hooke's law states that the force required to deform elastic objects should be Prop ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Potential Energy
In physics, potential energy is the energy of an object or system due to the body's position relative to other objects, or the configuration of its particles. The energy is equal to the work done against any restoring forces, such as gravity or those in a spring. The term ''potential energy'' was introduced by the 19th-century Scottish engineer and physicist William Rankine, although it has links to the ancient Greek philosopher Aristotle's concept of Potentiality and Actuality, ''potentiality''. Common types of potential energy include gravitational potential energy, the elastic potential energy of a deformed spring, and the electric potential energy of an electric charge and an electric field. The unit for energy in the International System of Units (SI) is the joule (symbol J). Potential energy is associated with forces that act on a body in a way that the total Work (physics), work done by these forces on the body depends only on the initial and final positions of the b ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Benoît Paul Émile Clapeyron
Benoît () is a French male given name. It is less frequently spelled Benoist. The name comes from the Latin word , which means "blessed", equivalent in meaning to Bénédicte or the English name Benedict. A female derivative of the name is Benoîte. The personal name Benoît is to be distinguished from Benoit as a family name, which is usually spelled without the circumflex accent. Early form of the name was spelled with an "s" (Benoist), but as with many words in the French language, the "s" was eventually replaced with a circumflex accent over the "i". Benoît in other languages *Arabic: بندكتوس * Aragonese: Benedet * Asturian: Benitu *Basque: Beñat * Breton: Beneat * Catalan : Benet * Croatian : Benedikt * Danish: Benedikt, Bendt *Czech: Benedikt, Beneš * Dutch: Benedictus, Benoot * English: Benedict * Finnish: Benediktus, Pentti * Galician : Bieito * German : Benedikt *Greek: Βενέδικτος (Venediktos) * Hungarian: Benedek * Irish: Bennett * Italian: Bened ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Theorem Of Three Moments
In civil engineering and structural analysis Clapeyron's theorem of three moments (by Émile Clapeyron) is a relationship among the bending moments at three consecutive supports of a horizontal beam. Let ''A,B,C-D be the three consecutive points of support, and denote by- ''l'' the length of ''AB'' and l' the length of ''BC'', by ''w'' and w' the weight per unit of length in these segments. Then the bending moments M_A,\, M_B,\, M_C at the three points are related by:'' :M_A l + 2 M_B (l+l') +M_C l' = \frac w l^3 + \frac w' (l')^3. This equation can also be written as :M_A l + 2 M_B (l+l') +M_C l' = \frac + \frac where ''a''1 is the area on the Shear and moment diagram, bending moment diagram due to vertical loads on AB, ''a''2 is the area due to loads on BC, ''x''1 is the distance from A to the centroid of the bending moment diagram of beam AB, ''x''2 is the distance from C to the centroid of the area of the bending moment diagram of beam BC. The second equation is more gene ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Journal Of Elasticity
''Journal of Elasticity: The Physical and Mathematical Science of Solids'' is a peer-reviewed scientific journal covering all aspects of elasticity. It is published seven times a year by Springer Science+Business Media. The editor-in-chief is Roger Fosdick (University of Minnesota). Abstracting and indexing According to the ''Journal Citation Reports'', the journal had a 2020 impact factor of 2.085. The journal is abstracted and indexed in: * Academic OneFile * Astrophysics Data System * GeoRef * INSPEC * VINITI * Science Citation Index * Scopus Scopus is a scientific abstract and citation database, launched by the academic publisher Elsevier as a competitor to older Web of Science in 2004. The ensuing competition between the two databases has been characterized as "intense" and is c ... References External links * {{Official website, https://www.springer.com/physics/classical+continuum+physics/journal/10659 Springer Science+Business Media academic journals Acad ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Structural Analysis
Structural analysis is a branch of solid mechanics which uses simplified models for solids like bars, beams and shells for engineering decision making. Its main objective is to determine the effect of loads on physical structures and their components. In contrast to theory of elasticity, the models used in structural analysis are often differential equations in one spatial variable. Structures subject to this type of analysis include all that must withstand loads, such as buildings, bridges, aircraft and ships. Structural analysis uses ideas from applied mechanics, materials science and applied mathematics to compute a structure's deformations, internal forces, stresses, support reactions, velocity, accelerations, and stability. The results of the analysis are used to verify a structure's fitness for use, often precluding physical tests. Structural analysis is thus a key part of the engineering design of structures. [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Continuum Mechanics
Continuum mechanics is a branch of mechanics that deals with the deformation of and transmission of forces through materials modeled as a ''continuous medium'' (also called a ''continuum'') rather than as discrete particles. Continuum mechanics deals with ''deformable bodies'', as opposed to rigid bodies. A continuum model assumes that the substance of the object completely fills the space it occupies. While ignoring the fact that matter is made of atoms, this provides a sufficiently accurate description of matter on length scales much greater than that of inter-atomic distances. The concept of a continuous medium allows for intuitive analysis of bulk matter by using differential equations that describe the behavior of such matter according to physical laws, such as mass conservation, momentum conservation, and energy conservation. Information about the specific material is expressed in constitutive relationships. Continuum mechanics treats the physical properties of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
