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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 Benoît Clapeyron. 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_1 - L_0). The actual force increased from 0 to ''F'' during the deformation; the work done can be computed by integration in distance. Clapeyron's equation, which uses the final force only, may be puzzling at first, but is nevertheless true because i ... [...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 metal A metal (from Greek μέταλλον ''métallon'', "mine, quarry, metal") is a material that, when freshly prepared, polished, or fractured, shows a lustrous appearance, and conducts electricity and heat relatively well. Metals are typi ...s, 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 b ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Potential Energy
In physics, potential energy is the energy held by an object because of its position relative to other objects, stresses within itself, its electric charge, or other factors. Common types of potential energy include the gravitational potential energy of an object, the elastic potential energy of an extended spring, and the electric potential energy of an electric charge in an electric field. The unit for energy in the International System of Units (SI) is the joule, which has the symbol J. The term ''potential energy'' was introduced by the 19th-century Scottish engineer and physicist William Rankine, although it has links to Greek philosopher Aristotle's concept of Potentiality and Actuality, potentiality. Potential energy is associated with forces that act on a body in a way that the total work done by these forces on the body depends only on the initial and final positions of the body in space. These forces, that are called Conservative force, ''conservative forces'', can b ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Benoît Paul 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.Milton Kerker (1960Sadi Carnot and the Steam Engine Engineers Isis 51: 257–70 via JSTOR He also studied at École des mines. In 1820 he and Gabriel Lamé went to Saint Petersburg to teach and work at the school of public works there. He returned to Paris only after the Revolution of July 1830, supervising the construction of the first railway line connecting Paris to Versailles and Saint-Germain. The half brothers Stéphane Mony and Eugène Flachat collaborated in this project, which was financed by Adolphe d'Eichthal( fr), Rothschild, Auguste Thurneyssen, Sanson Davillier and the Péreire brothers. Clapeyron took his steam engine designs to England in 1836 to find a manufacturer and engaged Sharp, Roberts and Co. From 1844 to 1859 Cla ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Theorem Of Three Moments
In civil engineering and structural analysis Clapeyron's theorem of three moments 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 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 general as it does not require that the weight of eac ... [...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 Elsevier's abstract and citation database launched in 2004. Scopus covers nearly 36,377 titles (22,794 active titles and 13,583 inactive titles) from approximately 11,678 publishers, of which 34,346 are peer-reviewed journals in top-l ... References External links * {{Official website, https://www.springer.com/physics/classical+continuum+physics/journal/10659 Springer Science+Business Media academic journals Aca ... [...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 the physical structures and their components. In contrast to theory of elasticity, the models used in structure 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 mechanical behavior of materials modeled as a continuous mass rather than as discrete particles. The French mathematician Augustin-Louis Cauchy was the first to formulate such models in the 19th century. Explanation A continuum model assumes that the substance of the object fills the space it occupies. Modeling objects in this way ignores the fact that matter is made of atoms, and so is not continuous; however, on length scales much greater than that of inter-atomic distances, such models are highly accurate. These models can be used to derive differential equations that describe the behavior of such objects using physical laws, such as mass conservation, momentum conservation, and energy conservation, and some information about the material is provided by constitutive relationships. Continuum mechanics deals with the physical properties of solids and fluids which are independent of any particular coordinate ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
