A non-smooth Newton method for the solution of magnetostatic field problems with hysteresis

2019 ◽  
Vol 38 (5) ◽  
pp. 1584-1594 ◽  
Author(s):  
Stephan Willerich ◽  
Hans-Georg Herzog
Keyword(s):  
Finite Element ◽  
Newton Method ◽  
Linear Equations ◽  
Element Formulation ◽  
Magnetostatic Field ◽  
Generalized Jacobian ◽  
Content Type ◽  
Non Linear ◽  
Generalized Framework ◽  
Gradient Based

Purpose The use of gradient-based methods in finite element schemes can be prevented by undefined derivatives, which are encountered when modeling hysteresis in constitutive material laws. This paper aims to present a method to deal with this problem. Design/methodology/approach Non-smooth Newton methods provide a generalized framework for the treatment of minimization problems with undefined derivatives. Within this paper, a magnetostatic finite element formulation that includes hysteresis is presented. The non-linear equations are solved using a non-smooth Newton method. Findings The non-smooth Newton method shows promising convergence behavior when applied to a model problem. The numbers of iterations for magnetization curves with and without hysteresis are within the same range. Originality/value Mathematical tools like Clarke's generalized Jacobian are applied to magnetostatic field problems with hysteresis. The relation between the non-smooth Newton method and other methods for solving non-linear systems with hysteresis like the M(B)-iteration is established.

scholarly journals A Kollár and Pluzsik anisotropic composite beam theory for arbitrary multicelled cross sections

2016 ◽  
Vol 35 (23) ◽  
pp. 1696-1711 ◽  
Author(s):  
Danilo S Victorazzo ◽  
Andre De Jesus
Keyword(s):  
Finite Element ◽  
Cross Sections ◽  
Composite Beam ◽  
Linear Equations ◽  
Beam Theory ◽  
Element Formulation ◽  
Compliance Matrix ◽  
Asymmetric System ◽  
Anisotropic Composite ◽  
Stiffness Matrices

In this paper we extend Kollár and Pluzsik’s thin-walled anisotropic composite beam theory to include multiple cells with open branches and booms, and present a finite element formulation utilizing the stiffness matrix obtained from this theory. To recover the 4 × 4 compliance matrix of a beam containing N closed cells, we solve an asymmetric system of 2N + 4 linear equations four times with unitary section loads and extract influence coefficients from the calculated strains. Finally, we compare 4 × 4 stiffness matrices of a multicelled beam using this method against matrices obtained using the finite element method to demonstrate accuracy. Similarly to its originating theory, the effects of shear deformation and restrained warping are assumed negligible.

Robustness evaluation of CSMM based finite element for simulation of shear critical hollow RC bridge piers

2019 ◽  
Vol 37 (1) ◽  
pp. 313-344
Author(s):  
Vijay Kumar Polimeru ◽  
Arghadeep Laskar
Keyword(s):  
Finite Element ◽  
Earthquake Engineering ◽  
Bridge Piers ◽  
Fe Model ◽  
Content Type ◽  
Aspect Ratios ◽  
Linear Behavior ◽  
Non Linear ◽  
Reversed Cyclic ◽  
Rc Bridge Piers

Purpose The purpose of this study is to evaluate the effectiveness of two-dimensional (2D) cyclic softened membrane model (CSMM)-based non-linear finite element (NLFE) model in predicting the complete non-linear response of shear critical bridge piers (with walls having aspect ratios greater than 2.5) under combined axial and reversed cyclic uniaxial bending loads. The effectiveness of the 2D CSMM-based NLFE model has been compared with the widely used one-dimensional (1D) fiber-based NLFE models. Design/methodology/approach Three reinforced concrete (RC) hollow rectangular bridge piers tested under reversed cyclic uniaxial bending and sustained axial loads at the National Centre for Research on Earthquake Engineering (NCREE) Taiwan have been simulated using both 1D and 2D models in the present study. The non-linear behavior of the bridge piers has been studied through various parameters such as hysteretic loops, energy dissipation, residual drift, yield load and corresponding drift, peak load and corresponding drift, ultimate loads, ductility, specimen stiffness and critical strains in concrete and steel. The results obtained from CSMM-based NLFE model have been critically compared with the test results and results obtained from the 1D fiber-based NLFE models. Findings It has been observed from the analysis results that both 1D and 2D simulation models performed well in predicting the response of flexure critical bridge pier. However, in the case of shear critical bridge piers, predictions from 2D CSMM-based NLFE simulation model are more accurate. It has, thus, been concluded that CSMM-based NLFE model is more accurate and robust to simulate the complete non-linear behavior of shear critical RC hollow rectangular bridge piers. Originality/value In this study, a novel attempt has been made to provide a rational and robust FE model for analyzing shear critical hollow RC bridge piers (with walls having aspect ratios greater than 2.5).

A two-dimensional simulation of solidification processes in materials with thermo-dependent properties using XFEM

2016 ◽  
Vol 26 (6) ◽  
pp. 1661-1683 ◽  
Author(s):  
Pawel Stapór
Keyword(s):  
Finite Element ◽  
Phase Change ◽  
Dimensional Space ◽  
Benchmark Problems ◽  
Liquid Region ◽  
Two Dimensional ◽  
Linear Phase ◽  
Content Type ◽  
Non Linear ◽  
Non Linear System

Purpose – The purpose of this paper is to carry out a finite element simulation of a physically non-linear phase change problem in a two-dimensional space without adaptive remeshing or moving-mesh algorithms. The extended finite element method (XFEM) and the level set method (LSM) were used to capture the transient solution and motion of phase boundaries. It was crucial to consider the effects of unequal densities of the solid and liquid phases and the flow in the liquid region. Design/methodology/approach – The XFEM and the LSM are applied to solve non-linear transient problems with a phase change in a two-dimensional space. The model assumes thermo-dependent properties of the material and unequal densities of the phases; it also allows for convection in the liquid phase. A non-linear system of equations is derived and a numerical solution is proposed. The Newton-Raphson method is used to solve the problem and the LSM is applied to track the interface. Findings – The robustness and utility of the method are demonstrated on several two-dimensional benchmark problems. Originality/value – The novel procedure based on the XFEM and the LSM was developed to solve physically non-linear phase change problems with unequal densities of phases in a two-dimensional space.

Variational multi-scale finite element approximation of the compressible Navier-Stokes equations

2016 ◽  
Vol 26 (3/4) ◽  
pp. 1240-1271 ◽  
Author(s):  
Camilo Andrés Bayona Roa ◽  
Joan Baiges ◽  
R Codina
Keyword(s):  
Finite Element ◽  
Stokes Equations ◽  
Finite Element Approximation ◽  
Shock Capturing ◽  
Navier Stokes ◽  
Element Approximation ◽  
Navier Stokes Equations ◽  
Content Type ◽  
Multi Scale ◽  
Non Linear

Purpose – The purpose of this paper is to apply the variational multi-scale framework to the finite element approximation of the compressible Navier-Stokes equations written in conservation form. Even though this formulation is relatively well known, some particular features that have been applied with great success in other flow problems are incorporated. Design/methodology/approach – The orthogonal subgrid scales, the non-linear tracking of these subscales, and their time evolution are applied. Moreover, a systematic way to design the matrix of algorithmic parameters from the perspective of a Fourier analysis is given, and the adjoint of the non-linear operator including the volumetric part of the convective term is defined. Because the subgrid stabilization method works in the streamline direction, an anisotropic shock capturing method that keeps the diffusion unaltered in the direction of the streamlines, but modifies the crosswind diffusion is implemented. The artificial shock capturing diffusivity is calculated by using the orthogonal projection onto the finite element space of the gradient of the solution, instead of the common residual definition. Temporal derivatives are integrated in an explicit fashion. Findings – Subsonic and supersonic numerical experiments show that including the orthogonal, dynamic, and the non-linear subscales improve the accuracy of the compressible formulation. The non-linearity introduced by the anisotropic shock capturing method has less effect in the convergence behavior to the steady state. Originality/value – A complete investigation of the stabilized formulation of the compressible problem is addressed.

Sign in / Sign up

Export Citation Format

Share Document