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By Peter Griesenbrock

In German underground coal mining mostly arch and some rectangular roadways are used in the development work. Due to its positive results from numerical and physical modeling techniques as well as good underground experiences, the numbers of rectangular roadways has increased significantly. Today the bolt support - independent of its cross-sectional shape - represents an undeniable support element. During the introduction of new bolt techniques a detailed investigation of the rock and support mechanical effectiveness of bolt support in roadways at all operation stages is of basic importance. This effectiveness can be predicted and verified using different simulation techniques. For the planning of rockbolted roadways two supplementary simulation techniques are presented in this paper. By combination of all available planning tools the best result for planning assurance can be achieved. Keywords: numerical modeling, physical modeling, arched roadway, rectangular roadway, roofbolting, advancing longwall.

Jan 1, 2002

By S. Bradshaw, A. Mabentsela

"Physical and numerical modelling methods were followed to identify mechanism(s) for tundish slag entrainment in a bare tundish and one with a flow control device (FCD).The physical and numerical models made use of water and paraffin to model steel and slag respectively. Observations from the physical model showed that the steel-slag interface remains immobile in both cases. Entrained paraffin formed droplets approximately 1 mm in diameter. Results from both models (numerical and physical) showed that in both cases (bare and FCD case), areas of high entrained slag concentration exist near the inlet region. The entrained slag concentration decreases towards the tundish endwalls.Flow patterns and velocities tangential to the steel-slag interface from the numerical model showed that slag entrainment in both the bare tundish and tundish with a FCD possibly takes place via two mechanisms. First, the slag moves across the steel-slag interface via mass transfer; secondly small velocities tangential to the interface at depths greater than 10 mm below the interface carry the already ‘entrained’ slag into the bulk steel phase. These tangential flow patterns are dominant in the inlet region, hence the high concentration of entrained slag in this region. IntroductionThe tundish serves as the last metallurgical vessel through which steel passes before solidifying in the moulds. It is in the tundish that the last traces of non-metallic inclusions should be removed, otherwise the inclusions carry over to the moulds and cause defects in the steel product. In the tundish, the slag is less dense than the melt and thus resides on the top of the melt. The slag provides a sink into which the non-metallic inclusions float to and dissolve. The slag also protects the melt from air and heat loss. However, when slag is entrained in the melt as a result of increased turbulence or shearing at the steel-slag interface, slag can become a source of nonmetallic inclusions.Numerous studies on flow patterns in the tundish have been carried out since the introduction of the tundish. These studies were aimed at improving the flow characteristics in the tundish (Chattopadhyay, Isac, and Guthri, 2010; Cloete, 2014; Jha, Dash, and Kumar, 2001; Jha, Rao, and Dewan, 2008;"

Jan 1, 2017

By R. J. Shaffer

Hydraulic fracturing in rock masses involves complex and coupled processes of fractures propagating in discontinuous media and of fluid flow in discrete channels. The Unconventional Gas Program at LLNL is actively developing numerical models to gain insight in the physics of these coupled processes. This paper describes the current status of the FEFFLAP code, which models fluid-driven discrete fracture propagation in jointed media. We also discuss the results of a preliminary series of physical tests in which hydrofractures were driven across slanted interfaces between dissimilar materials, in blocks loaded in biaxial compression.

Jan 1, 1984

By KeerthiRaaj Subrmanian, Muthukkumaran Kasinathan

"A railway embankment is under construction between Nagapattinam to Thiruthuraipoondi covering 36.5 km. The sub-soil strata comprises of soft clay extending up to 10 m below existing ground level, which is subjected to stability and settlement problems. A trial stretch covering about 5 kilometer was improved using Prefabricated Vertical Drains (PVD) with surcharge was recommended to accelerate the consolidation settlement. The geotechnical characteristics of the subsoil are examined through laboratory tests on representative soil samples. Recent improvement in the finite element analysis has facilitated modeling of PVD in finite element software for computing the settlement magnitude and time rate of consolidation. In this study the theoretically predicted settlement magnitude and time rate of consolidation from Terzaghi.s vertical consolidation, Barron's radial consolidation are compared with the analyzed FEM results for both the cases with and without PVD improved embankment. The comparative analysis between FEM and predicted data hold good for stresses and the associated deformations. The excess pore water pressure was significantly lower and their dissipation was faster in case of embankment with vertical drains. Thus PLAXIS 2D tool shows fairly convincing results in comparison to the theoretical solutions.1. INTRODUCTIONFrom the earlier times civilization has been developed in a fashion either at the banks of river or near to the shore region, because of the easier availability of food and water. This over centuries made them as huge cities, consequently population rise made the increased necessity of highway, railways, port and even more ground for construction. As a stake researchers are pushed to make a low bearing ground into a massive carrier of skyscrapers, embankment, bridges etc. These low bearing ground suffers from total and differential settlement, slope instability. Hence, numerous ground improvement techniques were followed to eradicate these concerns which include preloading, piling, stone column, vertical drains and geosynthetic reinforcement. Among them Prefabricated vertical drain (PVD) are often used to accelerate consolidation of soft subsoil and has been the main soil improvement method used in improving the soft marine clay deposit (Chu et al.(2004); Chai (2001) and Arulrajah et al.(2003)). Literature review of embankment over soft clay deposit reveals that combination of PVD with preloading is widely considered as an economical and less time consuming ground improvement technique."

Jan 1, 2015

By T. H. Yang, K. K. Lee, Z. Z. Liang, C. A. Tang, L. C. Li, Y. Tsui, L. G. Tham

Abstract: A series of numerical tests of hydraulic fracturing in heterogeneous rocks were performed to investigate the influence of pore pressure magnitude and gradient on initiation and propagation of tensile fractures. The numerical tests were run with a Rock Failure Process Analysis code, F-RFPA2D, incorporated with a Flow-Stress-Damage coupling model (FSD). To investigate the influence of pore pressure magnitude on fracture behaviour, “pinch-off” breaking tests, originally employed by Bridgeman to investigate the effective stress law for tensile fracture in a uniform pore pressure field, were numerically modelled. In another numerical test, a double-notched sample, with fluid pressure in one notch while keeping the other one open to the atmosphere, is numerically extended to investigate how the fluid flow direction or the pore pressure gradient will influence the fracture behaviour. The simulation results show that fracture is strongly influenced by both pore pressure magnitude and pore pressure gradient. Keywords: seepage mechanics; heterogeneous; pore pressure; numerical simulation; failure process ZUSAMMENFASSUNG: Um den Einfluss der Wasserdruckgroesse der Oeffnung und der Porisitaet auf den Bruchentstanden und Verbreiten der Tension von Gebirgen zu beurteilen, wurde viele nummerische Pruefungen auf den hydraulischen Bruch in dem Gebirgen aufgenommen. Diese Pruefungen wurden mittels der Analyse- Software F-RFPA2D und Flow-stress-Damage Coupling model ( FSD) durchgefuehrt. Um den Einfluess der Wasserdruckgroesse der Oeffnung auf den Bruch zu beurteilen, wurden auch Bruchpruefung und nummerische Analogexperimenten gemacht, und dadurch wurde die ganze Phase der Bruchentstanden und Verbreiten wiedergezeigt, und die Ergebnissen ergeben sich, dass die Wasserdruckgroesse der Oeffnung und der Porisitaet sehr viel auf den Bruchentstanden und Verbreiten der Tension von Gebirgen beeinfluessen. Schluesselwoerter: Durchlaessigkeit , ungeleichmaessig, Wasserdruck der Oeffnung, nummerische Analog, Zerstoerungspahse Résumé : Une série de simulations numériques a été ménée pour analyser l’influence de la grandeur de la pression de pore et du gradient sur la naissance et la propagation des fractures de tensions par le biais de la simulation numérique des fractures hydroliques dans des rochers hétérogènes . Le logiciel F-RFPA (Rock Failure Process Analysis code ) intégrant FSD ( Flow-Stress-Damage coupling model ) y a été employé. Les résultats des simultations montrent tout le processus de la naissance et de la propagation des fractures sous la pression de pore. Ces résultats nous ont permis de constater que la grandeur de la pression de pore et le gradient exercent une influence importante sur la naissance des fractures dans les rochers et sur leur mode de propagation . Mots de clé : le mécanisme de transfusion ; l’hétéogénéité ; la pression de pore ; la simultation numérique ; le processus destructif

Jan 1, 2003

By S. Peng, Vaughan R. Voller

"Free boundary problems are a common occurrence in materials processing operations. An important example is the filling of material into molds. This paper looks at filling problems associated with polymer processing, in particular Resin Transfer Molding (RTM) and Compression Molding. A general, single governing equation is developed which on numerical solution provides predictions for the position of the polymer front in the mold during filling. Both fixed and deforming finite element solutions are developed. Application to polymer filling test problems reveal that the fixed and deforming grid scheme are accurate and compare closely with each other.IntroductionProblems arising from the analysis of material processing operations often involve the tracking of a moving boundary, on which a balance conditions needs to be met, or the locating of a free surface that defines the solution domain. Material processing examples of so called ""free and moving boundary problems"" include; the tracking of solidification/melting fronts[l], the tracking of the metal/gas interface during the filling of a mold[2] and location and shape of a skull (freeze line) in a melting furnace[3].Computational solution of free and moving boundary problems usually fit into one of two classes, viz.1. Fixed grid scheme: In which the spatial domain is covered by a fixed grid (mesh) of node points and the solution uses an auxiliary variable (e.g. a local liquid fraction) to track the moving boundary or locate the free surface.2. Deforming grid scheme: In which the grid in the spatial domain is continuously deformed (or adapted in a steady state problem) such that a specified set of grid points lie on the moving boundary or the free surface.Details on the basic underlying features in these two classes of solution can be found in the excellent monograph by Crank [4]."

Jan 1, 1994

By W. G. Pariseau, C. H. Schmuck, Fei Duan

The Homestake Mine is located in steeply dipping Precambrian metasediaents, an environment common to a number of world class ore bodies. Development of a pronounced plane of schistosity raises a question concerning the importance of anisotropy to the design of vertical crater retreat stopes. Little is known about the actual influence of elastic anisotropy in such -circumstances; even less is known about strength anisotropy. A cautious step- by-step approach was therefore taken towards a numerical assessment of the role of anisotropy in the analysis of stress and stability. The sequence of analyses begins with elementary test problems for computer program checks and proceeds to the analysis of a study stope area between the 6950 and 7100 Levels of the Homestake Mine. Anisotropy (orthotropy) is important at the Homestake Yine. No simple guidelines for evaluating in advance the need for plastic and strength anisotropy in design analysis appear to be forthcoming, ;o that some physical properties testing is necessary where the question is in doubt

Jan 1, 1984

A number of issues relating to the computational aspects of pillar design are addressed in this paper. The computation of average pillar stress values is important when attempting to establish criteria for pillar design and in the analysis of the stability of tabular pillar layouts. One of the default ?classic? numerical methods that are used to determine pillar stresses is the displacement discontinuity method. In many instances it is not clearly understood that this approach does suffer from some limitations, particularly in relation to the fact that in coarse element simulations, the simulated average pillar stress (APS) can depend on the chosen mesh size. The nature of this error is highlighted in this paper and some strategies are suggested to bound the magnitude of these errors. It is demonstrated as well that the popular linear stiffness approximation to pillar or seam compressibility does appear to allow reasonably accurate estimates of the average pillar stress when either the pillar height is varied or when the seam modulus differs from the host rock modulus. A practical implication of this study is that if the seam modulus is noticeably lower than that of the host rock, such as for coal seams, it is important to use a linear stiffness constitutive model for the pillars rather than a ?rigid? pillar assumption. This added complexity seems unnecessary, however, when simulating hard rock pillars in mines where the seam modulus is very similar to that of the surrounding rock.

Jan 1, 2011

By Hideaki Kitajima, Daisuke Fukuda, Kazuma Moriya, Katsuya Sasaki, Katsuhiko Kaneko

The purpose of this research is to analyze the fracture process and achieve design optimization of a splitting method for concrete and rocks termed the electric discharge impulse crushing method (EDICM). The EDICM utilizes the cartridges being set in boreholes in the splitting target. The cartridge has a thin metal wire and is filled with nitromethane. By applying the electric discharge to the wire in the cartridge, plasma is caused leading to the vaporization of the wire. Then the deflagration of the nitromethane commences, which generates borehole pressure for splitting the target. Although the required splitting time is roughly several hundred micro-seconds and much slower than ordinary blasting, the fracturing still completes in quite short time and understanding the fracture process of opaque and brittle materials such as rock and concrete in this time scale is of academic importance.

Jan 1, 2011

By Gemei Yang, Yihui Zhao

In caved goaf, the friction loss of fluid head is: [h = (R'+ R/Q/ )] Q (for one-dimensional transition flow). The R' and R, which are the functions of two dimensional spaces, are calculated through an empirical formula. Then, the bulking factor and permeability are determined. It is supposed that the airflow in porous media are similar to those in tiny tubes crossing each other. Therefore, the network calculation technique can be used to tackle the field transition flow problem. A lot of case studies showed that the emission of methane in mines mainly depends on the air velocity and has little relation to air pressure. Summing up our experience and experiments, we provide an empirical formula to calculate the gas emission rate per unit area. By means of mass conservation and network calculation, the methane content distribution in steady-state is worked out. Then the dynamic change in airflows and gas content can be analyzed by the characteristic-difference method.

Jan 1, 1987

By Davar Abi-Zadeh, Cillian Brown, Deepak Kandra

"Grout backfill strategy for a particular subsurface concrete tunnel (~4.9km long, 3.5m in diameter, carrying 20” gas pipeline) was based on achieving 1:100 slope of the fill in order to progressively fill the tunnel, in a series of 350m section. Grout rheology, particularly its non-Newtonian and thixotropic behavior, determines the final fill slope for given backfill strategy. The objective of this study was to simulate the two-phase grout mix backfill process using Computational Fluid Dynamics (CFD) and determine the slope of the fill to validate and optimize the backfill strategy. Three dimensional CFD study showed that for a 500m long tunnel section with a single injection point of grout, given its rheology, it will likely keep flowing without filling the 500m section height wise. Design optimization for filling was carried out using two dimensional studies to make the backfill process “slope independent” by incorporating a 2.5m high bulkhead at ~1,000m. INTRODUCTION As part of a gas field development a 20” onshore gas pipeline is required from the landfall site to the processing terminal some 8km inland. At the landfall site the gas pipeline is routed in a ~5km underground tunnel underneath a bay. For operational reasons and planning consents as well as to mitigate environmental impact based on an environmental impact study, once the gas pipeline and the associated services and spares have been installed, the subsurface gas tunnel will be fully grouted. There will be no permanent access to the tunnel after construction is completed and the site compounds have been reinstated once works are complete. One of the key requirements is that “full grouting of the tunnel” is desired. The grouting material used is a non-Newtonian and thixotropic fluid mixture of bentonite, cement, plasticizer, retarder/stabilizer and water. The tunnel is filled progressively in 350m sections using a combination of existing and new pipework assuming the grout rheology will yield a fill slope of 1:100 in a 350m section. The proposed grouting system used one pump at the grouting compound to pump the grout into the tunnel using the existing tunneling pipework. For the longer runs a second booster pump was used in series to pump the grout to its final discharge location. The filling process is controlled via a system of flow meters, pressure transmitters and a tunnel CCTV system."

Jan 1, 2016

By R. L. Howell, L. C. Atkinson

Typical sedimentary sequences overlying coal seams consist of interbedded sandstones, siltstones, shales, and rider coal seams. In many surface coalmine settings, these sediments are saturated; and prior dewatering of them is necessary for effective and economic mining, including the stacking of saturated spoils. Such sedimentary sections usually have a very low vertical hydraulic conductivity that does not allow them to drain in a timely manner prior to their being stripped. One potential solution is installation of drainwells. Drainwells are small diameter wells that can collect water laterally from the various more permeable layers in the overburden and then gravity drain it to a lower layer – often the coal seam being mined – where it can be removed by pumping wells or sumps located in the bottom of the pit. A ground-water flow model utilizing the 3-dimensional finite element code MINEDW has been used to evaluate the effectiveness of usingdrainwells in a hydrogeologic setting that is typical of the Powder River Basin. A series of numerical simulations were completed using various combinations and spacings of drainwells and pumping wells to dewater the overburden and coal seams. The numerical simulations suggest that drainwells can be a very effective method of overburden dewatering.

Jan 1, 2000

By SONGHE WANG, YI XUE, PENG HOU, CAIHUI ZHU, XUANYE JIAO, Feng Gao

Coalbed methane development is an important way to effectively realize a source of clean energy and reduce emissions of carbon dioxide and other gases. However, due to the low permeability of coal seams, the development of coalbed methane in China has encountered substantial barriers. Protective layer mining can efficiently minimize in situ stress and increase coal seam permeability, thus improving gas drainage and avoiding gas disasters. This study analyzed the characteristics of gas migration and the change in permeability during the in situ stress releasing process through experiments and numerical simulation to study the gas drainage effect of a coal mine in an unloaded coal seam under specific geological conditions. First, a stress–strain-seepage coupled test of coal was carried out, and the evolution features of coal permeability during stress loading and unloading processes were investigated. Second, experimental results were used to develop a mathematical model of coal seepage under mining unloading conditions. Finally, a numerical model was developed based on the real geological conditions of the Wulan coal mine to explore the characteristics of in situ stress release and permeability evolution, as well as the gas drainage process in an unloaded coal seam. By combining protective layer mining and gas drainage technology, the risk of gas outburst is significantly reduced.

Oct 1, 2022

By Miguel Barron

Recently, a new lance design for BOF steelmaking has been proposed in the literature. This lance, in addition to six peripheral inclined supersonic nozzles, contains a vertical centered nozzle whose oxygen flow is independent from the main oxygen supply. The above authors affirm that their lance maximizes the droplet generation without causing spitting. In this work, the performance of a lance with four peripheral nozzles and one vertical centered nozzle is numerically modeled by means of Computational Fluid Dynamics software. Transient two dimensional computer simulations were carried out considering two phases, namely molten steel and gaseous oxygen. Numerical results confirm that bath agitation and droplet generation are enhanced as a result of the vertical centered nozzle, however a proper performance of this lance, related to a conventional one, strongly depends on the Mach number of the oxygen jets and the lance height.

Jan 1, 2008

By Zhang Wengang, L. John Endicott

The properties of many geological materials are variable. This is especially true for variations in elevation of the top of rock profile, strength of weathered rock, and conductivity of rock masses. Often the site investigation stage is completed by site specific ground investigation utilizing boring, sampling, and testing. Statistically this is a sampling procedure, but the borings are often widely spaced, and ground conditions between borings are deduced by interpolation. Often budgets are a limiting restraint and the information that is obtained may be less than desired. Sampling and testing is often biased. If claims for unforeseen ground conditions are to be avoided, the properties of the ground should be adequately identified. This paper describes how data can be used to evaluate the subsurface top of rock profiles, and can give insight into representative, maximum, and minimum strengths, and variation in conductivity relating to inflow of water into excavations, that can assist in planning the works and also in resolution, or avoidance, of disputes about unforeseen ground conditions. INTRODUCTION The mechanical properties of the ground are naturally variable. The work of Geologists, Engineering Geologists and Geotechnical Engineers is fundamentally investigative. Frequently, budgets for ground investigation are squeezed, resulting in widely spaced boreholes, with conditions between them determined by interpolation. Profiling can be adopted but the measurement, such as seismic velocity, is used as an indirect means of computing in-situ profiles and mass properties. Often a lot of test data are generated on large projects or by many projects in the same vicinity. Published data enlarge the database for a given project, and databases can be interrogated to gain insight into different categories of ground. Integration with geological studies can then lead to more reliable characterization of the ground in terms of identifying the materials present, their extent and their range of properties. This paper focuses on properties of rocks that are generally required for ground engineering, namely the top of rock profile, the unconfined strength of rock materials, and the mass conductivity. Data are obtained from Granodiorite and Granite in Hong Kong, and from Granite and the Jurong Series of weakly metamorphosed sedimentary rocks in Singapore. All four rock types have been tropically weathered, resulting in widely varying top of rock profiles, material strengths and mass conductivity. With a wide range in values for these parameters, project specific ground investigation conducted within a limited budget may run the risk of falling short of obtaining sufficiently reliable data sets, resulting in risk that unforeseen ground conditions may be encountered.

Jan 1, 2019

By Kyoosang Yoo

The report presents the results corresponding to the analysis of a lining system for tunnels in soil and soft rock in creep-active ground. The purpose of the analysis is to evaluate the performance of a lining at each construction stage. The steps include: 1. Accurate representation of the initial undisturbed state of stress 2. Excavation, 3. Lining installation 4. Injection of mortar and its curing, and 5. Short-, medium- and long-term creep behaviour in the surrounding soil/rock. The response of a prototype tunnel is simulated using the computational finite element framework MSC.marc2008.

Jan 1, 2010

By SONGHE WANG, YI XUE, PENG HOU, CAIHUI ZHU, XUANYE JIAO, Feng Gao

The abstract discusses the challenges of coalbed methane development in China due to low coal seam permeability. It highlights protective layer mining as a method to reduce in-situ stress and enhance permeability for improved gas drainage and disaster prevention. The study involves experimental and numerical simulations to analyze gas migration and permeability changes during stress release. It includes a stress-strain-seepage coupled test on coal, development of a mathematical model for coal seepage under mining unloading, and a numerical model based on the Wulan coal mine to explore in-situ stress release, permeability evolution, and gas drainage in an unloaded coal seam. The aim is to demonstrate the effectiveness of combining protective layer mining and gas drainage technology for gas outburst risk elimination.

Mar 14, 2022

By B. Y. Park

This paper develops a series of three-dimensional simulations for the Bayou Choctaw Strategic Petroleum Reserve. The U.S. Department of Energy plans to leach two new caverns and convert of one of the existing caverns within the Bayou Choctaw salt dome to expand its petroleum reserve storage capacity. An existing finite element mesh from previous analyses is modified by adding two caverns and increasing the size of existing Cavern 102. The structural integrity of the three expansion caverns and the interaction between all the caverns in the dome are investigated. The impacts of the expansion on underground creep closure, surface subsidence, infrastructure stability, and well integrity are quantified. The results show that from a structural viewpoint, the locations of the two newly proposed expansion caverns are acceptable, and all three expansion caverns can be safely constructed and operated.

May 1, 2009

By Yohan Cha, Eun-soo Hong, Gye-Chun Cho

"Rapid population growth and scarcity of space have led many developed cities to bury supply facilities. In line with this, utility tunnels have been employed in Korea since the 1970s. However, approximately 70% of structures were installed more than 20 years ago, in response to the issue of ageing, tunnel enlargement has been proposed. The aim of this study is to investigate geo-mechanical behavior due to tunnel enlargement. Tunnel enlargement methods have been researched to suggest a optimal method. A finite element analysis is conducted to evaluate ground behavior by the expansion of internal space. Vertical displacement and settlement trough width are investigated according to ground stiffness and different enlargement size. It was determined that displacement is affected by the enlargement size and ground stiffness. Based on the deformation results obtained from the numerical analysis, it is possible to predict ground behavior and stability upon tunnel enlargement. INTRODUCTION Various infrastructures such as electric lines, communication lines, gas pipes, and water pipes are jointly accommodated by utility tunnels. These utility tunnels improve the aesthetics of urban areas and help ensure stable supply. The first utility tunnel in Korea was adopted in 1978 and new tunnels are still being installed with the development of new suburb cities. Nevertheless, about 70% of the utility tunnels were installed over 20 years ago and they are still being used through ongoing repair. Moreover, 90% of utility tunnels were installed before 1995. With aging of the nation’s utility tunnels various problems such as concrete deterioration and scarcity of capacity have arisen. As solution, reconstruction has been considered. Reconstruction can enlarge space and improve the performance by replacing existing structures. For reconstruction, two routes have been proposed: underground excavation and cut and cover. In order to avoid traffic problems caused by road occupation and civil appeals during construction projects, underground excavation is the more attractive option. Tunnel enlargement methods have been classified (Seo et al., 2008; An et al 2013) and major considerations during tunnel enlargement have been outlined (Beak et al., 2007). Enlargement construction cases on road tunnels around the world were introduced (Kim et al., 2012) and the deformation curve during tunnel expansion was proposed to investigate the range of protection that should be offered (Kim et al., 2008; Beak et al., 2011). However, tunnel enlargement technology is limited to road tunnels and railway tunnels. Hence, a study on shallow box tunnel enlargement is required for practical application."

Jan 1, 2016

By Adriana Amaro Diacenco

Neste trabalho, os procedimentos para modelagem de estruturas de compósitos do tipo sanduíche que incorporam materiais viscoelásticos são apresentados. A análise numérica foi desenvolvida utilizando a Teoria de Deformação Cisalhante de Primeira Ordem (FSDT), que é implementada em um elemento Serendipity retangular contendo oito nós e cinco graus de liberdade. A incorporação do amortecimento para os modelos de elementos finitos em compósitos de placas laminadas é feita usando a abordagem de módulo complexo e a resolução numérica das equações resultantes do movimento são aspectos particularmente relevantes dos procedimentos de modelagem. Após as discussões de vários aspectos teóricos, as funções de resposta em frequências (FRF's) são calculadas para placas laminadas de compósitos com camada viscoelástica.

Aug 17, 2017