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| 2. |
- Bergman, Greger, et al.
(författare)
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A finite element model for thermomechanical analysis of sheet metal forming
- 2004
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Ingår i: International Journal for Numerical Methods in Engineering. - : Wiley. - 0029-5981 .- 1097-0207. ; 59:9, s. 1167-1186
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Tidskriftsartikel (refereegranskat)abstract
- A thermal model based on explicit time integration is developed and implemented into the explicit finite element code DYNA3D to model simultaneous forming and quenching of thin-walled structures. A staggered approach is used for coupling the thermal and mechanical analysis, wherein each analysis is performed with different time step sizes. The implementation includes a thermal shell element with linear temperature approximation in the plane and quadratic in the thickness direction, and contact heat transfer. The material behaviour is described by a temperature-dependent elastic-plastic model with a non-linear isotropic hardening law. Transformation plasticity is included in the model. Examples are presented to validate and evaluate the proposed model. The model is evaluated by comparison with a one-sided forming and quenching experiment
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| 4. |
- Fredriksson, Magnus, et al.
(författare)
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Fast and accurate 4-node quadrilateral
- 2004
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Ingår i: International Journal for Numerical Methods in Engineering. - : Wiley. - 1097-0207 .- 0029-5981. ; 61:11, s. 1809-1834
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Tidskriftsartikel (refereegranskat)abstract
- An accurate and variationally consistent 4-node quadrilateral element is introduced where high coarse mesh accuracy and low mesh distortion sensitivity are characteristic qualities, even when incompressibility is approached for plane strain. One-point quadrature integration procedure is adopted and a new improved stabilization technique is developed. Orthogonality conditions are utilized so that the patch test is satisfied for arbitrary quadrilaterals. Several numerical examples including a convergence rate study are presented which confirm the excellent performance of this element. Copyright (C) 2004 John Wiley Sons, Ltd.
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| 5. |
- Habbal, Abderrahmane, et al.
(författare)
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Multidisciplinary topology optimization solved as a Nash game
- 2004
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Ingår i: International Journal for Numerical Methods in Engineering. - : Wiley. - 0029-5981 .- 1097-0207. ; 61:7, s. 949-963
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Tidskriftsartikel (refereegranskat)abstract
- In the present work, multidisciplinary optimization is formulated in the game theory framework. We choose a coupled heat transfer—thermoelastic system as the case study for which a topology design approach is developed. The multidisciplinary optimization problem is solved as a non-cooperative game and we determine a Nash equilibrium. The game has two players and the parameterization of the design domain is such that the design variables describe the material density and a parameter which influences the heat flow by convection to the surrounding fluid. The first player controls the structure and the second player controls the temperature distribution in the structure. For the second player, we present mathematical proof of existence of a discrete valued optimal solution and it is concluded that no regularization of the suboptimization problem is needed. We present two numerical examples which illustrate the proposed methodology. One of the examples is also solved by weighting the objectives to a scalar valued objective function and the result is compared with the Nash game solution.
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| 6. |
- Heintz, Per, 1975, et al.
(författare)
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Adaptive strategies and error control for computing material forces in fracture mechanics
- 2004
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Ingår i: International Journal for Numerical Methods in Engineering. - : Wiley. - 0029-5981 .- 1097-0207. ; 60:7, s. 1287-1299
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Tidskriftsartikel (refereegranskat)abstract
- The concept of material forces pertains to a variation of the inverse motion map while the placement field is kept fixed. From the weak formulation of the self-equilibrating Eshelby (material) stress tensor it turns out that the classical J-integral formulations in fracture mechanics are just special cases due to the choice of particular weight functions. In this contribution, we discuss a posteriori error control of the material forces as part of an adaptive strategy to reduce the discretization error to an acceptable level. The data of the dual problem involves the quite non-conventional tangent stiffness of the (material) Eshelby stress tensor with respect to a variation of the (physical) strain field. The suggested strategy is applied to the common fracture mechanics problem of a single-edged crack, whereby different strategies for computing the J-integral are compared. We also consider the case in which the crack edges are not parallel, i.e. a notch.
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| 7. |
- Helsing, Johan, et al.
(författare)
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On the computation of stress fields on polygonal domains with V-notches
- 2002
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Ingår i: International Journal for Numerical Methods in Engineering. - : Wiley. - 1097-0207 .- 0029-5981. ; 53:2, s. 433-453
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Tidskriftsartikel (refereegranskat)abstract
- The interior stress problem is solved numerically for a single-edge notched specimen under uniaxial load. The algorithm is based on a modification of a Fredholm second-kind integral equation with compact operators due to Muskhelishvili. Several singular basis functions for each of the seven corners in the geometry enable high uniform resolution of the stress field with a modest number of discretization points. As a consequence, notch stress intensity factors can be computed directly from the solution. This is an improvement over other procedures where the stress field is not resolved in the corners and where notch stress intensity factors are computed in a roundabout way via a path-independent integral. Numerical examples illustrate the superior stability and economy of the new scheme.
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| 8. |
- Larsson, Fredrik, et al.
(författare)
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Space-time finite elements and an adaptive strategy for the coupled thermoelasticity problem
- 2003
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Ingår i: International Journal for Numerical Methods in Engineering. - : Wiley. - 0029-5981 .- 1097-0207. ; 56:2, s. 261-293
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Tidskriftsartikel (refereegranskat)abstract
- A space-time finite element method for the linear thermo-elasticity problem is outlined. By establishing the appropriate dual problem in space-time. it is possible to establish an exact a posteriori error representation formula based on residuals and the dual solution. In particular, we focus on the error generation in time. An adaptive strategy in the time-domain is proposed, and its performance is investigated with the aid of a numerical example in 2D. In particular. the excellent precision of the error estimate. in terms of the effectivity, index being close to unity, is noted.
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| 10. |
- Larsson, Fredrik, et al.
(författare)
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Strategies for computing goal-oriented a posteriori error measures in non-linear elasticity
- 2002
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Ingår i: International Journal for Numerical Methods in Engineering. - : Wiley. - 0029-5981 .- 1097-0207. ; 55:8, s. 879-894
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Tidskriftsartikel (refereegranskat)abstract
- We investigate the characteristics and performance of goal-oriented a posteriori error measures for a class of non-linear elasticity models, while restriction is made to small strain theory. The chosen error measure of the displacement field can be global or local (probing the chosen quantity in a specific spatial point). The error is computable with the aid of the solution of a dual problem whose data depend on the error measure. The main thrust of the paper is to evaluate the performance of a few different approximation strategies for computing the dual solution. The chosen strategies are compared in terms of accuracy, ease of implementation, reliability and cost-efficiency. A well-known numerical example, the Cook's membrane, is used for the numerical evaluations.
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