On variational formulations with rigid-body constraints for finite elasticity: Applications to 2D and 3D finite element simulations |
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| Affiliation: | 1. Institute of Vehicles, Warsaw University of Technology, Narbutta 84, 02-524 Warszawa, Poland;2. Institute of Machine Design Fundamentals, Warsaw University of Technology, Narbutta 84, 02-524 Warszawa, Poland;1. Department of Mechanics, School of Civil Engineering, Beijing Jiaotong University, Beijing 100044, PR China;2. College of Computer Science and Technology, Beijing Jiaotong University, Beijing 100044, PR China;1. Mechanics of Structures and Materials Laboratory, University Hadj Lakhdar, 05000 Batna, Algeria;2. Laboratoire de Mécanique de Lille UMR/CNRS 8107, Cité Scientique, 59655 Villeneuve d’Ascq, France |
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| Abstract: | We investigate a recently proposed variational principle with rigid-body constraints and present an extension of its implementation in three dimensional finite elasticity problems. Through numerical examples, we illustrate that the proposed variational principle with rigid-body constraints is applicable to both single field and mixed finite elements of arbitrary order and geometry, e.g. triangular/tetrahedral and quadrilateral/hexagonal elements, in two and three dimensions. Moreover, we demonstrate that, as compared to the commonly adopted approach of discretizing the rigid domains with standard finite elements, the proposed formulation requires neither discretization nor numerical integration in the interior of each rigid domain. As a comparative result, the variational formulation may reduce the total number of degrees of freedom of the resulting finite element system and provide improved accuracy. |
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| Keywords: | Variational principles Finite elastostatics Rigid inclusions 3D FEA |
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