| 1. |
- Becker, Roland, et al.
(författare)
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Energy norm a posteriori error estimation for discontinuous Galerkin methods
- 2003
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Ingår i: Computer Methods in Applied Mechanics and Engineering. - 0045-7825 .- 1879-2138. ; 192:5-6, s. 723-733
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Tidskriftsartikel (refereegranskat)abstract
- In this paper we present a residual-based a posteriori error estimate of a natural mesh dependent energy norm of the error in a family of discontinuous Galerkin approximations of elliptic problems. The theory is developed for an elliptic model problem in two and three spatial dimensions and general nonconvex polygonal domains are allowed. We also present some illustrating numerical examples.
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| 2. |
- Hansbo, Anita, 1960-, et al.
(författare)
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An unfitted finite element method, based on Nitsche's method, for elliptic interface problems
- 2002
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Ingår i: Computer Methods in Applied Mechanics and Engineering. - 0045-7825 .- 1879-2138. ; 191:47-48, s. 5537-5552
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Tidskriftsartikel (refereegranskat)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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| 3. |
- Hansbo, Peter, et al.
(författare)
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Discontinuous Galerkin methods for incompressible and nearly incompressible elasticity by Nitsche's method
- 2002
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Ingår i: Computer Methods in Applied Mechanics and Engineering. - 0045-7825 .- 1879-2138. ; 191:17-18, s. 1895-1908
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Tidskriftsartikel (refereegranskat)abstract
- We propose and analyze a discontinuous finite element method for nearly incompressible linear elasticity on triangular meshes. We show optimal error estimates that are uniform with respect to Poisson's ratio. The method is thus locking free. We also introduce an equivalent mixed formulation, allowing for completely incompressible elasticity problems. Numerical results are presented.
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| 4. |
- Hansbo, Peter F G, 1959
(författare)
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A new approach to quadrature for finite elemens incorporating hourglass control as a special case
- 1998
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Ingår i: Computer Methods in Applied Mechanics and Engineering. ; 158:3-4, s. 301-309
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Tidskriftsartikel (refereegranskat)abstract
- The purpose of this paper is to suggest a simple alternative approach to Gaussian quadrature in the finite element method. We show that this quadrature rule may be used to derive hourglass control stabilization matrices. We also show that the proposed quadrature scheme does not destroy the order of the bilinear finite element method.
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| 5. |
- Battini, Jean-Marc, et al.
(författare)
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Co-rotational beam elements with warping effects in instability problems
- 2002
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Ingår i: Computer Methods in Applied Mechanics and Engineering. - 0045-7825 .- 1879-2138. ; 191:17-18, s. 1755-1789
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Tidskriftsartikel (refereegranskat)abstract
- The present paper investigates the formulation of 3D co-rotational beam elements for the buckling and post-buckling analysis of frame structures. Following Pacoste and Eriksson [Comput. Methods Appl. Mech. Engrg. 144 (1997) 163], the term co-rotational relates here to the provision of a local reference frame that continuously rotates and translates with the element. Within this context, several issues are emphasised. The first one refers to the parameterisation of finite 3D rotations. The alternative put forth in the paper is based on the spatial form of the incremental rotational vector. The second issue concerns warping effects which are introduced by adding a seventh degree of freedom at each node. Different types of local formulations are considered and it is shown that at least some degree of non-linearity must be introduced in the local strain definition in order to obtain correct results for certain classes of problems. Within the present approach the centroid and shear center of the cross-section are not necessarily coincident. Finally, in the context of instability problems, a method for the direct computation of critical points is also briefly discussed, This is based on a minimal augmentation procedure as developed by Eriksson [Comput. Methods Appl. Mech. Engrg. 156 (1998) 45; Comput. Methods Appl. Mech. Engrg. 179 (1999) 265; Int. J. Struct. Stability Dynamic 1 (1) (2001)]. Ten examples, including large displacement and stability problems, are used in order to assess the performances of the elements.
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| 6. |
- Battini, Jean-Marc, et al.
(författare)
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Improved minimal augmentation procedure for the direct computation of critical points
- 2003
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Ingår i: Computer Methods in Applied Mechanics and Engineering. - 0045-7825 .- 1879-2138. ; 192:16-18, s. 2169-2185
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Tidskriftsartikel (refereegranskat)abstract
- This paper presents a new numerical procedure for the direct computation of critical points for elastic beam structures undergoing large displacements and rotations. Compared to the approach described by Wriggers et al. [Comput. Methods Appl. Mech. Engrg. 70 (1988) 329; Int. J. Numer. Methods Engrg. 30 (1990) 1551, two main modifications are introduced. First, following Eriksson [Comput. Methods Appl. Mech. Engrg. 114 (1994) 77; Comput. Methods Appl. Mech. Engrg. 156 (1998) 45; Comput. Methods Appl. Mech. Engrg. 179 (1999) 265; Int. J. Struct. Stability Dynam. l(l) (2001)], the condition of criticality is expressed by a scalar equation instead of a vectorial one. Next, the present procedure does not use exclusively the extended system obtained from the equilibrium equations and the criticality condition, but also introduces intermediate iterations based purely on equilibrium equations under load or displacement control, Eight numerical examples, presenting bifurcation and limit points, are used in order to compare the performances of this new method and the one presented in [Comput. Methods Appl. Mech. Engrg. 70 (1988) 329; Int. J. Numer. Methods Engrg. 30 (1990) 155].
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| 7. |
- Battini, Jean-Marc, et al.
(författare)
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Plastic instability of beam structures using co-rotational elements
- 2002
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Ingår i: Computer Methods in Applied Mechanics and Engineering. - 0045-7825 .- 1879-2138. ; 191:51-52, s. 5811-5831
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Tidskriftsartikel (refereegranskat)abstract
- In a previous paper [Comput. Methods Appl. Mech. Engrg. 191 (2002) 1755], the authors have presented a 3D co-rotational elastic beam element including warping effects. This formulation is now further developed in order to incorporate elasto-plastic deformations. The element possesses seven degrees of freedom at each node and can be used to model beams with arbitrary cross-sections. Thus, within the present approach, the centroid and shear center of the cross-section are not necessarily coincident. The main purpose of this element is to model elasto-plastic instability problems. In this context, two methods of branch-switching are tested and discussed. In the first one, the bifurcation point is isolated by successive bisections and the branch-switching is operated by using the eigenvector associated to the negative eigenvalue. In the second one, introduced by Petryk, an energy approach is used to select automatically the stable post-bifurcation path. Six examples, including large displacement and stability problems, are used in order to assess the performances of the element.
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| 8. |
- Borrvall, Thomas, et al.
(författare)
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Large-scale topology optimization in 3D using parallel computing
- 2001
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Ingår i: Computer Methods in Applied Mechanics and Engineering. - 0045-7825 .- 1879-2138. ; 190:46-47, s. 6201-6229
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Tidskriftsartikel (refereegranskat)abstract
- We consider large-scale topology optimization of elastic continua in 3D using the regularized intermediate density control introduced in [1]. The nested approach is used, i.e., equilibrium is solved at each iteration. To get a high-quality resolution of realistic designs in 3D, problems involving several hundreds of thousand finite elements are solved. In order to deal with problems of this size, parallel computing is used in combination with domain decomposition. The equilibrium equations are solved by a preconditioned conjugate gradient algorithm and the optimization part is solved using sequential convex programming. Several numerical results obtained from computations performed on a Cray parallel computer are presented. © 2001 Elsevier Science B.V. All rights reserved.
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| 9. |
- Borrvall, Thomas, et al.
(författare)
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Topology optimization using regularized intermediate density control
- 2001
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Ingår i: Computer Methods in Applied Mechanics and Engineering. - 0045-7825 .- 1879-2138. ; 190:37-38, s. 4911-4928
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Tidskriftsartikel (refereegranskat)abstract
- We consider topology optimization of elastic continua. The elasticity tensor is assumed to depend linearly on the design function (density) as in the variable thickness sheet problem. In order to get "black-white" design pictures, the intermediate density values are controlled by an explicit constraint. This constraint is regularized by including a compact and linear operator S to guarantee existence of solutions. A proof of convergence of the finite element (FE) discretized optimization problem's solutions to exact ones is also given, so the method is not prone to numerical anomalies such as mesh dependence or checkerboards. The procedure is illustrated in some minimum compliance examples where S is chosen to be a classical convolution-type operator. The FE-discretized optimization problems are solved by sequential convex approximations. © 2001 Elsevier Science B.V. All rights reserved.
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| 10. |
- Bängtsson, Erik, et al.
(författare)
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Shape optimization of an acoustic horn
- 2003
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Ingår i: Computer Methods in Applied Mechanics and Engineering. - 0045-7825 .- 1879-2138. ; 192, s. 1533-1571
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Tidskriftsartikel (refereegranskat)
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