The influence of the nonlinear temperature field on the behavior of the metallic plate induced by two electromagnetic waves obtained by GSP

U radu su prikazani rezultati istraživanja ponašanja elastične metalne ploče proizvedenog pomoću dva harmonijska elektromagnetna ravna talasa (jedan sa donje, a drugi sa gornje površi ploče). Pravci prostiranja oba talasa su upravni na ravan ploče (osa x3). U rezultatu vremenske promene elektromagnetnog polja javlja se struja. Temperaturno polje je pretpostavljeno u vidu nelinearne funkcije po koordinati u pravcu debljine ploče. Ponašanje sistema je opisano pomoću sistema od tri spregnute jednačine, koje su rešene za stacionarno stanje korišćenjem integralnih transformacija (dvostrukih konačnih Fourier-ovih transformacija). Polje napona i deformacija je dobijeno korišćenjem MKE za neke slučajeve. Razmotrene su strukture koje imaju simetrična svojstva i problem je analiziran korišćenjem grupne supermatrične procedure korišćenjem GSP metode koju je razvio Zloković. Upoređivani su rezultati dobijeni pomoću GSP kao i MKE analize.In the paper the behavior of the elastic metallic plate produced by two harmonic electromagnetic plane waves (one at the upper and the other at the lower surface) is considered. Direction of the propagation of the both waves is normal on the surfaces of the plate (axe x3). As a result of time-changing electromagnetic field conducting currents appear. Distribution of the power of the eddy-current losses across the plate thickness is obtained using complex calculation. It is of exponential type and depends of the plate thickness, wave frequency, electric conductivity, magnetic permeability and magnetic intensity. In further consideration that power is treated as a volume heat source. So, temperature field across the plate thickness is assumed in nonlinear form as è(x1,x2,t)= ô0(x1,x2,t) ô1(x1,x2,t)x3+ ô2(x1,x2,t)x3 2 and the system of three coupled differential equations governing temperature field is formed. Equations are solved in analytical form for the stationary state using by integral transform technique (Double Finite Fourier transform). Strain and stress fields are obtained using by FEM for several cases of support position. As the considered structure has symmetry properties, the problem is analyzed using by group supermatrix procedure in the direct stiffness method (GSP) developed by Zlokovic. Performances of GSP are compared with those of the standard finite element analysis (FEM)

The influence of the nonlinear temperature field on the behavior of the metallic plate induced by two electromagnetic waves obtained by GSP

U radu su prikazani rezultati istraživanja ponašanja elastične metalne ploče proizvedenog pomoću dva harmonijska elektromagnetna ravna talasa (jedan sa donje, a drugi sa gornje površi ploče). Pravci prostiranja oba talasa su upravni na ravan ploče (osa x3). U rezultatu vremenske promene elektromagnetnog polja javlja se struja. Temperaturno polje je pretpostavljeno u vidu nelinearne funkcije po koordinati u pravcu debljine ploče. Ponašanje sistema je opisano pomoću sistema od tri spregnute jednačine, koje su rešene za stacionarno stanje korišćenjem integralnih transformacija (dvostrukih konačnih Fourier-ovih transformacija). Polje napona i deformacija je dobijeno korišćenjem MKE za neke slučajeve. Razmotrene su strukture koje imaju simetrična svojstva i problem je analiziran korišćenjem grupne supermatrične procedure korišćenjem GSP metode koju je razvio Zloković. Upoređivani su rezultati dobijeni pomoću GSP kao i MKE analize.In the paper the behavior of the elastic metallic plate produced by two harmonic electromagnetic plane waves (one at the upper and the other at the lower surface) is considered. Direction of the propagation of the both waves is normal on the surfaces of the plate (axe x3). As a result of time-changing electromagnetic field conducting currents appear. Distribution of the power of the eddy-current losses across the plate thickness is obtained using complex calculation. It is of exponential type and depends of the plate thickness, wave frequency, electric conductivity, magnetic permeability and magnetic intensity. In further consideration that power is treated as a volume heat source. So, temperature field across the plate thickness is assumed in nonlinear form as è(x1,x2,t)= ô0(x1,x2,t) ô1(x1,x2,t)x3+ ô2(x1,x2,t)x3 2 and the system of three coupled differential equations governing temperature field is formed. Equations are solved in analytical form for the stationary state using by integral transform technique (Double Finite Fourier transform). Strain and stress fields are obtained using by FEM for several cases of support position. As the considered structure has symmetry properties, the problem is analyzed using by group supermatrix procedure in the direct stiffness method (GSP) developed by Zlokovic. Performances of GSP are compared with those of the standard finite element analysis (FEM)

Computational analysis method of the electromagnetic field propagation and deformation of conductive bodies

Introduction. The electromagnetic field is an integral attribute of the operation of many technical and technological systems. The action of an electromagnetic field leads to deformation, a change in temperature, a change in the physical properties of the materials. Problem. High-intensity electromagnetic fields can cause such a strong deformation of conductive bodies that it can lead to irreversible shape change or destruction. This fact is used in a class of technological operations: electromagnetic forming. Here, both the workpiece and the equipment are subjected to intense force action. As a result, equipment elements may become inoperable. Goal. Creation of a computational analysis method of the electromagnetic field propagation in systems of conductive bodies and subsequent analysis of deformation. Application of this method to the study of processes in electromagnetic forming systems in order to determine rational operational parameters that provide the result of a technological operation. Methodology. A variational formulation of the problems of an electromagnetic field propagation and deformation of conductive bodies systems is used. Numerical modeling and analysis are performed using the finite element method. Results. In a general form, a system of resolving equations for the values of the vector magnetic potential and displacements is obtained. The influence of the electromagnetic field is taken into account by introducing electromagnetic forces. The results of calculations for a technological system designed for electromagnetic forming of curved thin-walled workpieces are presented. Originality. For the first time, a method of computational analysis is presented, which involves modeling within the framework of one design scheme both the process of electromagnetic field propagation and the process of deformation. Practical significance. The proposed method of computational analysis can be used for various technological systems of electromagnetic forming in order to determine the rational parameters that ensure both the operability of the equipment and the purpose of the technological operation - the necessary shaping of the workpiece.Вступ. Електромагнітне поле є невід'ємним атрибутом роботи багатьох технічних і технологічних систем. Дія електромагнітного поля призводить до деформації, зміни температури, зміни фізичних властивостей матеріалів. Проблема. Електромагнітні поля високої інтенсивності можуть викликати настільки сильну деформацію провідних тіл, що це може призвести до незворотної зміни форми або руйнування. Цей факт використовується в класі технологічних операцій: електромагнітна обробка. Тут як заготовка, так і обладнання піддаються інтенсивній силовій дії. В результаті елементи обладнання можуть виходити з ладу. Мета. Створення методу розрахункового аналізу поширення електромагнітного поля в системах провідних тіл і подальшого аналізу деформування. Застосування цього методу для дослідження процесів в системах електромагнітної обробки з метою визначення раціональних робочих параметрів, що забезпечують результат технологічної операції. Методологія. Використано варіаційну постановку задач про поширення електромагнітного поля та деформування систем провідних тіл. Чисельне моделювання та аналіз виконано методом скінченних елементів. Результати. У загальному вигляді отримано систему визначальних рівнянь для значень векторного магнітного потенціалу та переміщень. Вплив електромагнітного поля враховується введенням електромагнітних сил. Наведено результати розрахунків для технологічної системи електромагнітної обробки вигнутих тонкостінних заготовок. Оригінальність. Вперше представлено метод розрахункового аналізу, який передбачає моделювання в рамках єдиної розрахункової схеми як процесу поширення електромагнітного поля, так і процесу деформування. Практичне значення. Запропонований метод розрахункового аналізу може бути використаний для різних технологічних систем електромагнітного формування з метою визначення раціональних параметрів, що забезпечують як працездатність обладнання, так і мету технологічної операції – необхідне формоутворення заготовки

A fully-coupled nonlinear magnetoelastic thin shell formulation

A geometrically exact dimensionally reduced order model for the nonlinear deformation of thin magnetoelastic shells is presented. The Kirchhoff-Love assumptions for the mechanical fields are generalised to the magnetic variables to derive a consistent two-dimensional theory based on a rigorous variational approach. The general deformation map, as opposed to the mid-surface deformation, is considered as the primary variable resulting in a more accurate description of the nonlinear deformation. The commonly used plane stress assumption is discarded due to the Maxwell stress in the surrounding free-space requiring careful treatment on the upper and lower shell surfaces. The complexity arising from the boundary terms when deriving the Euler-Lagrange governing equations is addressed via a unique application of Green's theorem.The governing equations are solved analytically for the problem of an infinite cylindrical magnetoelastic shell. This clearly demonstrates the model's capabilities and provides a physical interpretation of the new variables in the modified variational approach. This novel formulation for magnetoelastic shells serves as a valuable tool for the accurate design of thin magneto-mechanically coupled devices

Dynamic Response of Tunable Phononic Crystals and New Homogenization Approaches in Magnetoactive Composites

This research investigates dynamic response of tunable periodic structures and homogenization methods in magnetoelastic composites (MECs). The research on tunable periodic structures is focused on the design, modeling and understanding of wave propagation phenomena and the dynamic response of smart phononic crystals. High amplitude wrinkle formation is employed to study a one-dimensional phononic crystal slab consists of a thin film bonded to a thick compliant substrate. Buckling induced surface instability generates a wrinkly structure triggered by a compressive strain. It is demonstrated that surface periodic pattern and the corresponding large deformation can control elastic wave propagation in the low thickness composite slab. Simulation results show that the periodic wrinkly structure can be used as a smart phononic crystal which can switch band diagrams of the structure in a transformative manner. A magnetoactive phononic crystal is proposed which its dynamic properties are controlled by combined effects of large deformations and an applied magnetic field. Finite deformations and magnetic induction influence phononic characteristics of the periodic structure through geometrical pattern transformation and material properties. A magnetoelastic energy function is proposed to develop constitutive laws considering large deformations and magnetic induction in the periodic structure. Analytical and finite element methods are utilized to compute dispersion relation and band structure of the phononic crystal for different cases of deformation and magnetic loadings. It is demonstrated that magnetic induction not only controls the band diagram of the structure but also has a strong effect on preferential directions of wave propagation. Moreover, a thermally controlled phononic crystal is designed using ligaments of bi-materials in the structure.Comment: PhD mechanical engineering, University of Nevada, Reno (2015

Non-Linear Homogenization of Magnetorheological Elastomers at Finite Strain

Magnetorheological elastomers (MREs) are composite materials consisting of magnetizable particles embedded in an elastomeric matrix material. They are capable of magnetostriction, generating actuation traction, and magnetic field-dependent modulus effects. Because of these properties, MREs have a myriad of potential applications including magnetic position sensors, electromagnetic shielding, and flexible magnets, as well as controllable mounts, clutches and vibration absorbers. While experimental results demonstrate the promise of these materials, the effects that can be obtained are still relatively small. The goal of this thesis is to provide a better understanding of the properties of MREs using theoretical methods to help guide their continued development. For this purpose, we use homogenization, which determines an effective macroscopic constitutive model for an MRE based on the properties of the constituent phases and their arrangement within the composite. Variational homogenization methods were developed in this work which provide a framework to predict the behavior of general magnetoelastic composites. However, specializing this work to MREs, a somewhat simplified approach is developed which assumes that the microstructure evolves exactly as it would in the purely mechanical problem; we refer to it as the &ldquopartial decoupling approximation.&rdquo Specific constitutive models for MREs made with rigid inclusions are derived which incorporate the non-linear effects of magnetic saturation and the non-linearity inherent in finite strain mechanics. While the magnetoelastic coupling in MREs can be accounted for by considering the torques and forces exerted on particles by the applied magnetic field, the variational approach used here circumvents the need to explicitly compute these forces and torques. The results demonstrate that for aligned loading, where the magnetic torques vanish, the magnetoelastic coupling is proportional to the square of the particle concentrations to leading order. For non-aligned loading, the associated torques have effects proportional to the concentration and can be significantly larger. We optimize magnetoelastic properties like magnetostriction, actuation traction, and magnetoelastic modulus with respect to the microstructure. Furthermore, we investigate multi-scale composites that utilize magnetic torques and particle rotations to produce strong magnetoelastic coupling

Well-posedness for magnetoviscoelastic fluids in 3D

We show that the system of equations describing a magnetoviscoelastic fluid in three dimensions can be cast as a quasilinear parabolic system. Using the theory of maximal $L_p$-regularity, we establish existence and uniqueness of local strong solutions and we show that each solution is smooth (in fact analytic) in space and time. Moreover, we give a complete characterization of the set of equilibria and show that solutions that start out close to a constant equilibrium exist globally and converge to a (possibly different) constant equilibrium. Finally, we show that every solution that is eventually bounded in the topology of the state space exists globally and converges to the set of equilibria.Comment: 16 pages. Characterization of the set of equilibria is added in corollary 4.2. Theorem 4.3 is corrected. This manuscript has been accepted for publication in Nonlinear Analysis: Real World Application