| 1. |
- Ask, Anna, et al.
(författare)
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Inverse-motion-based form finding for quasi-incompressible finite electroelasticity
- 2013
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Ingår i: International Journal for Numerical Methods in Engineering. - : Wiley. - 1097-0207 .- 0029-5981. ; 94:6, s. 554-572
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Tidskriftsartikel (refereegranskat)abstract
- This work deals with inverse-motion-based form finding for electroelasticity. The inverse motion problem is formulated for the electroelastic case, and the resulting equations are implemented within a finite element framework. A four-field variational approach is adopted, taking into consideration the typically incompressible behavior of the elastomer materials commonly used in electromechanical applications. By means of numerical simulations, the inverse-motion-based form finding makes it possible to design the referential configuration so that a given set of loads and boundary conditions results in a prespecified deformed configuration. The computational finite element framework established in this work allows for such numerical simulations and testing and thereby the possibility to improve the design and accuracy in electroelastic applications such as grippers, sensors, and seals.
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| 2. |
- Becker, R., et al.
(författare)
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A hierarchical NXFEM for fictitious domain simulations
- 2011
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Ingår i: International Journal for Numerical Methods in Engineering. - : Wiley. - 0029-5981 .- 1097-0207. ; 86:4-5, s. 549-559
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Tidskriftsartikel (refereegranskat)abstract
- We suggest a fictitious domain method, based on the Nitsche XFEM method of (Comput. Meth. Appl. Mech. Engrg 2002; 191: 5537-5552), that employs a band of elements adjacent to the boundary. In contrast, the classical fictitious domain method uses Lagrange multipliers on a line (surface) where the boundary condition is to be enforced. The idea can be seen as an extension of the Chimera method of (ESAIM: Math. Model Numer. Anal. 2003; 37: 495-514), but with a hierarchical representation of the discontinuous solution field. The hierarchical formulation is better suited for moving fictitious boundaries since the stiffness matrix of the underlying structured mesh can be retained during the computations. Our technique allows for optimal convergence properties irrespective of the order of the underlying finite element method.
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| 3. |
- Bengzon, Fredrik, 1978-, et al.
(författare)
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Adaptive finite element approximation of multiphysics problems : a fluid structure interaction model problem
- 2010
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Ingår i: International Journal for Numerical Methods in Engineering. - : Wiley. - 0029-5981 .- 1097-0207. ; 84:12, s. 1451-1465
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Tidskriftsartikel (refereegranskat)abstract
- We consider computation of the displacement of an elastic object immersed into a viscous incompressible flow. For simplicity, we assume that the mechanics of the solid is governed by linear elasticity and the motion of the fluid by the Stokes equation. We derive an a posteriori error estimate for this one way coupled problem using duality techniques. Based on these estimates we develop an adaptive algorithm that automatically constructs a suitable adapted mesh for the fluid and solid domains given goal quantities specified on the solid problem.
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| 4. |
- Compere, Gaetan, et al.
(författare)
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A mesh adaptation framework for dealing with large deforming meshes
- 2010
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Ingår i: International Journal for Numerical Methods in Engineering. - : Wiley. - 0029-5981 .- 1097-0207. ; 82:7, s. 843-867
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Tidskriftsartikel (refereegranskat)abstract
- In this paper. we identify and propose solutions for several issues encountered when designing a mesh adaptation package, such as mesh-to-mesh projections and mesh database design, and we describe an algorithm to integrate a mesh adaptation procedure in a physics solver. The open-source MAdLib package is presented as an example of such a mesh adaptation library. A new technique combining global node repositioning and mesh optimization in order to perform arbitrarily large deformations is also proposed. We then present several test cases to evaluate the performances of the proposed techniques and to show their applicability to fluid-structure interaction problems with arbitrarily large deformations. Copyright (C) 2009 John Wiley & Sons, Ltd.
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| 5. |
- Dazel, Olivier, et al.
(författare)
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A normal modes technique to reduce the order of poroelastic models : application to 2D and coupled 3D models
- 2013
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Ingår i: International Journal for Numerical Methods in Engineering. - : Wiley-Blackwell. - 0029-5981 .- 1097-0207. ; 96:2, s. 110-128
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Tidskriftsartikel (refereegranskat)abstract
- A reduced-order model for structures involving poroelastic materials is proposed in this paper. The approach is based on a separation of the solid and fluid phases of the porous material into separate substructures. For each individual substructure, a decoupled normal mode basis is considered, from which a set of vectors for the decomposition is selected. The preserved modes are completed by an additional family to correct for the influence of the static response of the non-preserved. It is shown that the only neglected phenomenons in the model are the inertia of the non-preserved modes and part of their intercoupling. The following three features render the proposed scheme computationally attractive: (i) real valued matrices are involved in the transformations; (ii) the assembly of complex, frequency dependent matrices is only performed at the stage of solving for a particular frequency; and (iii) the number of normal modes required are selected using a novel method.The computational efficacy is demonstrated, on a simple but realistic 3D case, through numerical results obtained using a reduced number of DOFs, showing a significant reduction of computational cost compared with traditional methods.
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| 6. |
- Effenberger, Cedric, et al.
(författare)
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Linearization techniques for band structure calculations in absorbing photonic crystals
- 2012
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Ingår i: International Journal for Numerical Methods in Engineering. - : John Wiley & Sons. - 0029-5981 .- 1097-0207. ; 89:2, s. 180-191
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Tidskriftsartikel (refereegranskat)abstract
- Band structure calculations for photonic crystals require the numerical solution of eigenvalue problems. In this paper, we consider crystals composed of lossy materials with frequency-dependent permittivities. Often, these frequency dependencies are modeled by rational functions, such as the Lorentz model, in which case the eigenvalue problems are rational in the eigenvalue parameter. After spatial discretization using an interior penalty discontinuous Galerkin method, we employ a recently developed linearization technique to deal with the resulting rational matrix eigenvalue problems. In particular, the efficient implementation of Krylov subspace methods for solving the linearized eigenvalue problems is investigated in detail. Numerical experiments demonstrate that our new approach is considerably cheaper in terms of memory and computing time requirements compared with the naive approach of turning the rational eigenvalue problem into a polynomial eigenvalue problem and applying standard linearization techniques. Copyright © 2011 John Wiley & Sons, Ltd.
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| 7. |
- Engström, Christian, et al.
(författare)
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Complex dispersion relation calculations with the applications to absorptive photonic crystals
- 2010
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Ingår i: International Journal for Numerical Methods in Engineering. - : Wiley-Blackwell. - 0029-5981 .- 1097-0207. ; 84, s. 849-863
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Tidskriftsartikel (refereegranskat)abstract
- A high-order discontinuous Galerkin method for calculations of complex dispersion relations of two-dimensional photonic crystals is presented. The medium is characterized by a complex-valued permittivityand we relate for this absorptive system the spectral parameter to the time frequency. We transform thenon-linear eigenvalue problem for a Lorentz material in air into a non-Hermitian linear eigenvalue problemand uses a Krylov space method to compute approximate eigenvalues. Moreover, we study the impact ofthe penalty term numerically and illustrate the high convergence rate of the method.
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| 8. |
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| 9. |
- Eriksson, Anders, et al.
(författare)
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Optimization in simulations of human movement planning
- 2011
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Ingår i: International Journal for Numerical Methods in Engineering. - : Wiley. - 0029-5981 .- 1097-0207. ; 87:12, s. 1127-1147
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Tidskriftsartikel (refereegranskat)abstract
- This paper discusses optimization algorithms in movement simulations for models of humans, humanoid robots or other mechanisms. Targeted movements between two configurations define a dynamically redundant system, for which there is freedom in the choice of control force time variations. A previously developed formulation for the treatment of targeted dynamics for mechanisms was used as a basis. The paper describes the development of an algorithm related to the method of moving asymptotes for the necessary optimization. The algorithm is specifically adapted to problems which are large and non-linear but sparse, and which include very high numbers of design variables as well as constraints. In particular, non-linear equality constraints from dynamic equilibrium equations are important. The optimization algorithm was developed to include these, but also in order to allow successively increasing penalty factors for constraint violations. The resulting setting was shown to be able to handle the systems established, robustly giving convergence to at least a local minimum also for very distant start iterates. The existence of very closely situated local optima, representing very similar movements, was discovered for the problem formulation, calling for an ad hoc method for finding the best of these local optima.
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| 10. |
- Hansbo, Peter F G, 1959, et al.
(författare)
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An adaptive finite element method for second order plate theory
- 2010
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Ingår i: International Journal for Numerical Methods in Engineering. - : Wiley. - 0029-5981 .- 1097-0207. ; 81:5, s. 584-603
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Tidskriftsartikel (refereegranskat)abstract
- We present a discontinuous finite element method for the Kirchhoff plate model with membrane stresses. The method is based on P2-approximations on simplices for the out-of-plane deformations, using C0-continuous approximations. We derive a posteriori error estimates for linear functionals of the error and give some numerical examples.
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