1 Laboratory of Electromechanics, Helsinki University of Technology PO Box 3000, 02015 HUT, Finla... more 1 Laboratory of Electromechanics, Helsinki University of Technology PO Box 3000, 02015 HUT, Finland e-mail: anouar.belahcen@tkk.fi, katarzyna.fonteyn@tkk.fi ... 2Laboratory of Structural Mechanics, Helsinki University of Technology, PO Box 2100, 02015 HUT, Finland e-mail: ...
Determination of critical points along an equilibrium path of a structure is a non-linear eigenva... more Determination of critical points along an equilibrium path of a structure is a non-linear eigenvalue problem. If the external load is parametrized by a single parameter such an eigenvalue problem consist of solving the critical state variables, the eigenmode and the critical load parameter from the equation system consisting of the equilibrium equations, the criticality condition and some auxiliary conditions depending what kind of a critical point is in question. The non-linear eigenvalue problem can be solved by using the Newton's method. To obtain the Jacobian of the augmented equation system, second order derivatives of the residual vector with respect to the state variables need to be evaluated. Since correct computation of the critical points require geometrically exact kinematics, such derivatives are tedious to obtain. In this paper, explicit formulas for those second order derivatives of a 3D geometrically exact beam element based on the Reissner's model are presented. Additionally, some alternative iterative schemes which avoid the formation of the second order derivatives are presented and compared to the full Newton's method.
... 0 = rT 0 d0 and iterate i = 012 ::: until convergence: 1. compute: s = Adi i = i=dT i s, ... ... more ... 0 = rT 0 d0 and iterate i = 012 ::: until convergence: 1. compute: s = Adi i = i=dT i s, ... In this case the convergence is measured in the weighted norm kxk = (xTMx)1=2 and thus the tabulated values are not comparable to those of IC(0) preconditioning. ...
Communications in Numerical Methods in Engineering, 1998
Preconditioned Krylov subspace methods have proved to be ecient in solving large, sparse linear s... more Preconditioned Krylov subspace methods have proved to be ecient in solving large, sparse linear systems in many areas of scienti®c 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 signi®cant 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.
Page 1. Abstract Deformations in a cage-induction machine are investigated with simulations. Th... more Page 1. Abstract 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 ...
Summary. This paper focuses on modeling of a coupled magnetoelastic problem. The model for magnet... more Summary. This paper focuses on modeling of a coupled magnetoelastic problem. The model for magnetostriction is developed for isotropic ferromagnetic materials commonly used in electrical machines. The constitutive equations of the model are written on the basis of the Helmholtz free energy in which the strain tensor and the magnetic flux density vector are chosen as the basic variables. Numerical
A directly coupled magneto-mechanical model is proposed for simulating the effect of the magnetos... more 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.
A new low order facet type triangular shell finite element is presented. The element is combined ... more A new low order facet type triangular shell finite element is presented. The element is combined from the Arnold-Falk plate bending element and the membrane element based on the noncorming element of Crouzeix-Raviart with conforming drilling rotation. Formulation of the membrane element is based on the variational principle of Hughes and Brezzi employing independent rotation field. Interpolation for the in-plane translational components is nonconforming and continuous only at the midpoints of the element edges, while conforming linear interpolation is used for the drilling rotation. It will be shown that the utilization of the drilling rotation supresses the mechanism which is present in the Crouzeix-Raviart element, applied to plane stress or plain strain problems, for certain boundary conditions. In this element all three rotation components appear at corner nodes and translational components at the midpoints of the element edges resulting in 18 degrees of freedom.
This paper focuses on modeling of a coupled magnetoelastic problem. The model for magnetostrictio... more This paper focuses on modeling of a coupled magnetoelastic problem. The model for magnetostriction is developed for isotropic ferromagnetic materials commonly used in electrical machines. The constitutive equations of the model are written on the basis of the Helmholtz free energy in which the strain tensor and the magnetic flux density vector are chosen as the basic variables. Numerical solution is performed by using FEM.
This paper presents a coupled magnetoelastic model for isotropic ferromagnetic materials used in ... more This paper presents a coupled magnetoelastic model for isotropic ferromagnetic materials used in electrical machines. As proposed by Dorfmann et al. for general nonlinear magnetoelastic solids, the constitutive equations of the model are written on the basis of the Helmholtz free energy for which the strain tensor and the magnetic induction vector are chosen as the basic variables. As a
1 Laboratory of Electromechanics, Helsinki University of Technology PO Box 3000, 02015 HUT, Finla... more 1 Laboratory of Electromechanics, Helsinki University of Technology PO Box 3000, 02015 HUT, Finland e-mail: anouar.belahcen@tkk.fi, katarzyna.fonteyn@tkk.fi ... 2Laboratory of Structural Mechanics, Helsinki University of Technology, PO Box 2100, 02015 HUT, Finland e-mail: ...
Determination of critical points along an equilibrium path of a structure is a non-linear eigenva... more Determination of critical points along an equilibrium path of a structure is a non-linear eigenvalue problem. If the external load is parametrized by a single parameter such an eigenvalue problem consist of solving the critical state variables, the eigenmode and the critical load parameter from the equation system consisting of the equilibrium equations, the criticality condition and some auxiliary conditions depending what kind of a critical point is in question. The non-linear eigenvalue problem can be solved by using the Newton's method. To obtain the Jacobian of the augmented equation system, second order derivatives of the residual vector with respect to the state variables need to be evaluated. Since correct computation of the critical points require geometrically exact kinematics, such derivatives are tedious to obtain. In this paper, explicit formulas for those second order derivatives of a 3D geometrically exact beam element based on the Reissner's model are presented. Additionally, some alternative iterative schemes which avoid the formation of the second order derivatives are presented and compared to the full Newton's method.
... 0 = rT 0 d0 and iterate i = 012 ::: until convergence: 1. compute: s = Adi i = i=dT i s, ... ... more ... 0 = rT 0 d0 and iterate i = 012 ::: until convergence: 1. compute: s = Adi i = i=dT i s, ... In this case the convergence is measured in the weighted norm kxk = (xTMx)1=2 and thus the tabulated values are not comparable to those of IC(0) preconditioning. ...
Communications in Numerical Methods in Engineering, 1998
Preconditioned Krylov subspace methods have proved to be ecient in solving large, sparse linear s... more Preconditioned Krylov subspace methods have proved to be ecient in solving large, sparse linear systems in many areas of scienti®c 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 signi®cant 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.
Page 1. Abstract Deformations in a cage-induction machine are investigated with simulations. Th... more Page 1. Abstract 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 ...
Summary. This paper focuses on modeling of a coupled magnetoelastic problem. The model for magnet... more Summary. This paper focuses on modeling of a coupled magnetoelastic problem. The model for magnetostriction is developed for isotropic ferromagnetic materials commonly used in electrical machines. The constitutive equations of the model are written on the basis of the Helmholtz free energy in which the strain tensor and the magnetic flux density vector are chosen as the basic variables. Numerical
A directly coupled magneto-mechanical model is proposed for simulating the effect of the magnetos... more 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.
A new low order facet type triangular shell finite element is presented. The element is combined ... more A new low order facet type triangular shell finite element is presented. The element is combined from the Arnold-Falk plate bending element and the membrane element based on the noncorming element of Crouzeix-Raviart with conforming drilling rotation. Formulation of the membrane element is based on the variational principle of Hughes and Brezzi employing independent rotation field. Interpolation for the in-plane translational components is nonconforming and continuous only at the midpoints of the element edges, while conforming linear interpolation is used for the drilling rotation. It will be shown that the utilization of the drilling rotation supresses the mechanism which is present in the Crouzeix-Raviart element, applied to plane stress or plain strain problems, for certain boundary conditions. In this element all three rotation components appear at corner nodes and translational components at the midpoints of the element edges resulting in 18 degrees of freedom.
This paper focuses on modeling of a coupled magnetoelastic problem. The model for magnetostrictio... more This paper focuses on modeling of a coupled magnetoelastic problem. The model for magnetostriction is developed for isotropic ferromagnetic materials commonly used in electrical machines. The constitutive equations of the model are written on the basis of the Helmholtz free energy in which the strain tensor and the magnetic flux density vector are chosen as the basic variables. Numerical solution is performed by using FEM.
This paper presents a coupled magnetoelastic model for isotropic ferromagnetic materials used in ... more This paper presents a coupled magnetoelastic model for isotropic ferromagnetic materials used in electrical machines. As proposed by Dorfmann et al. for general nonlinear magnetoelastic solids, the constitutive equations of the model are written on the basis of the Helmholtz free energy for which the strain tensor and the magnetic induction vector are chosen as the basic variables. As a
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