The effect of latent heat of fusion on heat transfer in fluidized-bed coating of thin plates

This paper presents a numerical study of fluidized-bed coating on thin plates using an orthogonal collocation technique. Inclusion of the latent heat of fusion term in the boundary conditions of the mathematical model accounts for the fact that some polymer powders used in coating may be partially crystalline. Predictions of coating thickness on flat plates were made with actual polymers used in fluidized-bed coating. Reasonably good agreement between numerical predictions of the coating thickness and experimental coating data of Richart was obtained for steel panels preheated to 316 degreesC. A good agreement was also obtained between numerical predictions and our coating thickness data for nylon-11 and polyethylene powders. Predicted coating thickness for polyethylene powder on flat plates were obtained with values of heat transfer coefficient closer to those obtained from our experiments. (C) 2002 Elsevier Science B.V. All rights reserved.

Geometric nonlinear analysis of thin plates by a refined nonlinear non-conforming triangular plate element

Based on the refined non-conforming element method for geometric nonlinear analysis, a refined nonlinear non-conforming triangular plate element is constructed using the Total Lagrangian (T.L.) and the Updated Lagrangian (U.L.) approach. The refined nonlinear non-conforming triangular plate element is based on the Allman's triangular plane element with drilling degrees of freedom [1] and the refined non-conforming triangular plate element RT9 [2]. The element is used to analyze the geometric nonlinear behavior of plates and the numerical examples show that the refined non-conforming triangular plate element by the T.L. and U.L. approach can give satisfactory results. The computed results obtained from the T.L. and U.L. approach for the same numerical examples are somewhat different and the reasons for the difference of the computed results are given in detail in this paper. © 2003 Elsevier Science Ltd. All rights reserved.

Prediction of welding distortion in butt joint of thin plates

This paper investigates distortions and residual stresses induced in butt joint of thin plates using Metal Inert Gas welding. A moving distributed heat source model based on Goldak's double-ellipsoid heat flux distribution is implemented in Finite Element (FE) simulation of the welding process. Thermo-elastic-plastic FE methods are applied to modelling thermal and mechanical behaviour of the welded plate during the welding process. Prediction of temperature variations, fusion zone and heat affected zone as well as longitudinal and transverse shrinkage, angular distortion, and residual stress is obtained. FE analysis results of welding distortions are compared with existing experimental and empirical predictions. The welding speed and plate thickness are shown to have considerable effects on welding distortions and residual stresses. © 2009 Elsevier Ltd. All rights reserved.

Cubic approximation for the transverse displacement in BEM for elastic plates analysis

This work presents an application for the plate analysis formulation by BEM where 3 boundary equations are used, written for the transverse displacement w and the normal and tangential derivatives partial derivativew/partial derivativen and partial derivativew/partial derivatives. In this extension, the transverse displacement w is approximated by a cubic polynomial and, as a consequence, partial derivativew/partial derivatives has a quadratic approximation. This alternative BEM formulation improves the analysis of thin plates, when compared to the formulation using the linear approximation for the displacements, mainly in the obtaining of the bending moments at the boundary of the plate. The implementation of this proposal to the computational codes is simple. (C) 2004 Published by Elsevier Ltd.

Dynamic stationary response of reinforced plates by the boundary element method

A direct version of the boundary element method (BEM) is developed to model the stationary dynamic response of reinforced plate structures, such as reinforced panels in buildings, automobiles, and airplanes. The dynamic stationary fundamental solutions of thin plates and plane stress state are used to transform the governing partial differential equations into boundary integral equations (BIEs). Two sets of uncoupled BIEs are formulated, respectively, for the in-plane state ( membrane) and for the out-of-plane state ( bending). These uncoupled systems are joined to formamacro-element, in which membrane and bending effects are present. The association of these macro-elements is able to simulate thin-walled structures, including reinforced plate structures. In the present formulation, the BIE is discretized by continuous and/or discontinuous linear elements. Four displacement integral equations are written for every boundary node. Modal data, that is, natural frequencies and the corresponding mode shapes of reinforced plates, are obtained from information contained in the frequency response functions (FRFs). A specific example is presented to illustrate the versatility of the proposed methodology. Different configurations of the reinforcements are used to simulate simply supported and clamped boundary conditions for the plate structures. The procedure is validated by comparison with results determined by the finite element method (FEM).

Implementação de formulações do método dos elementos de contorno para associação de placas no espaço

Tese (doutorado)—Universidade de Brasília, Faculdade de Tecnologia, Departamento de Engenharia Mecânica, 2016.

Criação de programa informático em ambiente Matlab® para estudo de estruturas planas pelo Método de Elementos Finitos.

Os modelos a ser analisados pelo Método de Elementos Finitos são cada vez mais complexos e, nos tempos que correm, seria impensável realizar tais análises sem um apoio computorizado. Existe para esta finalidade uma vasta gama de programas que permitem realizar tarefas que passam pelo desenho de estruturas, análise estática de cargas, análise dinâmica e vibrações, visualização do comportamento físico (deformações) em tempo real, que permitem a otimização da estrutura. Sob o pretexto de permitir a qualquer utilizador uma análise de estruturas simples com o Método dos Elementos Finitos, surge esta tese, onde se irá criar de raiz um programa com interface gráfica no ambiente MATLAB® para análise de estruturas simples com dois tipos de elemento finito, triangular de deformação constante e quadrangular de deformação linear. O software desenvolvido, verificado por comparação com um software comercial dedicado para o efeito, efetua malhagem com elementos bidimensionais triangulares e quadriláteros e resolve modelos arbitrados pelo Método de Elementos Finitos, representando estes resultados visualmente e em formato tabular.

Multivariable regression analysis and hot-spot stress approach into fatigue life estimations of welded joints

Kolmen eri hitsausliitoksen väsymisikä arvio on analysoitu monimuuttuja regressio analyysin avulla. Regression perustana on laaja S-N tietokanta joka on kerätty kirjallisuudesta. Tarkastellut liitokset ovat tasalevy liitos, krusiformi liitos ja pitkittäisripa levyssä. Muuttujina ovat jännitysvaihtelu, kuormitetun levyn paksuus ja kuormitus tapa. Paksuus effekti on käsitelty uudelleen kaikkia kolmea liitosta ajatellen. Uudelleen käsittelyn avulla on varmistettu paksuus effektin olemassa olo ennen monimuuttuja regressioon siirtymistä. Lineaariset väsymisikä yhtalöt on ajettu kolmelle hitsausliitokselle ottaen huomioon kuormitetun levyn paksuus sekä kuormitus tapa. Väsymisikä yhtalöitä on verrattu ja keskusteltu testitulosten valossa, jotka on kerätty kirjallisuudesta. Neljä tutkimustaon tehty kerättyjen väsymistestien joukosta ja erilaisia väsymisikä arvio metodeja on käytetty väsymisiän arviointiin. Tuloksia on tarkasteltu ja niistä keskusteltu oikeiden testien valossa. Tutkimuksissa on katsottu 2mm ja 6mm symmetristäpitkittäisripaa levyssä, 12.7mm epäsymmetristä pitkittäisripaa, 38mm symmetristä pitkittäisripaa vääntökuormituksessa ja 25mm/38mm kuorman kantavaa krusiformi liitosta vääntökuormituksessa. Mallinnus on tehty niin lähelle testi liitosta kuin mahdollista. Väsymisikä arviointi metodit sisältävät hot-spot metodin jossa hot-spot jännitys on laskettu kahta lineaarista ja epälineaarista ekstrapolointiakäyttäen sekä paksuuden läpi integrointia käyttäen. Lovijännitys ja murtumismekaniikka metodeja on käytetty krusiformi liitosta laskiessa.

Laser-TIG hybrid welding process

Joining processes and techniques need to meet the trend of new applications and the development of new materials. The application in connection with thick and thin plates in industrial fields is wide and the joining technology is in very urgent need. The laser-TIG hybrid welding technology can play the respective advantages of both of them. One major advantage of the hybrid laser-TIG welding technology is its efficient use of laser energy. Additionally, it can develop into a high and new advanced welding technology and become a hot spot in both the application and research area. This thesis investigated laser –TIG hybrid welding with the aim of enlightening the reader on its advantages, disadvantages and future areas of improvement. The main objective is to investigate laser-TIG hybrid on the welding of various metals (steels, magnesium, aluminium etc.). In addition, it elaborates on various possible combinations on hybrid laser-TIG welding technology and their benefits. The possibility of using laser-TIG hybrid in welding of thick materials was investigated. The method applied in carrying out this research is by using literature review. The results showed that hybrid laser-TIG is applicable to almost all weldable metals. Also it proves to be effective in welding refractive metals. The possibility of welding with or without filler materials is of economic advantage especially in welding of materials with no filler material. Thick plate’s hybrid laser-TIG welding is showing great prospects although it normally finds its used in welding thin materials in the range of 0.4 to 0.8 mm. The findings show that laser-TIG hybrid welding can be a versatile welding process and therefore will be increasingly used industrially due to its numerous advantages and the development of new TIG arc that enhances its capabilities.

Blysmasphaera broennimanni : a new recent allogromiine species (order Foraminiferida, Eichwald, 1830) from Brazil.

Blysmasphaera broennimanni, a new recent allogromiine species from Brazil, is here introduced. This species was mainly found in freshwater and acidic sediments (pH ranged from 4.4 to 5.8). This new species differs from Blysmasphaera brasiliensis Broennimann, 1988 in its wall's outer layer, which is characterized by thin "plates" with everted borders that give the surface an overall net-like appearance. An emendation to the genus Blysmasphaera Broennimann, 1988 incorporating this new observed feature is also proposed.

Effects of temperature and of the addition of accelerating and retarding agents on the kinetics of hydration of tricalcium silicate

The formation of calcium silicate hydrates (C-S-H) during the hydration of tricalcium silicate (C3S) in pure water and in water solutions containing 1% CaCl2 (accelerator) and 0.01% saccharose (retarder) was studied by small-angle X-ray scattering (SAXS). SAXS measurements were performed under isothermal conditions within the temperature range 25 °C T < 52 °C. The experimental results indicate that the time variation of the mass fraction of the C-S-H product phase, α(f), can be fitted, under all conditions of paste setting, by Avrami equation, α(t) = 1 -exp(-(kt)′), k being a rate parameter and n an exponent depending on the characteristics of the transformation. The parameter n is approximately equal to 2 for hydration of C^S in pure water. Depending on temperature, n varies from 2 to 2.65 for hydration in the presence of CaC^ and saccharose. The value n = 2 is theoretically expected for lateral growth of thin C-S-H plates of constant thickness. The time dependence of SAXS intensity indicates that the transformed phase (C-S-H) consists of colloidal particles in early stages of hydration, evolving by two-dimensional growth toward a disordered lamellar structure composed of very thin plates. The activation energy ΔE for the growth of C-S-H phase was determined from the time dependence of X-ray scattering intensity. These data were obtained by in situ measurements at different temperatures of hydration. The values of ΔE are 37.7, 49.4, and 44.3 kJ/mol for hydration in pure water and in water solutions containing CaCl2 and saccharose, respectively. © 2000 American Chemical Society.

Análise dinâmica de placas delgadas utilizando elementos finitos triangulares e retangulares

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Some issues concerning the dynamic response and damage of composite laminates subjected to low velocity impact

Abstract. This thesis presents a discussion on a few specific topics regarding the low velocity impact behaviour of laminated composites. These topics were chosen because of their significance as well as the relatively limited attention received so far by the scientific community. The first issue considered is the comparison between the effects induced by a low velocity impact and by a quasi-static indentation experimental test. An analysis of both test conditions is presented, based on the results of experiments carried out on carbon fibre laminates and on numerical computations by a finite element model. It is shown that both quasi-static and dynamic tests led to qualitatively similar failure patterns; three characteristic contact force thresholds, corresponding to the main steps of damage progression, were identified and found to be equal for impact and indentation. On the other hand, an equal energy absorption resulted in a larger delaminated area in quasi-static than in dynamic tests, while the maximum displacement of the impactor (or indentor) was higher in the case of impact, suggesting a probably more severe fibre damage than in indentation. Secondly, the effect of different specimen dimensions and boundary conditions on its impact response was examined. Experimental testing showed that the relationships of delaminated area with two significant impact parameters, the absorbed energy and the maximum contact force, did not depend on the in-plane dimensions and on the support condition of the coupons. The possibility of predicting, by means of a simplified numerical computation, the occurrence of delaminations during a specific impact event is also discussed. A study about the compressive behaviour of impact damaged laminates is also presented. Unlike most of the contributions available about this subject, the results of compression after impact tests on thin laminates are described in which the global specimen buckling was not prevented. Two different quasi-isotropic stacking sequences, as well as two specimen geometries, were considered. It is shown that in the case of rectangular coupons the lay-up can significantly affect the damage induced by impact. Different buckling shapes were observed in laminates with different stacking sequences, in agreement with the results of numerical analysis. In addition, the experiments showed that impact damage can alter the buckling mode of the laminates in certain situations, whereas it did not affect the compressive strength in every case, depending on the buckling shape. Some considerations about the significance of the test method employed are also proposed. Finally, a comprehensive study is presented regarding the influence of pre-existing in-plane loads on the impact response of laminates. Impact events in several conditions, including both tensile and compressive preloads, both uniaxial and biaxial, were analysed by means of numerical finite element simulations; the case of laminates impacted in postbuckling conditions was also considered. The study focused on how the effect of preload varies with the span-to-thickness ratio of the specimen, which was found to be a key parameter. It is shown that a tensile preload has the strongest effect on the peak stresses at low span-to-thickness ratios, leading to a reduction of the minimum impact energy required to initiate damage, whereas this effect tends to disappear as the span-to-thickness ratio increases. On the other hand, a compression preload exhibits the most detrimental effects at medium span-to-thickness ratios, at which the laminate compressive strength and the critical instability load are close to each other, while the influence of preload can be negligible for thin plates or even beneficial for very thick plates. The possibility to obtain a better explanation of the experimental results described in the literature, in view of the present findings, is highlighted. Throughout the thesis the capabilities and limitations of the finite element model, which was implemented in an in-house program, are discussed. The program did not include any damage model of the material. It is shown that, although this kind of analysis can yield accurate results as long as damage has little effect on the overall mechanical properties of a laminate, it can be helpful in explaining some phenomena and also in distinguishing between what can be modelled without taking into account the material degradation and what requires an appropriate simulation of damage. Sommario. Questa tesi presenta una discussione su alcune tematiche specifiche riguardanti il comportamento dei compositi laminati soggetti ad impatto a bassa velocità. Tali tematiche sono state scelte per la loro importanza, oltre che per l’attenzione relativamente limitata ricevuta finora dalla comunità scientifica. La prima delle problematiche considerate è il confronto fra gli effetti prodotti da una prova sperimentale di impatto a bassa velocità e da una prova di indentazione quasi statica. Viene presentata un’analisi di entrambe le condizioni di prova, basata sui risultati di esperimenti condotti su laminati in fibra di carbonio e su calcoli numerici svolti con un modello ad elementi finiti. È mostrato che sia le prove quasi statiche sia quelle dinamiche portano a un danneggiamento con caratteristiche qualitativamente simili; tre valori di soglia caratteristici della forza di contatto, corrispondenti alle fasi principali di progressione del danno, sono stati individuati e stimati uguali per impatto e indentazione. D’altro canto lo stesso assorbimento di energia ha portato ad un’area delaminata maggiore nelle prove statiche rispetto a quelle dinamiche, mentre il massimo spostamento dell’impattatore (o indentatore) è risultato maggiore nel caso dell’impatto, indicando la probabilità di un danneggiamento delle fibre più severo rispetto al caso dell’indentazione. In secondo luogo è stato esaminato l’effetto di diverse dimensioni del provino e diverse condizioni al contorno sulla sua risposta all’impatto. Le prove sperimentali hanno mostrato che le relazioni fra l’area delaminata e due parametri di impatto significativi, l’energia assorbita e la massima forza di contatto, non dipendono dalle dimensioni nel piano dei provini e dalle loro condizioni di supporto. Viene anche discussa la possibilità di prevedere, per mezzo di un calcolo numerico semplificato, il verificarsi di delaminazioni durante un determinato caso di impatto. È presentato anche uno studio sul comportamento a compressione di laminati danneggiati da impatto. Diversamente della maggior parte della letteratura disponibile su questo argomento, vengono qui descritti i risultati di prove di compressione dopo impatto su laminati sottili durante le quali l’instabilità elastica globale dei provini non è stata impedita. Sono state considerate due differenti sequenze di laminazione quasi isotrope, oltre a due geometrie per i provini. Viene mostrato come nel caso di provini rettangolari la sequenza di laminazione possa influenzare sensibilmente il danno prodotto dall’impatto. Due diversi tipi di deformate in condizioni di instabilità sono stati osservati per laminati con diversa laminazione, in accordo con i risultati dell’analisi numerica. Gli esperimenti hanno mostrato inoltre che in certe situazioni il danno da impatto può alterare la deformata che il laminato assume in seguito ad instabilità; d’altra parte tale danno non ha sempre influenzato la resistenza a compressione, a seconda della deformata. Vengono proposte anche alcune considerazioni sulla significatività del metodo di prova utilizzato. Infine viene presentato uno studio esaustivo riguardo all’influenza di carichi membranali preesistenti sulla risposta all’impatto dei laminati. Sono stati analizzati con simulazioni numeriche ad elementi finiti casi di impatto in diverse condizioni di precarico, sia di trazione sia di compressione, sia monoassiali sia biassiali; è stato preso in considerazione anche il caso di laminati impattati in condizioni di postbuckling. Lo studio si è concentrato in particolare sulla dipendenza degli effetti del precarico dal rapporto larghezza-spessore del provino, che si è rivelato un parametro fondamentale. Viene illustrato che un precarico di trazione ha l’effetto più marcato sulle massime tensioni per bassi rapporti larghezza-spessore, portando ad una riduzione della minima energia di impatto necessaria per innescare il danneggiamento, mentre questo effetto tende a scomparire all’aumentare di tale rapporto. Il precarico di compressione evidenzia invece gli effetti più deleteri a rapporti larghezza-spessore intermedi, ai quali la resistenza a compressione del laminato e il suo carico critico di instabilità sono paragonabili, mentre l’influenza del precarico può essere trascurabile per piastre sottili o addirittura benefica per piastre molto spesse. Viene evidenziata la possibilità di trovare una spiegazione più soddisfacente dei risultati sperimentali riportati in letteratura, alla luce del presente contributo. Nel corso della tesi vengono anche discussi le potenzialità ed i limiti del modello ad elementi finiti utilizzato, che è stato implementato in un programma scritto in proprio. Il programma non comprende alcuna modellazione del danneggiamento del materiale. Viene però spiegato come, nonostante questo tipo di analisi possa portare a risultati accurati soltanto finché il danno ha scarsi effetti sulle proprietà meccaniche d’insieme del laminato, esso possa essere utile per spiegare alcuni fenomeni, oltre che per distinguere fra ciò che si può riprodurre senza tenere conto del degrado del materiale e ciò che invece richiede una simulazione adeguata del danneggiamento.

Analytical model for the prediction of wrinkling of rear pressure bulkheads

In Airbus GmbH (Hamburg) has been developed a new design of Rear Pressure Bulkhead (RPB) for the A320-family. The new model has been formed with vacuum forming technology. During this process the wrinkling phenomenon occurs. In this thesis is described an analytical model for prediction of wrinkling based on the energetic method of Timoshenko. Large deflection theory has been used for analyze two cases of study: a simply supported circular thin plate stamped by a spherical punch and a simply supported circular thin plate formed with vacuum forming technique. If the edges are free to displace radially, thin plates will develop radial wrinkles near the edge at a central deflection approximately equal to four plate thicknesses w0/ℎ≈4 if they’re stamped by a spherical punch and w0/ℎ≈3 if they’re formed with vacuum forming technique. Initially, there are four symmetrical wrinkles, but the number increases if the central deflection is increased. By using experimental results, the “Snaptrhough” phenomenon is described.