| 1. |
- Appelo, D., et al.
(författare)
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An energy-based discontinuous Galerkin method for coupled elasto-acoustic wave equations in second-order form
- 2019
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Ingår i: International Journal for Numerical Methods in Engineering. - : Wiley. - 0029-5981 .- 1097-0207. ; 119:7, s. 618-638
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Tidskriftsartikel (refereegranskat)abstract
- We consider wave propagation in a coupled fluid-solid region separated by a static but possibly curved interface. The wave propagation is modeled by the acoustic wave equation in terms of a velocity potential in the fluid, and the elastic wave equation for the displacement in the solid. At the fluid solid interface, we impose suitable interface conditions to couple the two equations. We use a recently developed energy-based discontinuous Galerkin method to discretize the governing equations in space. Both energy conserving and upwind numerical fluxes are derived to impose the interface conditions. The highlights of the developed scheme include provable energy stability and high order accuracy. We present numerical experiments to illustrate the accuracy property and robustness of the developed scheme.
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| 2. |
- Assis da Silva, Gustavo, 1991-, et al.
(författare)
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Topology optimization of continuum structures subjected to uncertainties in material properties
- 2016
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Ingår i: International Journal for Numerical Methods in Engineering. - : John Wiley & Sons. - 0029-5981 .- 1097-0207. ; 106:3, s. 192-212
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Tidskriftsartikel (refereegranskat)abstract
- This work addresses the use of the topology optimization approach to the design of robust continuum structures under the hypothesis of uncertainties with known second order statistics. To this end, the second-order perturbation approach is used to model the response of the structure and the midpoint discretization technique is used to discretize the random field. The objective function is a weighted sum of the expected compliance and its standard deviation. The optimization problem is solved using a traditional optimality criteria method. It is shown that the correlation length plays an important role in the obtained topology and statistical moments when only the minimization of the standard deviation is considered, resulting in more and thinner reinforcements as the correlation length decreases. It is also shown that the minimization of the expected value is close to the minimization of the deterministic compliance for small variations of Young's modulus.
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| 3. |
- Assis da Silva, Gustavo, 1991-, et al.
(författare)
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Topology optimization of continuum structures with stress constraints and uncertainties in loading
- 2017
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Ingår i: International Journal for Numerical Methods in Engineering. - : John Wiley & Sons. - 0029-5981 .- 1097-0207. ; 113:1, s. 153-178
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Tidskriftsartikel (refereegranskat)abstract
- Topology optimization using stress constraints and considering uncertainties is aserious challenge, since a reliability problem has to be solved for each stress con-straint, for each element in the mesh. In this paper, an alternative way of solvingthis problem is used, where uncertainty quantification is performed through thefirst-order perturbation approach, with proper validation by Monte Carlo simulation.Uncertainties are considered in the loading magnitude and direction. The mini-mum volume problem subjected to local stress constraints is formulated as a robustproblem, where the stress constraints are written as a weighted average betweentheir expected value and standard deviation. The augmented Lagrangian method isused for handling the large set of local stress constraints, whereas a gradient-basedalgorithm is used for handling the bounding constraints. It is shown that even in thepresence of small uncertainties in loading direction, different topologies are obtainedwhen compared to a deterministic approach. The effect of correlation between uncer-tainties in loading magnitude and direction on optimal topologies is also studied,where the main observed result is loss of symmetry in optimal topologies.
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| 4. |
- Bernland, Anders, et al.
(författare)
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Acoustic shape optimization using cut finite elements
- 2018
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Ingår i: International Journal for Numerical Methods in Engineering. - Hoboken : John Wiley & Sons. - 0029-5981 .- 1097-0207. ; 113:3, s. 432-449
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Tidskriftsartikel (refereegranskat)abstract
- Fictitious domain methods are attractive for shape optimization applications, since they do not require deformed or regenerated meshes. A recently developed such method is the CutFEM approach, which allows crisp boundary representations and for which uniformly well-conditioned system matrices can be guaranteed. Here, we investigate the use of the CutFEM approach for acoustic shape optimization, using as test problem the design of an acoustic horn for favorable impedance-matching properties. The CutFEM approach is used to solve the Helmholtz equation, and the geometry of the horn is implicitly described by a level-set function. To promote smooth algorithmic updates of the geometry, we propose to use the nodal values of the Laplacian of the level-set function as design variables. This strategy also improves the algorithm's convergence rate, counteracts mesh dependence, and, in combination with Tikhonov regularization, controls small details in the optimized designs. An advantage with the proposed method is that the exact derivatives of the discrete objective function can be expressed as boundary integrals, as opposed to when using a traditional method that uses mesh deformations. The resulting horns possess excellent impedance-matching properties and exhibit surprising subwavelength structures, not previously seen, which are possible to capture due to the fixed mesh approach.
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| 5. |
- Burman, Erik, et al.
(författare)
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Augmented Lagrangian and Galerkin least-squares methods for membrane contact
- 2018
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Ingår i: International Journal for Numerical Methods in Engineering. - : John Wiley & Sons. - 0029-5981 .- 1097-0207. ; 114:11, s. 1179-1191
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Tidskriftsartikel (refereegranskat)abstract
- In this paper, we propose a stabilized finite element method for the numerical solution of contact between a small deformation elastic membrane and a rigid obstacle. We limit ourselves to friction-free contact, but the formulation is readily extendable to more complex situations.
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| 6. |
- Burman, Erik, et al.
(författare)
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CutFEM : Discretizing geometry and partial differential equations
- 2015
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Ingår i: International Journal for Numerical Methods in Engineering. - : Wiley. - 0029-5981 .- 1097-0207. ; 104:7, s. 472-501
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Tidskriftsartikel (refereegranskat)abstract
- We discuss recent advances on robust unfitted finite element methods on cut meshes. These methods are designed to facilitate computations on complex geometries obtained, for example, from computer-aided design or image data from applied sciences. Both the treatment of boundaries and interfaces and the discretization of PDEs on surfaces are discussed and illustrated numerically.
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| 7. |
- Cardoso, E. L., et al.
(författare)
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Robust topology optimization of compliant mechanisms with uncertainties in output stiffness
- 2019
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Ingår i: International Journal for Numerical Methods in Engineering. - : John Wiley & Sons. - 0029-5981 .- 1097-0207. ; 119:6, s. 532-547
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Tidskriftsartikel (refereegranskat)abstract
- This work addresses the topology optimization approach to design robust compliant mechanisms with respect to uncertainties in the output stiffness, when compared to the traditional deterministic approach. To this end, two formulations are proposed: probabilistic and nonprobabilistic. The probabilistic formulation minimizes a joint objective function of expected output displacement plus a measure of its standard deviations, for given statistical distribution of the output stiffness. The nonprobabilistic formulation is written as minimization of a joint function of the median of output displacements, plus the width of the intervals that contains the extreme values of the output displacements, for a given interval of output stiffness. The Monte Carlo simulation method is used to evaluate expected values and standard deviations of output displacements in the probabilistic formulation and to assess results obtained with the deterministic approach. It is shown that both formulations lead to designs where output displacements are less sensitive to variations of output stiffness when compared to the traditional deterministic approach. Furthermore, as an additional benefit, it is observed that large variations of output stiffness can hinder the appearance of one-node connected hinges, usually found in the deterministic design of compliant mechanisms.
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| 8. |
- Carlsson, Kristoffer, 1989, et al.
(författare)
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Bounds on the effective response for gradient crystal inelasticity based on homogenization and virtual testing
- 2019
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Ingår i: International Journal for Numerical Methods in Engineering. - : Wiley. - 0029-5981 .- 1097-0207. ; 119:4, s. 281-304
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Tidskriftsartikel (refereegranskat)abstract
- This paper presents the application of variationally consistent selective homogenization applied to a polycrystal with a subscale model of gradient-enhanced crystal inelasticity. Although the full gradient problem is solved on Statistical Volume Elements (SVEs), the resulting macroscale problem has the formal character of a standard local continuum. A semi-dual format of gradient inelasticity is exploited, whereby the unknown global variables are the displacements and the energetic micro-stresses on each slip-system. The corresponding time-discrete variational formulation of the SVE-problem defines a saddle point of an associated incremental potential. Focus is placed on the computation of statistical bounds on the effective energy, based on virtual testing on SVEs and an argument of ergodicity. As it turns out, suitable combinations of Dirichlet and Neumann conditions pertinent to the standard equilibrium and the micro-force balance, respectively, will have to be imposed. Whereas arguments leading to the upper bound are quite straightforward, those leading to the lower bound are significantly more involved; hence, a viable approximation of the lower bound is computed in this paper. Numerical evaluations of the effective strain energy confirm the theoretical predictions. Furthermore, heuristic arguments for the resulting macroscale stress-strain relations are numerically confirmed.
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| 9. |
- Casselbrant, Anna, 1970, et al.
(författare)
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Effects of fixation on electrophysiology and structure of human jejunal villi
- 2018
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Ingår i: Microscopy Research and Technique. - : Wiley. - 1059-910X. ; 81:4, s. 376-383
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Tidskriftsartikel (refereegranskat)abstract
- The villi of human jejunum vary in size and shape during different functional conditions. In the base the lamina propria is isotonic with blood, in the tip hyperosmotic. Here we study electrophysiological and morphological effects of incubation in hypotonic, isotonic, or hypertonic solutions, and to test various isotonic fixatives for microscopy. Samples of jejunal mucosae, obtained during surgery in obese patients, were studied in Ussing chambers where electrical parameters were registered during incubation in Krebs solution at various osmolarities, and during fixation in formaldehyde, glutaraldehyde, or osmium tetroxide (OsO4). The same fixatives were used for other jejunal specimens that were fixed directly for light microscopy. Morphometry was carried out to determine size and height of villi, proportion of lamina propria, and surface enlargement due to villi. Ussing chamber incubation in fluids with low osmolarity resulted in increased electrical resistance and epithelial swelling. Opposite results were obtained at high osmolality. Fixation was faster in formaldehyde than in glutaraldehyde or OsO4. In biopsies processed directly for light microscopy the proportions of lamina propria of the mucosa, and of lamina propria of villi, were significantly larger in biopsies fixed in formaldehyde than after fixation in glutaraldehyde or OsO4. The villus tips sometimes ended with a bleb with prominent spaces between the epithelial cells. In summary, jejunal villi swell in vitro when exposed to hypotonic solutions, and shrink in hypertonic solutions. Much of the morphological changes occurring during fixation can be related to the physiological hyperosmolar milieu in villus tips.
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| 10. |
- Cenanovic, Mirza, et al.
(författare)
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Minimal surface computation using a finite element method on an embedded surface
- 2015
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Ingår i: International Journal for Numerical Methods in Engineering. - : Wiley. - 0029-5981 .- 1097-0207. ; 104:7, s. 502-512
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Tidskriftsartikel (refereegranskat)abstract
- We suggest a finite element method for finding minimal surfaces based on computing a discrete Laplace-Beltrami operator operating on the coordinates of the surface. The surface is a discrete representation of the zero level set of a distance function using linear tetrahedral finite elements, and the finite element discretization is carried out on the piecewise planar isosurface using the shape functions from the background three-dimensional mesh used to represent the distance function. A recently suggested stabilized scheme for finite element approximation of the mean curvature vector is a crucial component of the method.
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