Ivo Doležel

Higher-Order Finite Element Methods

INTRODUCTION Finite Elements Orthogonal Polynomials A One-Dimensional Example HIERARCHIC MASTER ELEMENTS OF ARBITRARY ORDER De Rham Diagram H^1-Conforming Approximations H(curl)-Conforming Approximations H(div)-Conforming Approximations L^2-Conforming Approximations HIGHER-ORDER FINITE ELEMENT DISCRETIZATION Projection-Based Interpolation on Reference Domains Transfinite Interpolation Revisited Construction of Reference Maps Projection-Based Interpolation on Physical Mesh Elements Technology of Discretization in Two and Three Dimensions Constrained Approximation Selected Software-Technical Aspects HIGHER-ORDER NUMERICAL QUADRATURE One-Dimensional Reference Domain K(a) Reference Quadrilateral K(q) Reference Triangle K(t) Reference Brick K(B) Reference Tetrahedron K(T) Reference Prism K(P) NUMERICAL SOLUTION OF FINITE ELEMENT EQUATIONS Direct Methods for Linear Algebraic Equations Iterative Methods for Linear Algebraic Equations Choice of the Method Solving Initial Value Problems for ordinary Differential Equations MESH OPTIMIZATION, REFERENCE SOLUTIONS, AND hp-ADAPTIVITY Automatic Mesh Optimization in One Dimension Adaptive Strategies Based on Automatic Mesh Optimization Goal-Oriented Adaptivity Automatic Goal-Oriented h-, p-, and hp-Adaptivity Automatic Goal-Oriented hp-Adaptivity in Two Dimensions

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...

Numerical model of a thermoelastic actuator solved as a coupled contact problem

Purpose – The purpose of this paper is to investigate the parameters and operation characteristics of an actuator working on the principle of thermoelasticity whose structure was designed by the authors.Design/methodology/approach – The mathematical model of the system describes the effects of three physical fields (electromagnetic field, temperature field, and field of mechanical strains and stresses due to thermoelasticity). While the electromagnetic field was solved independently, the thermomechanical task in common with the contact problem was solved in the hard‐coupled formulation. The computations were mostly carried out by own codes.Findings – This type of actuator is characterized by extremely high forces acting in its dilatation element.Research limitations/implications – The parameters of the system may still be improved using a longer field coil and dilatation element. Attention has to be paid, however to the mechanical stability of the system. Another improvement could be achieved by suitably ...

Evolutionary algorithm-based multi-criteria optimization of triboelectrostatic separator

Abstract A device for electrostatic separation of triboelectrically charged plastic particles is modeled and optimized. Electric field in the system is solved numerically by a fully adaptive higher-order finite element method. The movement of particles in the device is determined by an adaptive Runge–Kutta–Fehlberg algorithm. The shape optimization of the electrodes is carried out by a technique based on genetic algorithm NSGA-II and also on simulated annealing.

On a fieldless method for the computation of induction-generated heat in 3D non-ferromagnetic metal bodies

The paper deals with the mathematical and computer modeling of the induction heating of non-ferromagnetic metal bodies in harmonic electromagnetic fields. One of the main advantages of the presented method is the elimination of the surrounding air from the electromagnetic model, which strongly reduces the necessity of meshing and simplifies the computation. The task is formulated as a non-stationary quasi-coupled problem, with respect to the temperature dependencies of all important material parameters. Distribution of the eddy currents and Joule losses in the metal body is solved by a system of second-kind Fredholm integral equations. Existence and uniqueness of solution for the continuous as well as discrete problem is shown. Convergence results for the numerical scheme are presented. The theoretical analysis is supplemented with two illustrative examples.

Induction thermoelastic actuator with controllable operation regime

Purpose – The purpose of this paper is to present a new device (thermoelastic actuator) for accurate control of position whose principle is based on thermal dilatation of its working unit brought about by induction heating.Design/methodology/approach – The device must satisfy the prescribed operation parameters (mainly the above thermal dilatation). The task to find them is a multiply coupled problem (interaction of electromagnetic field, temperature field and field of thermoelastic displacements) that is solved by the finite element method supplemented with a number of other procedures.Findings – The control of position based on the described thermoelastic effect is very accurate and ranges from 1×10−6 to 1×10−3u2009m.Research limitations/implications – The device also contains two self‐locking friction clutches of conical shapes whose purpose is to fix the position of the plunger in the prescribed position. Further attention should be paid to their dynamic behaviour during the process of fixing.Practical im...

Induction Heating of Thin Slabs in Nonmagnetic Media

The paper deals with the mathematical and computer modelling of the induction heating of thin non-ferromagnetic slabs in transverse electromagnetic fields. The task is formulated as a non-stationary quasi-coupled problem, with respecting the temperature dependencies of all important material parameters. Distribution of the eddy currents and Joule losses in the slab is solved by integral equations while the temperature field by means of non-stationary balance equations. The theoretical analysis is supplemented with an illustrative example.

Finite element technique for solution of thermo-contact problems and its application in numerical analysis of devices working with induction heating

Purpose. To develop an effective approach for the numerical solution of transient thermo-contact problems and present a typical example of its utilization regarding devices working on the principle of thermoelasticity produced by induction heating and specific technological processes intended for assembly and disassembly of systems containing shrink fits. Methodology. A finite element technique for solution of 2D multiphysics (electromagnetic, thermal and structural) problems is developed, taking into account temperature dependences of material properties and continuous variations of the contact surfaces. Modeling of the contact interaction between two parts is based on the concept of a special contact finite element having no thickness. The functional for the temperature problem is supplemented with components corresponding to the thermal conductivity of this contact layer. The heat generated due to mutual sliding of both parts can also be taken into account, but the heat capacity (specific heat) of the contact layer is neglected. Using a special 1D 4-node finite elements a system of equations for the description of the thermo-contact problem is obtained. Originality. Relatively simple analytical formulae for calculation of the contact thermal resistances occurring in specific parts of electrical machines are known. The paper offers an alternative approach for the numerical solution of transient thermo-contact problems based on the concept of a special 1D contact finite element having no thickness. Results. The presented technique is applied for the computer simulation of assembly and disassembly of a shrink fit using induction heating. Conclusions regarding the choice of technological modes are made. Comparative computations for drills made from hard alloy and alloyed tool steel are carried out.