Pavel Karban

Numerical solution of coupled problems using code Agros2D

New code Agros2D for 2D numerical solution of coupled problems is presented. This code is based on the fully adaptive higher-order finite element method and works with library Hermes2D containing the most advanced numerical algorithms for the numerical processing of systems of second-order partial differential equations. It is characterized by several quite unique features such as work with hanging nodes of any level, multimesh technology (every physical field can be calculated on a different mesh generally varying in time) and a possibility of combining triangular, quadrilateral and curved elements. The power of the code is illustrated by three typical coupled problems.

Non-Linear Multi-Physics Analysis and Multi-Objective Optimization in Electroheating Applications

The design optimization of an induction heating device is considered. The non-linear multi-physics analysis is carried out by means of finite-element method, while the optimal design problem is solved by NSGA-II genetic algorithm. A comparison with the results obtained by a simplified linear analysis is shown. The original contribution of this paper is the Pareto front identification for a design problem in which the field analysis is multi-physics, dynamic, and non-linear.

Limit Operation Regimes of Actuators Working on the Principle of Thermoelasticity

Actuators working on the principle of thermoelasticity exhibit specific properties (particularly very high forces at small shifts) and may be used, for example, as prospective fixing elements in numerous industrial applications. However, huge mechanical strains and stresses in their active structural parts may lead to irreversible damage or even destruction of the whole device. This paper deals with the limit operation regimes of a typical actuator of this kind that are influenced by geometry of the device, materials, and parameters of the field current. The task is solved as a coupled problem where the electromagnetic field is supposed to be independent of the fields of the temperature and mechanical strains and stresses. On the other hand, the two last fields are solved simultaneously. The methodology is illustrated on a typical example.

Multiphysics field analysis and multiobjective design optimization: a benchmark problem

A magneto-thermal inverse problem, dealing with the optimal design of an induction heating device, is proposed as a benchmark. The coupled-field problem is analysed by means of a higher order finite element method. Then the optimal design problem is solved in terms of the Pareto front trading off two conflicting objective functions.

Higher‐order finite element modeling of rotational induction heating of nonferromagnetic cylindrical billets

Purpose – The purpose of this paper is to present a methodology of high‐precision finite element modeling of induction heating of rotating nonferromagnetic cylindrical billets in static magnetic field produced by appropriately arranged permanent magnets.Design/methodology/approach – The mathematical model consisting of two partial differential equations describing the distribution of the magnetic and temperature fields are solved by a fully adaptive higher‐order finite element method in the monolithic formulation and selected results are validated experimentally.Findings – The method of solution realized by own code is very fast, robust and exhibits much more powerful features when compared with classical low‐order numerical methods implemented in existing commercial codes.Research limitations/implications – For sufficiently long arrangements the method provides good results even for 2D model. The principal limitation consists in problems with determining correct boundary conditions for the temperature fi...

Model of Induction Heating of Rotating Non-Magnetic Billets and its Experimental Verification

Induction heating of non-magnetic cylindrical billets is modeled. The billet rotates in static magnetic field generated by appropriately distributed permanent magnets. The mathematical model of the process consists of two second-order partial differential equations describing the distributions of magnetic and temperature fields. Its solution is solved numerically in the quasi-coupled formulation respecting all important non-linearities. The computations are carried out by the code Agros2-D, based on a fully adaptive higher-order finite element method. Some results are verified experimentally on an industrial prototype of the device. Presented are also other important results obtained by measurements.

Numerical Model of Induction Shrink Fits in Monolithic Formulation

Induction heating-based assembly of axisymmetric shrink fits is modeled. The task represents a triply coupled evolutionary problem characterized by mutual interaction of electromagnetic field, temperature field, and field of thermoelastic displacements. Its numerical solution is performed by a fully adaptive higher-order finite element method in monolithic formulation, using a code developed by the authors. All nonlinearities of the system (magnetic permeability and temperature dependencies of all material parameters) are respected. The methodology is illustrated by a typical example whose results are discussed.

Modelling of continual induction hardening in quasi‐coupled formulation

Purpose – As far as the authors know, no sufficiently complete model of continual induction hardening was developed and solved so far. The paper presents both mathematical model of the process and algorithm of its solution in the quasi‐coupled formulation.Design/methodology/approach – Computation of electromagnetic and temperature fields is based on the finite element method, while time variable boundary conditions are determined by means of an original theoretically‐empirical procedure.Findings – Substantial are backgrounds for design of the inductor and parameters of the field current as well as parameters of the cooling medium.Research/limitations/implications – The model reached a good level of accuracy validated by suitable experiments. Nevertheless, next work in the field will also have to respect history of the heating before cooling itself (the austenitizing temperature is a function of the velocity of heating). Very important is also appropriate meshing of the investigated region to suppress nume...

Finite-Element 2-D Model of Induction Heating of Rotating Billets in System of Permanent Magnets and its Experimental Verification

An alternative way of induction heating of nonmagnetic cylindrical billets is modeled. The billet rotates in static magnetic field generated by permanent magnets. The mathematical model of the process consisting of two second-order partial differential equations describing the distributions of magnetic and temperature fields is solved numerically in the quasi-coupled formulation. The computations are carried out by a fully adaptive higher order finite-element method that is implemented in own codes Agros2D and library Hermes. The most important results are verified experimentally on a prototype device built in our laboratory.

Continual induction hardening of steel bodies

Continual induction hardening is a modern technological process whose mathematical model is given by two generally nonlinear partial differential equations (PDEs) describing electromagnetic and temperature fields characterized by time-variable boundary conditions. The authors propose an algorithm of its solution that is used for computation of two illustrative examples.