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Bjørn Haugen

Bio: Bjørn Haugen is an academic researcher from Norwegian University of Science and Technology. The author has contributed to research in topics: Finite element method & Turbine. The author has an hindex of 9, co-authored 21 publications receiving 676 citations. Previous affiliations of Bjørn Haugen include University of Colorado Boulder & Norwegian Institute of Technology.

Papers
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Journal ArticleDOI
TL;DR: A unified theoretical framework for the corotational (CR) formulation of finite elements in geometrically nonlinear structural analysis is presented in this paper, which permits the derivation of a set of CR variants through selective simplifications.

389 citations

Journal ArticleDOI
TL;DR: In this article, a 3-node, 9-dof membrane elements with normal-to-its-plane rotational freedoms (drilling freedoms) using parametrized variational principles is derived.

92 citations

Journal ArticleDOI
TL;DR: The present paper concentrates on the patch test and evolved versions of the test that have played a key role in this research, and presents the Individual Element Test of Bergan and Hanssen in an expanded context that encompasses several important classes of new elements.
Abstract: This paper starts a sequence of three articles that follow an unconventional approach in finite element research. The ultimate objective is to construct high-performance elements and element-level error estimators for those elements. The approach takes off from our previous work in high-performance elements and culminates with the development of finite element templates. The present paper concentrates on the patch test and evolved versions of the test that have played a key role in this research. Following a brief review of the historical roots, we present the Individual Element Test (IET) of Bergan and Hanssen in an expanded context that encompasses several important classes of new elements. The relationship of the IET to the multielement forms A, B and C of the patch test and to the single-element test are investigated. An important consequence of the IET application is that the element stiffness equations decompose naturally into basic and higher-order parts. The application of this decomposition to the “sanitization” of the non-convergent BCIZ element is described and verified with numerical experiments. Two sequel papers in preparation are subtitled ‘the algebraic approach’ and ‘element-level error estimation’. These apply the fundamental decomposition to the derivation of templates for specific mechanical elements and to the construction of element-level error estimators, respectively.

58 citations

Journal ArticleDOI
TL;DR: In this article, a co-rotated formulation of shell deformation is employed, where the deformation of the shell is decomposed in to a contribution from large rigid body rotation and a strain producing term.
Abstract: Due to the very non-linear behaviour of thin shells under collapse, numerical simulations are subject to challenges. Shell finite elements are attractive in these simulations. Rotational degrees of freedom do, however, complicate the solution. In the present study a co-rotated formulation is employed. The deformation of the shell is decomposed in to a contribution from large rigid body rotation and a strain producing term. A triangular assumed strain shell finite element is used. Hence, a high performance elastic element is combined with the co-rotated formulation. In the co-rotated co-ordinate system the plasticity is accounted for by a simplifyed Ilyushin stress resultant yield surface. The stress update is determined from the backward Euler difference, and a consistent geometrical and material tangent stiffness is derived. Comparison with other published analysis results show that the present formulation gives acceptable accuracy. Copyright © 1999 John Wiley & Sons, Ltd.

37 citations

Journal ArticleDOI
TL;DR: The core-congruential formulation (CCF) as discussed by the authors is a generalization of the total Lagrangian (TL) kinematic description of finite element stiffness equations for geometrically nonlinear mechanical finite elements.
Abstract: This article presents a survey of the core-congruential formulation (CCF) for geometrically nonlinear mechanical finite elements based on the total Lagrangian (TL) kinematic description. Although the key ideas behind the CCF can be traced back to Rajasekaran and Murray in 1973, it has not subsequently received serious attention. The CCF is distinguished by a two-phase development of the finite element stiffness equations. The initial phase developed equations for individual particles. These equations are expressed in terms of displacement gradients as degrees of freedom. The second phase involves congruential-type transformations that eventually binds the element particles of an individual element in terms of its node-displacement degrees of freedom. Two versions of the CCF, labeled direct and generalized, are distinguished. The direct CCF (DCCF) is first described in general form and then applied to the derivation of geometrically nonlinear bar, and plane stress elements using the Green-Lagrange strain measure. The more complex generalized CCF (GCCF) is described and applied to the derivation of 2D and 3D Timoshenko beam elements. Several advantages of the CCF, notably the physically clean separation of material and geometric stiffnesses, and its independence with respect to the ultimate choice of shape functions and element degrees of freedom, are noted. Application examples involving very large motions solved with the 3D beam element display the range of applicability of this formulation, which transcends the kinematic limitations commonly attributed to the TL description.

36 citations


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Book
01 Jan 1996
TL;DR: A review of the collected works of John Tate can be found in this paper, where the authors present two volumes of the Abel Prize for number theory, Parts I, II, edited by Barry Mazur and Jean-Pierre Serre.
Abstract: This is a review of Collected Works of John Tate. Parts I, II, edited by Barry Mazur and Jean-Pierre Serre. American Mathematical Society, Providence, Rhode Island, 2016. For several decades it has been clear to the friends and colleagues of John Tate that a “Collected Works” was merited. The award of the Abel Prize to Tate in 2010 added impetus, and finally, in Tate’s ninety-second year we have these two magnificent volumes, edited by Barry Mazur and Jean-Pierre Serre. Beyond Tate’s published articles, they include five unpublished articles and a selection of his letters, most accompanied by Tate’s comments, and a collection of photographs of Tate. For an overview of Tate’s work, the editors refer the reader to [4]. Before discussing the volumes, I describe some of Tate’s work. 1. Hecke L-series and Tate’s thesis Like many budding number theorists, Tate’s favorite theorem when young was Gauss’s law of quadratic reciprocity. When he arrived at Princeton as a graduate student in 1946, he was fortunate to find there the person, Emil Artin, who had discovered the most general reciprocity law, so solving Hilbert’s ninth problem. By 1920, the German school of algebraic number theorists (Hilbert, Weber, . . .) together with its brilliant student Takagi had succeeded in classifying the abelian extensions of a number field K: to each group I of ideal classes in K, there is attached an extension L of K (the class field of I); the group I determines the arithmetic of the extension L/K, and the Galois group of L/K is isomorphic to I. Artin’s contribution was to prove (in 1927) that there is a natural isomorphism from I to the Galois group of L/K. When the base field contains an appropriate root of 1, Artin’s isomorphism gives a reciprocity law, and all possible reciprocity laws arise this way. In the 1930s, Chevalley reworked abelian class field theory. In particular, he replaced “ideals” with his “idèles” which greatly clarified the relation between the local and global aspects of the theory. For his thesis, Artin suggested that Tate do the same for Hecke L-series. When Hecke proved that the abelian L-functions of number fields (generalizations of Dirichlet’s L-functions) have an analytic continuation throughout the plane with a functional equation of the expected type, he saw that his methods applied even to a new kind of L-function, now named after him. Once Tate had developed his harmonic analysis of local fields and of the idèle group, he was able prove analytic continuation and functional equations for all the relevant L-series without Hecke’s complicated theta-formulas. Received by the editors September 5, 2016. 2010 Mathematics Subject Classification. Primary 01A75, 11-06, 14-06. c ©2017 American Mathematical Society

2,014 citations

Journal ArticleDOI
TL;DR: In this article, the Natural Element Method (NEM) is applied to boundary value problems in two-dimensional small displacement elastostatics, where the trial and test functions are constructed using natural neighbour interpolants.
Abstract: The application of the Natural Element Method (NEM) 1; 2 to boundary value problems in two-dimensional small displacement elastostatics is presented. The discrete model of the domain consists of a set of distinct nodes N, and a polygonal description of the boundary @. In the Natural Element Method, the trial and test functions are constructed using natural neighbour interpolants. These interpolants are based on the Voronoi tessellation of the set of nodes N. The interpolants are smooth (C 1 ) everywhere, except at the nodes where they are C 0 . In one-dimension, NEM is identical to linear nite elements. The NEM interpolant is strictly linear between adjacent nodes on the boundary of the convex hull, which facilitates imposition of essential boundary conditions. A methodology to model material discontinuities and non-convex bodies (cracks) using NEM is also described. A standard displacement-based Galerkin procedure is used to obtain the discrete system of linear equations. Application of NEM to various problems in solid mechanics, which include, the patch test, gradient problems, bimaterial interface, and a static crack problem are presented. Excellent agreement with exact (analytical) solutions is obtained, which exemplies the accuracy and robustness of NEM and suggests its potential application in the context of other classes of problems|crack growth, plates, and large deformations to name a few. ? 1998 John Wiley & Sons, Ltd.

626 citations

Journal ArticleDOI
TL;DR: A unified theoretical framework for the corotational (CR) formulation of finite elements in geometrically nonlinear structural analysis is presented in this paper, which permits the derivation of a set of CR variants through selective simplifications.

389 citations

Reference EntryDOI
15 Nov 2004
TL;DR: In this paper, the authors provide an overview of modeling and discretization aspects in finite element analysis of thin-walled structures, focusing on nonlinear finite element formulations for large displacements and rotations in the context of elastostatics.
Abstract: The present study provides an overview of modeling and discretization aspects in finite element analysis of thin-walled structures. Shell formulations based upon derivation from three-dimensional continuum mechanics, the direct approach, and the degenerated solid concept are compared, highlighting conditions for their equivalence. Rather than individually describing the innumerable contributions to theories and finite element formulations for plates and shells, the essential decisions in modeling and discretization, along with their consequences, are discussed. It is hoped that this approach comprises a good amount of the existing literature by including most concepts in a generic format. The contribution focuses on nonlinear finite element formulations for large displacements and rotations in the context of elastostatics. Although application to dynamics and problems involving material nonlinearities is straightforward, these subjects are not taken into account explicitly.

262 citations