| dbo:abstract |
In continuum mechanics, a compatible deformation (or strain) tensor field in a body is that unique tensor field that is obtained when the body is subjected to a continuous, single-valued, displacement field. Compatibility is the study of the conditions under which such a displacement field can be guaranteed. Compatibility conditions are particular cases of integrability conditions and were first derived for linear elasticity by Barré de Saint-Venant in 1864 and proved rigorously by Beltrami in 1886. In the continuum description of a solid body we imagine the body to be composed of a set of infinitesimal volumes or material points. Each volume is assumed to be connected to its neighbors without any gaps or overlaps. Certain mathematical conditions have to be satisfied to ensure that gaps/overlaps do not develop when a continuum body is deformed. A body that deforms without developing any gaps/overlaps is called a compatible body. Compatibility conditions are mathematical conditions that determine whether a particular deformation will leave a body in a compatible state. In the context of infinitesimal strain theory, these conditions are equivalent to stating that the displacements in a body can be obtained by integrating the strains. Such an integration is possible if the Saint-Venant's tensor (or incompatibility tensor) vanishes in a simply-connected body where is the infinitesimal strain tensor and For finite deformations the compatibility conditions take the form where is the deformation gradient. (en) Kompatibilitet är i mekanik en likformig deformation hos kroppar, på så sätt att de sitter ihop med varandra. Kompatibilitet brukar vara ett villkor i ekvationer i hållfasthetslära. Denna mekanikartikel saknar väsentlig information. Du kan hjälpa till genom att lägga till den. (sv) 应变协调性（英語：strain compatibility）在连续介质力学中是指使得物体的位移单值连续的应变张量所满足的条件。应变协调是可积条件的特殊情况。1864年，法国力学家圣维南最早得到了线弹性体的协调条件。1886年，意大利数学家贝尔特拉米对此进行了严格证明。 (zh) |
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http://www.imechanica.org/node/3786 https://web.archive.org/web/20100331022415/http:/www.ce.berkeley.edu/~coby/plas/pdf/book.pdf |
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| rdfs:comment |
Kompatibilitet är i mekanik en likformig deformation hos kroppar, på så sätt att de sitter ihop med varandra. Kompatibilitet brukar vara ett villkor i ekvationer i hållfasthetslära. Denna mekanikartikel saknar väsentlig information. Du kan hjälpa till genom att lägga till den. (sv) 应变协调性（英語：strain compatibility）在连续介质力学中是指使得物体的位移单值连续的应变张量所满足的条件。应变协调是可积条件的特殊情况。1864年，法国力学家圣维南最早得到了线弹性体的协调条件。1886年，意大利数学家贝尔特拉米对此进行了严格证明。 (zh) In continuum mechanics, a compatible deformation (or strain) tensor field in a body is that unique tensor field that is obtained when the body is subjected to a continuous, single-valued, displacement field. Compatibility is the study of the conditions under which such a displacement field can be guaranteed. Compatibility conditions are particular cases of integrability conditions and were first derived for linear elasticity by Barré de Saint-Venant in 1864 and proved rigorously by Beltrami in 1886. For finite deformations the compatibility conditions take the form (en) |
| rdfs:label |
Compatibility (mechanics) (en) Kompatibilitet (mekanik) (sv) 应变协调性 (zh) |
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