Reijo Kouhia

A linear nonconforming finite element method for nearly incompressible elasticity and stokes flow

Abstract We introduce a new triangular element for nearly incompressible elasticity and incompressible fluid flow. The method consists of conforming linear elements for one of the displacement (or velocity for flows) component and linear non-conforming elements for the other component. The element is proved to give an optimal approximation and this is also confirmed by several numerical examples.

Stabilized and block approximate inverse preconditioners for problems in solid and structural mechanics

The solution of linear systems arising in the finite element analysis of shells and solids by the preconditioned conjugate gradient method is considered. Stabilized and block versions of the AINV factorized approximate inverse preconditioner are presented and tested on a variety of difficult problems. Comparisons with other preconditioning methods are also included.

On the solution of non-linear finite element equations

Abstract The paper deals with the basic requirements in the construction of a reliable continuation procedure. Adaptive step length determination and calculation of critical equilibrium states are discussed. For simple critical points an algorithm, which does not need classification between different types of bifurcations or even distinction between limit vs bifurcation point, is described. Situations where the extension of the parameter space could reveal vital information concerning the behaviour of the structure being analysed, are addressed.

FEM for Directly Coupled Magneto-Mechanical Phenomena in Electrical Machines

A directly coupled magneto-mechanical model is proposed for simulating the effect of the magnetostriction and electromagnetic stress in iron. The model is based on the general balance laws of electromagnetism, mechanics, and continuum thermodynamics. It is implemented in 2-D by using a conforming finite element method for the magnetic vector potential and the displacement field. The method is applied to two different types of induction machines.

AN ASSESSMENT OF SOME PRECONDITIONING TECHNIQUES IN SHELL PROBLEMS

SUMMARY Preconditioned Krylov subspace methods have proved to be eAcient in solving large, sparse linear systems in many areas of scientific computing. The success of these methods in many cases is due to the existence of good preconditioning techniques. In problems of structural mechanics, like the analysis of heat transfer and deformation of solid bodies, iterative solution of the linear equation system can result in a significant reduction of computing time. Also many preconditioning techniques can be applied to these problems, thus facilitating the choice of an optimal preconditioning on the particular computer architecture available. However, in the analysis of thin shells the situation is not so transparent. It is well known that the stiAness matrices generated by the FE discretization of thin shells are very ill-conditioned. Thus, many preconditioning techniques fail to converge or they converge too slowly to be competitivewith direct solvers. In this study, the performance of some general preconditioning techniques on shell problems is examined. #1998 John Wiley & Sons, Ltd.

SOME ASPECTS ON EFFICIENT PATH-FOLLOWING

Abstract Techniques to solve non-linear algebraic equations in finite element analysis are considered. In particular, aspects which influence the computational cost of the continuation process are discussed, e.g. step length determination, choice of the corrector iteration, and solution of the linear equations. Different parametrization techniques are also compared. Results from structural and heat transfer analyses are presented.

On step size adjustments in structural continuation problems

Procedures for automatic step size control in non-linear structural equilibrium analyses are discussed. Some algorithms found in the literature are briefly described and compared. The main emphasis ...

Modeling of Hysteresis Losses in Ferromagnetic Laminations Under Mechanical Stress

A novel approach for predicting magnetic hysteresis loops and losses in ferromagnetic laminations under mechanical stress is presented. The model is based on combining a Helmholtz free-energy-based anhysteretic magnetoelastic constitutive law to a vector Jiles-Atherton hysteresis model. This paper focuses only on unidirectional and parallel magnetic fields and stresses, albeit the model is developed in a full 3-D configuration in order to account also for strains perpendicular to the loading direction. The model parameters are fitted to magnetization curve measurements under compressive and tensile stresses. Both the hysteresis loops and the losses are modeled accurately for stresses ranging from -50 to 80 MPa.

On kinematical relations of spatial framed structures

Abstract In three-dimensional space the non-commutative nature of finite rotations complicates the formulation of incremental equilibrium equations, capable for handling large rotational increments. The rotation matrix can be expressed in concise and elegant form as an exponential of a skew-symmetric matrix, a result which can be deduced by arguments based on Lies theory of groups as is done in quantum mechanics. Keeping in mind that the kinematical relations for an updated incremental finite element formulation are sought, the rotation matrix can be expressed as a series expansion in which higher order terms than quadratic can be omitted, if small incremental rotations are assumed. In this paper the shortcomings of using a linear rotation matrix in deriving the equilibrium equations of spatial beam structures are discussed. Stability problems are considered especially. The resulting discretized non-linear equilibrium equations are solved using Frieds orthogonal trajectory method, which allows easy handling of bifurcation and snap-through instability points. Numerical examples of lateral buckling analyses of beams are presented

Contribution of Maxwell Stress in Air on the Deformations of Induction Machines

Deformations in a cage-induction machine are investigated with simulations. The contribution of the Maxwell stress in the air gap and coil regions of the machine on the deformation is studied by comparing results obtained with and without inclusion of the stress into the calculation. The work attests the acceptability of an energy-based magneto-mechanical model for a 2D mesh of two different rotating electrical machines.