Temperature and stress fields in thin metallic partially fixed plate induced by harmonic electromagnetic wave

U radu se razmatra ponašanje tanke elastične metalne ploče izazvano harmonijskim elektromagnetskim ravanskim talasom. Ploča je slobodno oslonjena duž tri ivice i ukleštena duž četvrte. Kao rezultat dejstva vremenski promenljivog elektromagnetskog polja pojavljuju se kondukcione struje u ploči. Raspodela snage kondukcionih i histerezisnih gubitaka po debljini ploče određena je primenom kompleksnog računa. U daljem proračunu ta snaga je tretirana kao zapreminski izvor toplote. Diferencijalne jednačine polja temperature rešene su metodom integralnih transformacija. Razmatran je i uticaj debljine ploče, frekvencije talasa i faktora histerezisnih gubitaka na temperaturno polje. Polja napona i deformacije određena su primenom metode konačnih elemenata i metode integralnih transformacija.In the paper the behavior of thin elastic metallic plate influenced by the harmonic electromagnetic plane wave is considered. The plate is simply supported along three edges and fixed along the fourth one. As a result of time-varying electromagnetic field the conducting currents appear in the plate. Distribution of eddy-currents and hysterisis power losses across the plate thickness are obtained by use of complex analysis. There after, by treating this power stemming from a volume heat source, differential equations governing distribution of the temperature field are formulated and solved by using integral-transform technique. The influence of the plate thickness, wave frequency and hysterisis factor on the temperature field are considered, as well. Strain and stress fields are obtained by using finite element method (FEM) and integral-transform technique

Temperature and stress fields in thin metallic partially fixed plate induced by harmonic electromagnetic wave

U radu se razmatra ponašanje tanke elastične metalne ploče izazvano harmonijskim elektromagnetskim ravanskim talasom. Ploča je slobodno oslonjena duž tri ivice i ukleštena duž četvrte. Kao rezultat dejstva vremenski promenljivog elektromagnetskog polja pojavljuju se kondukcione struje u ploči. Raspodela snage kondukcionih i histerezisnih gubitaka po debljini ploče određena je primenom kompleksnog računa. U daljem proračunu ta snaga je tretirana kao zapreminski izvor toplote. Diferencijalne jednačine polja temperature rešene su metodom integralnih transformacija. Razmatran je i uticaj debljine ploče, frekvencije talasa i faktora histerezisnih gubitaka na temperaturno polje. Polja napona i deformacije određena su primenom metode konačnih elemenata i metode integralnih transformacija.In the paper the behavior of thin elastic metallic plate influenced by the harmonic electromagnetic plane wave is considered. The plate is simply supported along three edges and fixed along the fourth one. As a result of time-varying electromagnetic field the conducting currents appear in the plate. Distribution of eddy-currents and hysterisis power losses across the plate thickness are obtained by use of complex analysis. There after, by treating this power stemming from a volume heat source, differential equations governing distribution of the temperature field are formulated and solved by using integral-transform technique. The influence of the plate thickness, wave frequency and hysterisis factor on the temperature field are considered, as well. Strain and stress fields are obtained by using finite element method (FEM) and integral-transform technique

Temperature loading of a thin metallic plate subjected transversal to law-frequency electromagnetic field

Pošto mnoge konstrukcije tipa magnetskih kola elektromotora, generatora, induktora ili transformatora rade pod uticajem elektromagnetskih polja, u radu je prikazano određivanje Džulove toplote kao termičkog opterećenja tanke metalne ploče. Ploča je postavljena transverzalno u odnosu na homogeno vremenski promenljivo elektromagnetsko polje. Pravac prostiranja polja je upravan na srednju ravan ploče. Debljina ploče je mala u poređenju sa dubinom prodiranja magnetnog polja. Vremenski promenljivo elektromagnetno polje dovodi do pojave kondukcionih struja u materijalu ploče. Problem je rešen u analitičkom obliku kao unutrašnji Dirihleov granični problem. Intenzitet toplotnog opterećenja ploče određen je u dinamičkom obliku primenom tehnike integralnih transformacija (dvostruke konačne sinusne Furijeove transformacije i Laplasove transformacije). On zavisi od debljine ploče, električne provodnosti materijala, magnetske permeabilnosti, frekvencije i indukcije spoljašnjeg magnetnog polja, impulsnog ciklusa... Razmatran je uticaj dimenzija ploče, frekvencije polja i karakterističnih vremena impulsa na dinamičko termičko opterećenje ploče. Tako definisano termičko opterećenje predstavlja ulazni podatak za određivanje ponašanja ploče (napon, deformacija), koje se uobičajeno određuje primenom metode konačnih elemenata.Since many devices (such as magnetic circuits of motors, generators, inductors, transformers) work under the influence of the electromagnetic fields, obtaining Joule's heat as a thermal loading of the thin metallic plate subjected transversal in homogenous, time-varying electromagnetic field is presented in this paper. The direction of the field propagation is normal to the surfaces of the plate. Plate thickness is small compared to the depth of penetration of the magnetic field. Time-varying electromagnetic field is the reason of the conducting currents appearance in the material. The problem is solved in analytical form as the interior Dirichlet boundary problem. The intensity of thermal loading of the plate is obtained in dynamic form using the integral-transformation technique (Double Fourier finite-sine transformation and Laplace transformation). It depends on the plate thickness, electric conductivity, magnetic permeability, frequency and magnetic intensity of the external electromagnetic field, impulse's cycle... The influence of the plate thickness, field frequency and characteristic times of an impulse on the dynamic thermal loading are considered. Thermal loading is the entrance for the further calculation of the behavior of the plate, which is usually done by 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)

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)

An approach to the optimization of thin-walled cantilever open section beams

U ovom radu je razmatran jedan pristup optimizaciji tankozidih konzolnih konstrukcionih elemenata otvorenih poprečnih preseka izloženih savijanju i ograničenoj torziji. Problem je redukovan na određivanje minimalne mase t.j. minimalne površine konstrukcionih tankozidih elemenata oblika I i U-profila za zadata opterećenja, materijal i geometrijske karakteristike. Površina poprečnog preseka nosaca je izabrana za funkciju cilja. Uvedeno je naponsko ograničenje. Primenom metode Lagranžovog množitelja formirane su jednačine čija rešenja predstavljaju optimalne odnose dimenzija poprečnog preseka izabranog oblika. Dobijeni rezultati su iskorišćeni pri numeričkom proračunu.An approach to the optimization of the thin-walled cantilever open section beams subjected to the bending and to the constrained torsion is considered. The problem is reduced to the determination of minimum mass, i.e. minimum cross-sectional area of structural thin-walled I-beam and channel-section beam elements for given loads, material and geometrical characteristics. The area of the cross-section is assumed to be the objective function. The stress constraints are introduced. Applying the Lagrange multiplier method the equations, whose solutions represent the optimal values of the ratios of the parts of the chosen cross-section, are formed. The obtained results are used for numerical calculation

Stress constraints applied to the optimization of a thin-walled Z-beam

Razmatran je jedan pristup optimizaciji tankozidih otvorenih poprečnih preseka oblika Z - profila, izloženih savijanju i ograničenoj torziji. Za data opterećenja, materijal i geometrijske karakteristike, problem se svodi na određivanje minimalne mase, odnosno minimalne površine poprečnog preseka konstruktivnih tankozidih poprečnih preseka izabranog oblika. Površina poprečnog preseka je izabrana za funkciju cilja. Uvedena su naponska ograničenja. Primenjuje se Metoda Lagranžovog množitelja. Rezultati analitički dobijenih jednačina za matematički model, numerička rešenja, kao i ušteda u masi, izračunati su za tri slučaja opterećenja. Neki rezultati su provereni primenom programa COSMOS.One approach to the optimization of a thin-walled open section Z-beam subjected to the bending and to the constrained torsion is considered. For given loads, material and geometrical characteristics, the problem is reduced to the determination of minimum mass i.e. minimum crosssectional area of structural thin-walled beam of the chosen shape. The area of the cross-section is assumed to be the objective function. The stress constraints are introduced. The Lagrange multiplier method is applied. Solutions of analitically obtained expressions for the mathematical model, numerical solutions, as well as the saved mass, are calculated for three loading cases

Condition and behavior diagnostics of boiler constructions

U radu je prikazana metodologija dijagnostike stanja i ponašanja kotlovskih konstrukcija, koja je neophodna pri donošenju odluka o njihovom daljem radu. Definisan je algoritam koji ilustruje metode prikupljanja podataka neophodnih za dijagnostiku: analiza konstrukcije, vizuelna kontrola, ispitivanje bez i sa razaranjem, inženjerska analiza, eksperimentalna merenja i ekspertska ocena stanja - dijagnostika ponašanja. Dijagnostika se može značajno poboljšati primenom metode konačnih elemenata. Osnovna prednost ove numeričke metode u odnosu na proračun definisan normama je prikazana kroz mogućnost određivanja skoro realne slike deformacija i napona, i pouzdane procene i predviđanja ponašanja kotlovske konstrukcije u uslovima opterećenja. Primena metode konačnih elemenata je ilustrovana na primeru projektovanja novog plameno-dimnocevnog kotla i pri dijagnostici ponašanja vodocevnog kotla pri održavanju.In the paper the methodology of condition and behavior diagnostics of boiler constructions is presented, which is necessary to perform in order to make decision on further operation. An algorithm is defined that illustrates the methods for collecting data needed for the diagnostics: analysis of construction, visual inspection, non-destructive and destructive examinations, engineering analysis, experimental measurements and expert condition assessment-diagnostics of behavior. The diagnostics can be significantly improved by the application of finite element method-FEM. The main advantages of this numerical method over the calculation by design norms are expressed through possibilities of determining a nearly realistic image of deformation and stress, and reliable assessment and prediction of boiler construction behavior under service condition. The application of FEM is illustrated by the examples of designing a new firetube boiler and behavior diagnostics of water-tube boiler in service

Stress constraints applied to the optimization of a thin-walled Z-beam

Razmatran je jedan pristup optimizaciji tankozidih otvorenih poprečnih preseka oblika Z - profila, izloženih savijanju i ograničenoj torziji. Za data opterećenja, materijal i geometrijske karakteristike, problem se svodi na određivanje minimalne mase, odnosno minimalne površine poprečnog preseka konstruktivnih tankozidih poprečnih preseka izabranog oblika. Površina poprečnog preseka je izabrana za funkciju cilja. Uvedena su naponska ograničenja. Primenjuje se Metoda Lagranžovog množitelja. Rezultati analitički dobijenih jednačina za matematički model, numerička rešenja, kao i ušteda u masi, izračunati su za tri slučaja opterećenja. Neki rezultati su provereni primenom programa COSMOS.One approach to the optimization of a thin-walled open section Z-beam subjected to the bending and to the constrained torsion is considered. For given loads, material and geometrical characteristics, the problem is reduced to the determination of minimum mass i.e. minimum crosssectional area of structural thin-walled beam of the chosen shape. The area of the cross-section is assumed to be the objective function. The stress constraints are introduced. The Lagrange multiplier method is applied. Solutions of analitically obtained expressions for the mathematical model, numerical solutions, as well as the saved mass, are calculated for three loading cases

Transient Cellular Structures in Developing Corpus Callosum of the Human Brain

The corpus callosum connects two cerebral hemispheres as the most voluminous fiber system in the human brain. The developing callosal fibers originate from immature pyramidal neurons, grow through complex pathways and cross the midline using different substrates in transient fetal structures. We analyzed cellular structures in the human corpus callosum on postmortem brains from the age of 18 weeks post conception to adult, using glial fibrillary acidic protein, neuron- specific nuclear protein, and chondroitin sulphate immunocytochemistry. We found the presence of transient cellular structures, callosal septa, which divide major fiber bundles and ventrally merge with subcallosal zone forming grooves for callosal axons. The callosal septa are composed of glial fibrillary acidic protein reactive meshwork, neurones and the chondroitin sulphate immunoreactive extracellular matrix. The developmental window of prominence of the callosal septa is between 18-34 weeks post conception which corresponds to the period of most intensive growth of callosal axons in human. During the early postnatal period the callosal septa become thinner and shorter, lose their neuronal and chondroitin sulphate content. In conclusion, transient expression of neuronal, glial and extracellular, growing substrate in the callosal septa, as septa itself, indicates their role in guidance during intensive growth of callosal fibers in the human brain. These findings shed some light on the complex morphogenetic events during the growth of the corpus callosum and represent normative parameters necessary for studies of structural plasticity after perinatal lesions