| 1. |
- Hansbo, Anita, 1960-, et al.
(author)
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A finite element method for the simulation of strong and weak discontinuities in solid mechanics
- 2004
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In: Computer Methods in Applied Mechanics and Engineering. - : Elsevier BV. - 0045-7825 .- 1879-2138. ; 193:33-35, s. 3523-3540
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Journal article (peer-reviewed)abstract
- In this paper we introduce and analyze a finite element method for elasticity problems with interfaces. The method allows for discontinuities, internal to the elements, in the approximation across the interface. We propose a general approach that can handle both perfectly and imperfectly bonded interfaces without modifications of the code. For the case of linear elasticity, we show that optimal order of convergence holds without restrictions on the location of the interface relative to the mesh. We present numerical examples for the linear case as well as for contact and crack propagation model problems.
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| 2. |
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| 3. |
- Hansbo, Anita, 1960-, et al.
(author)
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A finite element method on composite grids based on Nitsche's method
- 2003
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In: Mathematical Modelling and Numerical Analysis. - : EDP Sciences. - 0764-583X .- 1290-3841. ; 37:3, s. 495-514
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Journal article (peer-reviewed)abstract
- In this paper we propose a finite element method for the approximation of second order elliptic problems on composite grids. The method is based on continuous piecewise polynomial approximation on each grid and weak enforcement of the proper continuity at an artificial interface defined by edges (or faces) of one the grids. We prove optimal order a priori and energy type a posteriori error estimates in 2 and 3 space dimensions, and present some numerical examples.
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| 4. |
- Hansbo, Anita, 1960-, et al.
(author)
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An unfitted finite element method, based on Nitsche's method, for elliptic interface problems
- 2002
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In: Computer Methods in Applied Mechanics and Engineering. - 0045-7825 .- 1879-2138. ; 191:47-48, s. 5537-5552
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Journal article (peer-reviewed)abstract
- In this paper we propose a method for the finite element solution of elliptic interface problem, using an approach due to Nitsche. The method allows for discontinuities, internal to the elements, in the approximation across the interface. We show that optimal order of convergence holds without restrictions on the location of the interface relative to the mesh. Further, we derive a posteriori error estimates for the purpose of controlling functionals of the error and present some numerical examples.
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| 5. |
- Hansbo, Anita, 1960-, et al.
(author)
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Modeling of Spray Deposition and Robot Motion Optimization for a Gas Turbine Application
- 2000
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In: Thermal spray surface engineering via applied research. - Montreal, QUE : ASM International. - 9780871706805 ; , s. 203-209
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Conference paper (other academic/artistic)abstract
- The complexity of many components being coated in the aircraft industry today makes the traditional trial and error approach to obtain uniform coatings inadequate. To reduce programming time and further increase process accuracy a more systematic approach to develop robot trajectories is needed. In earlier work, a mathematical model was developed to predict coating thickness for thermal spray deposition on rotating objects with rotationally invariant surfaces. The model allows for varying spray distance and spray direction but is simple enough to give very short simulation times. An iterative method for robot feed optimization to obtain uniform coatings was also proposed. Currently, the use of the model in engineering practice is being evaluated. A MATLAB implementation of the model has been integrated with a commercial off-line programming system, giving a powerful and efficient tool to predict and optimize coating thickness. Simulations and experimental verifications are presented for two zirconia plasma sprayed parts.
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| 6. |
- Hansbo, Anita, 1960-, et al.
(author)
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Models for the simulation of spray deposition and robot motion optimization in thermal spraying of rotating objects
- 1999
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In: Surface & Coatings Technology. - 0257-8972 .- 1879-3347. ; 122:2-3, s. 191-201
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Journal article (peer-reviewed)abstract
- In this paper we consider methods to simulate deposit build-up in thermal spraying and to optimize the robot motion so as to obtain the desired layer thickness. We derive a simplified mathematical model for spray deposition on a rotating large object with a smooth, rotationally symmetric, curved surface, yet allowing varying spray distance and direction. Further, we discuss how to obtain and incorporate an empirically determined deposit rate model. In particular, the simplified spray deposition model is chosen to make possible a reasonably cheap method to approximate a deposit rate from the results of layer thickness measurements. We also propose an iterative method to obtain good initial values for robot feed optimization. Numerical examples are presented. © 1999 Elsevier Science S.A.
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| 7. |
- Hansbo, Anita, 1960-
(author)
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Nonsmooth data error estimates for damped single step methods for parabolic equations in Banach space
- 1999
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In: Calcolo. - : Springer Science and Business Media LLC. - 0008-0624 .- 1126-5434. ; 36:2, s. 75-101
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Journal article (peer-reviewed)abstract
- We consider a time discretization method for a parabolic initial boundary value problem obtained from a combination of an A-stable single step method of order p and a lower order method with good smoothing properties. Such methods, including the Crank-Nicolson method combined with the backward Euler method, were analyzed in Hilbert space by Luskin and Rannacher, and nonsmooth data error estimates of order p were obtained. We extend this result to Banach space, and also consider approximations of the time derivative. Further, we apply the results to obtain error estimates in the supremum norm for fully discrete methods obtained by discretizing the space variable by a finite element method. © Springer-Verlag 1999.
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| 8. |
- Hansbo, Anita, 1960-
(author)
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Strong stability and non-smooth data error estimates for discretizations of linear parabolic problems
- 2002
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In: BIT Numerical Mathematics. - 0006-3835 .- 1572-9125. ; 42:2, s. 351-379
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Journal article (peer-reviewed)abstract
- We study smoothing properties of discretizations of a linear parabolic initial boundary value problem with a possibly non-selfadjoint elliptic operator. The solution at time t > 0 of this problem, as well as its time derivatives, are in Lr for initial values in Ls even when r > s. We show that similar strong stability results hold for discrete solutions obtained by discretizing in space by linear finite elements and in time by a class of A(Ξ)-stable implicit rational multistep methods (including single step methods as a special case) with good smoothing properties, as well as for certain combinations of single step methods. Most of our results are derived from the corresponding L2-bounds, shown by semigroup techniques, together with a discrete Gagliardo-Nirenberg inequality, and generalize previously known estimates with respect to admissible problems and time discretization methods. Our techniques make it possible to obtain, e.g., supremum norm error estimates for initial data which are only required to be in L1.
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