Grioli's theorem: rotation minimizing deformation
| Autor: | Martti Mikkola |
|---|---|
| Přispěvatelé: | Rakennustekniikan laitos, Aalto-yliopisto, Aalto University |
| Rok vydání: | 2020 |
| Předmět: |
Physics
Timoshenko beam theory Biot number Plane (geometry) Mechanical Engineering Mathematical analysis Infinitesimal strain theory 02 engineering and technology Deformation (meteorology) 021001 nanoscience & nanotechnology Displacement (vector) Grioli's minimization theorem Simple shear 020303 mechanical engineering & transports Emeritusprofessori Tapio Salmen muistonumero 0203 mechanical engineering Mechanics of Materials rotaatiotensori Finite strain theory rotation tensor suuret siirtymät 0210 nano-technology large deformation Griolin minimointiteoreema |
| Zdroj: | Rakenteiden Mekaniikka |
| ISSN: | 1797-5301 0783-6104 |
| DOI: | 10.23998/rm.77296 |
| Popis: | Artikkelissa on tarkasteltu Griolin teoreemaa, jonka mukaan deformaatiogradientin mukainen rotaatiotensori minimoi tapahtuvan muodonmuutoksen. Teoreema on esitetty sekä pienten että suurten siirtymien tapauksessa. Teoreemaa on demonstroitu muutamien yksinkertaisten esimerkkien avulla. In this paper, the celebrated theorem of G. Grioli is considered according to which the rotation factor in the polar decomposition of the deformation gradient minimizes Biot's strain tensor. The theorem is demonstrated by applications to some cases in large displacement theory: simple shear, plane deformation, Euler-Bernoulli and Timoshenko beam theories, and bar element in space. An interpretation could be that the material behaves economically: first occurs the part of deformation which does not induce any stresses and then the material starts to resist the deformation. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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