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  • Articles  (4,109)
  • Engineering General  (4,090)
  • Elastic analysis
  • fire
  • 1990-1994  (3,162)
  • 1975-1979  (947)
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  • Articles  (4,109)
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  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Fire technology 26 (1990), S. 290-309 
    ISSN: 1572-8099
    Keywords: Diesel engine ; railcar ; railroad ; fire ; fire investigation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying
    Notes: Abstract A fire broke out on a diesel railcar while running on a line of the Japan Railways Group. After an exhaustive investigation into the cause of the fire, it was found that the origin had been the lubricating oil of the engine. The lubricating oil vaporized from a long idling engine while the car was standing and accumulated in the exhaust silencer in considerable amounts. When the car was climbing up a long slope, the oil was exposed to a high-temperature exhaust gas and ignited. The flame attacked and melted the exhaust funnel, and eventually caused a fire.
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  • 2
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    Fire technology 27 (1991), S. 321-333 
    ISSN: 1572-8099
    Keywords: Hydraulic fluids ; spray combustion ; fire ; flame
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying
    Notes: Abstract The combustion intensity of hydraulic fluids and mineral oil, methanol, ethanol, and heptane, ejected vertically up ward through a pressure-jet hollow cone nozzle and stabilized by a ring burner, has been characterized in terms of heat release rates. A relationship has been established between the chemical heat release rate, fluid exit velocity, and chemical heat of combustion. Mineral oil, along with some organic esters, has the highest combustion intensity as indicated by heat release rate, followed by esters (organic and phosphates), heptane, water-in-oil emulsion, ethanol, methanol, and polyglycol-in-water. Variations in combustion intensities in hydraulic fluids are found to be due to variations in the chemical structures and additives. The efficiency of combustion is found to be sensitive to fluid exit velocity. The radiative fraction of the efficiency of combustion for phosphate esters is found to be the highest (0.38–0.40), followed by mineral oil (0.36), organic esters (0.28–0.35), water-in-oil emulsion (0.27–0.28), and polyglycol-in-water (0.12–0.25). The radiative fraction of the efficiency of combustion for ethanol and heptane spray fires is found to be less than for the pool fires. For methanol spray fire, radiative fraction of the efficiency of combustion is found to be about the same as for the pool fire. The visible flame length of hydraulic fluid spray fires varies with the chemical heat release rate to the power of 0.6 for both hollow and solid cone nozzles.
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  • 3
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    Fire technology 29 (1993), S. 246-267 
    ISSN: 1572-8099
    Keywords: fire ; plume ; hot layer ; smoke control ; computer software
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying
    Notes: Abstract A Program Plume has been created to compute the air entrainment for a given fire size and a specified hot layer height. The solution is based on integration of conservation law equations. The empirical assumptions are related to the flame height and to the coefficient of entrainment and are based on the experimental data of California's Institute of Technology. Calculations are compared with the experimental results obtained in the field tests. The program seems to describe the experimental data better than other known methods. A software package called “Firecalc” includes seven modules, based on the plume model, which describe hot layer properties in confined compartments relevant to practical situations. The computational results of these modules are also in good agreement with available results of field and laboratory tests.
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  • 4
    ISSN: 1572-8099
    Keywords: accelerants ; arson ; bedsprings ; fire ; fire investigation ; fire origin ; furniture ; springs ; glass ; metallurgy ; metals
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying
    Notes: Abstract The authors examined the remains of fifty structures destroyed in the October, 1991 fire in the hills east of Oakland, California. Traditional indicators of “abnormal fire behavior” were examined in each of the structures, including apparently melted steel items, melted copper, and melted as well as crazed glass. These indicators were found to have no probative value as to the presence of liquid accelerants, abnormally heavy fuel loads, or abnormally high temperatures.
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  • 5
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    Queueing systems 7 (1990), S. 101-124 
    ISSN: 1572-9443
    Keywords: Police ; fire ; queueing ; travel time ; simulation ; city government
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Notes: Abstract Cities with under 100,000 in population expend a significant portion of their budgets on emergency services. One option that a number of these cities have considered for improving service and cutting costs is training personnel to handle both police and fire roles. In this paper we describe a hierarchy of models that we have used to assess the performance viability of a merger as well as to design specific deployment plans. The modeling environment is more complex than a traditional police or fire system. We need to model the response pattern of four or more patrol units along with the simultaneous dispatch of fire equipment from one or more fire stations. The major contribution of the paper is the manner in which a series of models is linked together to forecast a wide range of performance measures under differing dispatch assumptions. We use a queueing model of police patrol to calculate steady state probabilities and expected delays without preemption. We then model two types of preemptive dispatch strategies utilized in responding initially to a major fire by superimposing a binomial distribution on the basic queueing model. There is also a travel time simulation model to calculate conditional expected response time statistics. The queueing models and the travel time simulation are then combined to estimate unconditional expected values. Lastly, we describe a simulation model used to address transient performance issues that are of concern during a major fire.
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  • 6
    ISSN: 1573-0417
    Keywords: palaeolimnolgy ; pollen ; diatoms ; pigments ; southern boreal forest ; fire ; Alberta
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Geosciences
    Notes: Abstract Palaeoenvioonmental investigations based upon sediment cores retrieved from Baptiste Lake, Alberta (longitude 114° 34′ W; latitude 54° 45′ N) show that the sedimentary record spans approximately 4600 years. The pollen record reflects the dynamic nature of the southern boreal forest. These dynamic changes are reflected in the lake record itself. Climate and vegetation do not appear to have changed significantly; however, the lake does appear to have responded to climate change, particularly during the last 1000 to 700 years when temperatures decreased to modern values. It is at this time that there is a marked change from laminated to unlaminated sediments suggesting a change from meromixis to one where complete circulation takes place. As a result monolimnetic nutrients are released into the epilimnion. Catchment perturbations have occurred with fire appearing most important. Sedimentation rates are high on average and irregular, due in part to the many inflowing streams, catchment topography and fire. Lake production has always been high. Carbonate bands occur in the core at irregular intervals and appear to originate biogenically. Peaks in the number of pyrite spherules suggest that deoxygenation of the water column occurs irregularly, and the intensity of anaerobic conditions again varies. The diatom record indicates a eutrophic lake with Stephanodiscus hantzschii the dominant species. The lake appears to have steadily become more eutrophic with time and a succession of species has occurred with Asterionella formosa being succeeded in turn by Stephanodiscus niagare, Cyclotella comta and finally, Melosira granulata. The appearance of Melosira granulata corresponds to the change from laminated to unlaminated sediments, and to then both autochthonous and allochthonous nutrient input.
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  • 7
    ISSN: 1572-9761
    Keywords: disturbance ; fire ; heterogeneity ; landscape pattern ; topography ; Wisconsin
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology
    Notes: Abstract The presettlement tree cover (1831–33) of 3 townships in a southern Wisconsin landscape was analyzed using original survey records. Four forest types were identified: closed forest, open forest, savanna, and prairie. Comparisons of vegetation types and landscape pattern were made between the east and west sides of the Pecatonica River, which bisects the landscape and could have acted as a natural fire barrier. West of the river, presettlement tree species richness and diversity were lower and trees were smaller in diameter and less dense than to the east. The major vegetation types to the west were prairie (42% of landscape) and savanna (40%), both fire-susceptible types. Prairie was more common on gentle slopes than on other landforms. To the east, the landscape was 70% forested (closed plus open forest). Here, prairie was more frequent on steep dry sites. These vegetation differences, including the contrasting landscape placement of prairie, are attributed to distinct site characteristics and to disturbance (fire) regimes, with the west likely having more frequent fires. In terms of the four vegetation types, the east landscape was more homogeneous, being dominated by closed forest (50%). West of the Pecatonica River, the landscape was more heterogeneous because of the high proportion of both prairie and savanna; however, in terms of flammability of vegetation, the west was essentially homogeneous (82% prairie plus savanna).
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  • 8
    ISSN: 1572-9729
    Keywords: fire ; climate change ; boreal forest ; stream ; sulfate ; acidity ; watershed
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Energy, Environment Protection, Nuclear Power Engineering , Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition
    Notes: Abstract In a boreal forest catchment in the Experimental Lakes Area in northwestern Ontario, wildfire caused an increase in the concentrations of strong acid anions and base cations of the stream. In the naturally base-poor Northwest (NW) Subbasin, a 1980 wildfire caused exports of strong acid anions to increase more than export of base cations, causing a 2.5 fold increase in the acidity of the stream. Mean annual stream pH declined from 5.15 prior to fire to 4.76 two years after fire. Acid-neutralizing capacity (ANC), calculated as the difference between total base cations and strong acid anions, decreased to 20% of pre-fire values. Sulfate and chloride were the strong acid anions responsible for the decline in ANC, increasing four-fold. While nitrate increased eleven-fold, concentrations were too low to significantly affect ANC. There was a significant correlation between weekly sulfate concentration and base cation concentration (r 2 = 0.83) in the two years after fire. Recovery of ANC was caused by the more rapid decline in concentration of sulfate than by changes in base cations. Drought produced a similar but weaker response than fire, with increased sulfate concentrations and decreased stream pH. Climatic warming that increases drought and fire frequency would have effects that mimic the impacts of acidic precipitation (i.e. higher sulfate concentrations and acidic stream waters). Areas which have higher concentrations of stored S from past acid precipitation or have large areas of peatlands in the watershed may have aggravated losses of S and H+ after drought and fire.
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  • 9
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    Biodiversity and conservation 3 (1994), S. 573-585 
    ISSN: 1572-9710
    Keywords: rodents ; fire ; Mediterranean ecosystem ; succession
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology
    Notes: Fire is a common disturbance in the Mediterranean ecosystem. A fire that broke out in the eastern Mediterranean pine forest on Mount Carmel in September 1989 destroyed thousands of hectares of natural forest. We carried out a comparative study of rodent recovery after fire under three different management regimes in order to establish the best treatment for recovery. Rodents were used as ‘bio-indicators’, because of their limited home range, to assess the best management practice to be used in the recovery of the post-fire habitat. Our results show that the three arboreal Palaeoarctic species which lived in this habitat before the fire either died during the fire or left the habitat as a result of its destruction. A succession of rodent species was observed. The untreated burned forest had the highest species diversity in the initial stage, while during a later stage the highest diversity was observed in plots where the burned trees were cut down, the trunks removed and the twigs collected into small piles. The results also suggest that removing the trunks and twigs at the initial stage of recolonization results in a more xeric and warm habitat which will postpone the reinvasion of the forest species.
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  • 10
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    Hydrobiologia 218 (1991), S. 177-192 
    ISSN: 1573-5117
    Keywords: fire ; South Africa ; fynbos ; stream chemistry ; water yield ; nitrate
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology
    Notes: Abstract The effects of a late-summer prescribed burn on the chemistry of a second-order mountain stream in the south-western Cape, South Africa, were investigated. Nitrate concentrations in stream water were significantly higher during the winter of the post-burn year. Increased concentrations of chloride, bicarbonate, polyphenols and potassium and decreased sodium concentrations were also recorded. Concentrations of ammonium, phosphate, calcium, magnesium, total dissolved solids and hydrogen ions were not significantly affected by the burn. Ionic export from the catchment was generally greater in the post-burn year. Apart from nitrate, however, values probably lie within the natural range of year-to-year variation. It is predicted that enhanced losses of nitrate will decrease progressively with the recovery of the vegetation and the re-establishment of soil/plant nutrient cycles. Atmospheric losses of nutrients in smoke were unquantified, but may be of more significance to site productivity than losses through surface runoff, which, in the case of nitrogen, appear to be compensated by precipitation inputs.
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  • 11
    ISSN: 1573-5117
    Keywords: storms ; stream chemistry ; antecedent conditions ; fire ; South Africa
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology
    Notes: Abstract The influence of different antecedent conditions on hydrochemical response during storm events was investigated in a small, south-western Cape mountain catchment. Winter and summer storms (four in total) were sampled both before and after the catchment was deliberately burnt. During winter storms, discharge responded rapidly to rainfall, and direct runoff represented the major component of streamflow. Marked lags were observed between rainfall and discharge peaks during the summer storms, and streamflow was dominated by delayed interflow. Chloride, PO inf4 sup3− -P and NO inf3 sup− -N exhibited variable response to discharge according to seasonal variations in soil-moisture levels, whereas the response of HCO inf3 sup− , H+ and NH inf4 sup+ -N was not influenced by season. The movement of ions appears to be affected more by geochemical processes operating within the soil than by plant-uptake dynamics, as the prescribed burn appeared to have little effect on relationships between ionic concentration and discharge. The findings of the study highlight the complexity of relationships between solute concentration and discharge.
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  • 12
    ISSN: 1573-515X
    Keywords: fire ; nitrification ; S.E. Spain ; semi-arid shrublands ; soil nitrogen
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Geosciences
    Notes: Abstract The short-term effect of a single fire, and the long-term effect of recent fire history and successional stage on total and mineral N concentration, net nitrogen mineralization, and nitrification were evaluated in soils from a steep semi-arid shrubland chronosequence in southeast Spain. A single fire significantly increased soil mineral N availability and net nitrification. Increasing fire frequency in the last few decades was. associated with a sharp decrease in surface soil organic matter and total N concentrations and pools, and with changes in the long-term N dynamic patterns. The surface-soil extractable NH4 +:NO3 − ratio increased throughout the chronosequence. All net mineralized N in laboratory incubations from all sites was converted to nitrate, suggesting that allelochemic inhibition of net nitrification is probably not important in this system. Net nitrification in samples during incubation increased through the sere. The maximum rate of net nitrification (kmax) increased through the first three stages of the sere. A linear relationship was found between total soil N and N mineralization, and both kmax and net nitrification for the first three stages of the sere, suggesting that total N and ammonification are likely to be the control mechanisms of nitrification within the sere. The oldest site exhibited the lowest specific kmax and the highest, potential soil respiration rate suggesting that a lower N quality and increasing competition for ammonium might also limit nitrification at least in the long-unburned garrigue site.
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  • 13
    ISSN: 1573-515X
    Keywords: carbon ; fire ; immobilization ; mineralization ; nitrogen use efficiency ; soil organic matter ; tallgrass prairie
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Geosciences
    Notes: Abstract Fires in the tallgrass prairie are frequent and significantly alter nutrient cycling processes. We evaluated the short-term changes in plant production and microbial activity due to fire and the long-term consequences of annual burning on soil organic matter (SOM), plant production, and nutrient cycling using a combination of field, laboratory, and modeling studies. In the short-term, fire in the tallgrass prairie enhances microbial activity, increases both above-and belowground plant production, and increases nitrogen use efficiency (NUE). However, repeated annual burning results in greater inputs of lower quality plant residues causing a significant reduction in soil organic N, lower microbial biomass, lower N availability, and higher C:N ratios in SOM. Changes in amount and quality of below-ground inputs increased N immobilization and resulted in no net increases in N availability with burning. This response occurred rapidly (e.g., within two years) and persisted during 50 years of annual burning. Plant production at a long-term burned site was not adversely affected due to shifts in plant NUE and carbon allocation. Modeling results indicate that the tallgrass ecosystem responds to the combined changes in plant resource allocation and NUE. No single factor dominates the impact of fire on tallgrass plant production.
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  • 14
    ISSN: 1573-515X
    Keywords: carbon ; fire ; immobilization ; mineralization ; nitrogen use efficiency ; soil organic matter ; tallgrass prairie
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Geosciences
    Notes: Abstract Fires in the tallgrass prairie are frequent and significantly alter nutrient cycling processes. We evaluated the short-term changes in plant production and microbial activity due to fire and the long-term consequences of annual burning on soil organic matter (SOM), plant production, and nutrient cycling using a combination of field, laboratory, and modeling studies. In the short-term, fire in the tallgrass prairie enhances microbial activity, increases both above-and belowground plant production, and increases nitrogen use efficiency (NUE). However, repeated annual burning results in greater inputs of lower quality plant residues causing a significant reduction in soil organic N, lower microbial biomass, lower N availability, and higher C:N ratios in SOM. Changes in amount and quality of below-ground inputs increased N immobilization and resulted in no net increases in N availability with burning. This response occurred rapidly (e.g., within two years) and persisted during 50 years of annual burning. Plant production at a long-term burned site was not adversely affected due to shifts in plant NUE and carbon allocation. Modeling results indicate that the tallgrass ecosystem responds to the combined changes in plant resource allocation and NUE. No single factor dominates the impact of fire on tallgrass plant production.
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  • 15
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    Rock mechanics and rock engineering 7 (1975), S. 35-65 
    ISSN: 1434-453X
    Keywords: Tunnelling ; Soil Mechanics ; Tunnel shield ; Elastic analysis ; Ground deformation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Geosciences
    Description / Table of Contents: Summary Ground Disturbance Associated with Shield Tunnelling, in Overconsolidated Stiff Clay The present paper attempts to describe the ground disturbance which occurs during a shield tunnelling, in an overconsolidated stiff clay. In particular, an effort has been made to find the possible main factors, which might affect the form and the magnitude of the detected ground movements. However, a correlation between the former factors and the actual performance of the clay was attempted, when it seemed possible and realizable. This was due to the fact that the overall process of tunnelling where the ground disturbance propagates in space, evolving in time is of some complexity like any multiparameter problem. Finally, by using the elasto-plastic approach, a simple analysis has been carriedout, on which the stress regime has been evaluated and properly connected with the tunnel advance. Ground deformations, predicted on that basis, were compared to the in-situ measurements making it easy to check the adopted concept.
    Abstract: Résumé Perturbation du terrain relative au tunnel construit par la méthode du bouclier, dans l'argile raide surconsolidée Le présent article décrit la perturbation du terrain qui prend lieu, lors des travaux de construction d'un tunnel, par la méthode du bouclier, dans un milieu d'argile raide surconsolidée. Un effort tout spécial s'est déployé, afin de localiser et mettre en évidenceles facteurs probables, qui par leur influence donnent naissance à la formation, comme aussi, aux formes et amplitudes des mouvements du terrain, enregistrés. L'examen tenté de la corrélation, entre les facteurs en question et le comportement du terrain, s'est avéré réaliste et opportun. Ceci est dû à la procédure compliquée de la construction d'un tunnel, qui donne lieu, à la propagation de la perturbation du terrain dans son milieu, comme aussi à l'évolution ultérieure temporelle. En somme, ce sujet présente les mêmes complication qu tout problème multiparamétral. Finalement, faisant emploi de l'adoption élastique-plastique et par le moyen d'une simple analyse, il fut possible d'évaluer l'étát des contraintes pour le tunnel á section droite circulaire. L'étát des contraintes fut ensuite combinée à la progression du tunnel. Les données prévues au moyen de la théorie d'élasticité, des déplacements radiales du terrain, après avoir été comparées avec les mensurations prises in-situ, ont donné la possibilité de la vérification et de l'adoption du principe théorique.
    Notes: Zusammenfassung Die Erdreichstörung bei der Konstruktion eines Schildtunnels im überkonsolidierten steifen Ton Die vorliegende Arbeit betrifft die Erdreichstörung, die bei der Konstruktion eines Schildtunnels im überkonsolidierten steifen Ton vorkommt. Besondere Bemühungen wurden vorgenommen, um die möglichen Faktoren aufzufinden, welche Gestaltung und Größe der registrierten Bodenbewegung beeinflussen. Vergleiche zwischen diesen und den beobachteten Eigenheiten des Bodens wurden dann vorgenommen, wenn sie angemessen und realistisch erschienen. Das ist der Grund, daß der Fortschritt eines Tunnelbaues, welcher die Übertragung in den Raum der Erdreichstörung voraussieht und synchron die zeitliche Entwicklung dieser, ein kompliziertes dynamisches Problem darstellt. Zum Schluß wurde mit Hilfe der elastisch-plastischen Annahme eine einfache Analyse aufgestellt, aus der der Druckzustand um den Querschnitt des Tunnelhohlraumes berechnet wurde. Der Spannungszustand wurde mit dem Fortschritt des Tunnelaushubes kombiniert. Schließlich ergeben die aus der elastischen Theorie aufgefundenen Werte des Hohlraumquerschnittes, verglichen mit den Resultaten der an Ort und Stelle vorgenommenen Messungen, die Kontrollmöglichkeit der angenommenen theoretischen Annahme.
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  • 16
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    Experimental and applied acarology 18 (1994), S. 703-710 
    ISSN: 1572-9702
    Keywords: Soil mites ; forest reserve ; fire ; recovery
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology
    Notes: Abstract Mite populations in a forest reserve, where accidental fire swept through almost half of the total area covered by the forest, were enumerated at one, three, and six months after burning. Mite densities in both burnt and unburnt plots were extremely low immediately after burning. Six months after burning, the density of juvenile cryptostigmatid mites were higher in the burnt area than the unburnt area and several mite genera had recovered from the deleterious effect of burning, but overall mite densities were still lower in the burnt than the unburnt area. Some of the typical dominant mite genera of the tropical rainforest, namely Haplozetes sp., Scheloribates sp., Nothrus sp. and Carabodes sp. did not recover from the effect of burning within six months. The selective influence of burning on mite genera/families, as well as the different rates of recovery observed in this study, were attributed to differences in feeding requirements, phenological patterns and life history tactics of the mites. Juvenile cryptostigmatid mites were more in the burnt than unburnt plots suggesting that reproductive activities of this group increased after burning.
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  • 17
    ISSN: 1573-5117
    Keywords: disturbance ; recovery ; fire ; streams ; stability ; macroinvertebrates ; watershed
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology
    Notes: Abstract Macroinvertebrate communities of five headwater streams in catchments disturbed by wildfire were compared with five similar streams with no catchment disturbance. Over the five years of observation, communities in disturbed streams were more similar to one another than they were to reference streams. Communities in disturbed streams exhibited more year-to-year variation than reference streams, although some indication of decreasing variation was evident through time, and species richness was greater in reference streams than disturbed streams. No increasing trend in richness over time was observed in disturbed streams. Stability of the relative abundance structure and persistence of dominant taxa through time may be characteristic of temperate streams over moderate time intervals. Local effects of catchment-wide disturbance have persistent effects that alter these trends.
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  • 18
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    Biogeochemistry 15 (1992), S. 191-211 
    ISSN: 1573-515X
    Keywords: acid deposition ; ammonia volatilization ; cattle ; fertilizer ; fire ; nitrogen cycling ; soil nitrogen ; urea
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Geosciences
    Notes: Abstract We provide an assessment of the global sources of NH3 in the atmosphere, which indicates an annual flux of about 75 Tg of N as NH3. The emissions from land are dominated by the release of NH3 during the hydrolysis of urea from the urine of domestic animals (32 TgN/yr) and by emanations from soils in unmanaged ecosystems (10 TgN/yr) and from fertilized agricultural soils (9 TgN/yr). Emissions from the sea surface may approach 13 TgN/yr. The total annual source of NH3 is in reasonable agreement with estimates of global NH 4 + deposition from the atmosphere, the major fate of atmospheric NH3. As an alkaline atmospheric species, NH3 emitted to the atmosphere each year can neutralize only about 32% of the annual production of H+ in the atmosphere from natural and anthropogenic sources.
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  • 19
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper describes a practical implementation of the Galerkin finite element procedure for solving systems of parabolic partial differential equations with non-linear boundary conditions. This technique consists of finding an approximation in the form of a finite sum of cubic B-splines, which yield high-order accurate results, and consequently, solutions can be developed with remarkable precision and speed up to the steady state region where conventional finite difference methods often fail. In addition, the choice of mesh width and nodal spacing can be automatically determined for a predictor-corrector routine, thereby relieving the engineer of a great deal of ‘guess work’ that is normally characteristic of solving such problems.
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  • 20
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    International Journal for Numerical Methods in Engineering 9 (1975), S. 101-107 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The optimum profile of a beam is obtained by using finite elements with mathematical programming techniques. Beam profiles of preceding studies can be diplicated by the finite element method with the appropriate choice of numerical tolerance used in the convergence test.
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  • 21
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    International Journal for Numerical Methods in Engineering 9 (1975), S. 149-168 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A cutting plane algorithm for the solution of generalized geometric programs with bounded variables is described and then illustrated by the detailed solution of a small numerical example. Convergence of this algorithm to a Kuhn-Tucker point of the program is assured if an initial feasible solution is available to initiate the algorithm. An algorithm for determining a feasible solution to a set of generalized posynomial inequalities which may be used to find a global minimum to the program as well as test for consistency of the constraint set, is also presented. Finally an application in optimal engineering design with seven variables and fourteen non-linear inequality constraints is formulated and solved.
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  • 22
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    International Journal for Numerical Methods in Engineering 9 (1975), S. 259-270 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A class of approximations to the matrix linear differential equation is presented. The approximations range, in accuracy, from the simplest forward difference scheme to the exact solution. The infinite series defining the exponential matrix is used to ascertain the accuracy of the various approximations. A clear distinction is made between approximations to the system equations and the forcing function, with the forcing term being represented by a piecewise linear function. Special application is given to the equations arising in structural dynamics of the form For these structural dynamic equations, the measure of the energy of the system is used to analyse the stability of the numerical approximations.
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  • 23
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    International Journal for Numerical Methods in Engineering 9 (1975), S. 209-218 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
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    Notes: Advances in technology and interest in limit state design have made the inclusion of non-linear effects, such as elasto-plastic behaviour, desirable in the analysis of many structures. Improvements in solution algorithms coupled with parallel developments in high speed digital computers have now made the practical solution of such problems possible. The paper presents numerical solutions to three-dimensional elasto-plastic problems illustrating the applicability of isoparametric elements and the order of computation times involved.
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    International Journal for Numerical Methods in Engineering 9 (1975), S. 245-250 
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    Keywords: Engineering ; Engineering General
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    International Journal for Numerical Methods in Engineering 9 (1975), S. 691-699 
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    Keywords: Engineering ; Engineering General
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    Notes: The utility of the method of orthogonal collocation for solving stiff boundary value problems is investigated. To this end, the method is applied to a number of very stiff problems from the engineering and applied mathematics literature. The examples include both linear and non-linear problems defined on both finite and infinite intervals, a singular perturbation problem, and an inherently unstable problem. The examples demonstrate the usefulness of the method for a wide variety of stiff problems, as well as some of its limitations.
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    International Journal for Numerical Methods in Engineering 9 (1975), S. 461-476 
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    Notes: The boundary integral equation known as Green's Theorem has been solved to generate displacement and stress fields directly on the boundary for cylinders and solids of revolution in pure elastic torsion. The computer programs which effect the solution utilize conventional numerical methods and discrete analytical elemental integrations and are applicable to multiply-connected shapes. The integral equation has been differentiated in each case, so that internal stresses may be generated directly, where required.Computed results are compared with analytical solutions and with experimental evidence produced by photoelastic techniques.
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    International Journal for Numerical Methods in Engineering 9 (1975), S. 491-491 
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    International Journal for Numerical Methods in Engineering 9 (1975), S. 833-845 
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    Keywords: Engineering ; Engineering General
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    Notes: Elemental mass matrices have been produced for the vibration of conical and cylindrical shells, based on a semi-analytical approach. Frequencies and modes of vibration have been compared with existing solutions and also with experimental results obtained from other sources. Good agreement has been found between theory and experiment for thin-walled circular cylinders and cones, a cone-cylinder combination, and a cooling tower model.A theoretical investigation was also made on the vibration of a circular cylinder when subjected to uniform pressure.
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    International Journal for Numerical Methods in Engineering 9 (1975), S. 948-949 
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    International Journal for Numerical Methods in Engineering 10 (1976), S. 59-66 
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    Notes: A method is presented to calculate the eigenvalues of the Helmholtz equation Δ2ø + k2ø = 0 in a two-dimensional area when ø vanishes on the boundary. The method is based on an integral equation, which can be easily solved numerically. Results obtained for circular and rectangular geometries are also given and compared to the exact values.
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    International Journal for Numerical Methods in Engineering 10 (1976), S. 77-91 
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    Keywords: Engineering ; Engineering General
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    Notes: This paper presents the results of an aeroelastic optimization study. In this study the weight of a large aspect ratio panel immersed in high Mach number supersonic flow is minimized subject to the requirement that a critical aeroelastic parameter for flutter be held within specified limits. A refined finite element technique is used to model the panel flutter equilibrium equations, equations which act as constraints on the design search. The optimization mechanism itself is studied and discussed to provide qualitative results which may be useful to the solution of other aeroelastic optimization problems. The numerical results of this investigation are compared to converged numerical results to illustrate finite element accuracy. The results of the study show that the weight savings and material distribution found with an effective finite element model are comparable to those found by more complicated numerical methods.
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    International Journal for Numerical Methods in Engineering 10 (1976), S. 185-196 
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    Notes: A computer solution for two-dimensional fluid-particle flows using the cellular approach is presented. The euqations describing the flow of the continuous (fluid) phase are formulated using stream function, vorticity and enthalpy as the dependent variables. The effect of the disperse (particle) phase on the continous phase is represented by vorticity and energy sources in each cell. To illustrate the capability of the solution scheme, the flow of gas laden with hot particles issuing into a sudden expansion is analysed.
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    International Journal for Numerical Methods in Engineering 10 (1976), S. 283-299 
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    Notes: This paper presents the optimum design of stiffened cylindrical panels with weight as the objective function and constraints on the frequencies in the presence of initial stresses, using unconstrained minimization techniques of non-linear mathematical programming problem. The interaction between the buckling constraints and the frequency constraints in the presence of initial stresses are included in the formulation. Loss of load carrying capacity due to imperfection and due to suddenly applied loads are included in the buckling analyses. Results for cylindrical shell are obtained by setting the panel angle to 360 degrees. The relationship between the weight of the cylinder and the panel (a segment of the cylinder) is examined.
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    International Journal for Numerical Methods in Engineering 10 (1976), S. 361-377 
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    Notes: The solutions of plane elasto-plastic problems usually use one or two field variables - namely a stress functions or the displacements. The use of three, four or five field variables is investigated and it is concluded that the three stresses from the best basis for a multivariable approach. Attempts to solve the governing equations with an initial value technique were exhaustively tried and discarded in preference to a boundary value or elliptical technique. The problem solved to check the method is that of a hole in plane strain uniaxial tension. Effective plastic strain distributions are plotted, along with stress and strain concentration data and distributions of the mean to effective stress ratio. Comparison is made between solutions produced using incremental and deformation theories.
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    International Journal for Numerical Methods in Engineering 10 (1976), S. 437-456 
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    Notes: Finite element procedures and related illustrative numerical examples for incompressible viscous fluid motion are discussed in this paper. The steady flow problem is solved by the Newton-Raphson method and the perturbation method. By numerical examples, it can be shown that the combined use of the Newton-Raphson method and perturbation method is suitable. For the analysis of unsteady flow, the perturbation method is employed. Assuming that the basic flow is known, unsteady flow is calculated by accumulating the solution of the linearized equation in which the boundary values are varied by small amounts. Steady flows of temperature dependent free convection are also discretized and analyzed by the same procedure as the conventional finite element Galerkin method. For shape functions, quadratic polynomials are used for velocity and temperature, and linear polynomials for pressure. It is to be noted that the selections of shape functions and solution method are the keys to the analysis of highly non-linear fluid flow problems such as those discussed in this paper.
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    International Journal for Numerical Methods in Engineering 10 (1976), S. 488-488 
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    International Journal for Numerical Methods in Engineering 10 (1976), S. 503-525 
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    Notes: A procedure of applying the perturbation method is presented for the incremental numerical analysis of materially and combined non-linear problems of discrete and discretized structral systems. Small but finite strain and stress increments are strictly distinguished from the strain rates and stress rates, respectively. It is shown that, by applying the perturbation procedure not only to the non-linear strain-displacement relations and equilibrium equations, but also to the constitutive equations in terms of rate quantities, all the governing equations can be satisfied to any desired accuracy at every instantaneous configuration in between the starting and terminal points of an incremental step. The proposed method provides also means of finding, to a desired accuracy, every point on an equilibrium path of a discrete system at which a new element will start yielding or unloading and possible critical points on the path. The significance of the proposed method is expected to be appreciated particularly in numerical investigations of critical behaviours and post-buckling behaviours.
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    International Journal for Numerical Methods in Engineering 10 (1976), S. 301-343 
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    Notes: This paper is concerned with the development of a numerical procedure for solving complex boundary value problems in plane elastostatics. This procedure - the displacement discontinuity method - consists simply of placing N displacement discontinuities of unknown magnitude along the boundaries of the region to be analyzed, then setting up and solving a system of algebraic equations to find the discontinuity values that produce prescribed boundary tractions or displacements. The displacement discontinuity method is in some respects similar to integral equation or ‘influence function’ techniques, and contrasts with finite difference and finite element procedures in that approximations are made only on the boundary contours, and not in the field. The method is illustrated by comparing computed results with the analytical solutions of two boundary value problems: a circular disc subjected to diametral compression, and a circular hole in an infinite plate under a uniaxial stress field. In both cases the numerical results are in excellent agreement with the exact solutions.
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    International Journal for Numerical Methods in Engineering 10 (1976), S. 423-435 
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    Notes: The application of the finite element method to the supersonic flutter of circular cylindrical shells subjected to internal pressure and axial compression is presented. A circular cylindrical shell element is used. The element stiffness, mass and initial stiffness matrices are given. The element aerodynamic matrix is derived based on a first order high Mach number approximation to the linear potential flow theory. The eigenvalue problem is solved by the QR algorithm. Numerical results are presented and these are compared with analytical solutions and experimental data.
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    International Journal for Numerical Methods in Engineering 10 (1976), S. 401-412 
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    Notes: A straightforward and general computer program for assembling and solving (using Gauss elimination technique) widely sparsed finite element matrix equations with very large bandwidth and capable of handling different degrees-of-freedom and variable bandwidth at different nodes, is described herein. The program assembles any type of finite elements having arbitrary number of nodes and each node may have differnt degrees-of-freedom. It requires only a small core memory in the computer, although a fast random access device is also needed. The two very important features of this program are (i) it does not store any zero submatrices within the band and (ii) during the solution of equations all operations dealing with zero submatrices within the band are automatically skipped and thus the savings of a considerable amount of disc storage space and computer time can be effected in many cases. Another feature is that many right hand sides can be handled simultaneously. Hence the program is very economical for structures having widely sparsed matrix equations. A listing of the computer program written in FORTRAN IV for CDC 6400 computer is readily available from the authors, but unfortunately could not be given here because of lack of space. The program is so general that it can be used to solve a wide class of finite element problems without actually having to understand fully the techniques behind it.
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    International Journal for Numerical Methods in Engineering 10 (1976), S. 465-470 
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    Notes: The Peaceman-Rachford ADI technique is a well-known iterative method for solving large systems of linear equations arising from finite difference methods of solution of partial differntial equations. The present note demonstrates how the algorithm can be conveniently rearranged for computation in a virtual storage system with paging. Timing results are given for a sample problem typical of those encountered in nuclear diffusion computation.
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    International Journal for Numerical Methods in Engineering 10 (1976), S. 472-474 
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    International Journal for Numerical Methods in Engineering 11 (1977), S. 115-130 
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    Notes: The investigation of the convergence properties of matrix iterative processes usually involves test matrices of high order. This fact may prohibit an analytic approach to the problem. In this paper a method is presented which converts the multidimensional test procedure into a scalar one. The method is presented in conjunction with the problem of matrix orthogonalization which exists in Strapdown Inertial Navigation. Three examples are presented in which the convergence of matrix orthogonalization techniques is investigated. The examples demonstrate the use of the unidimensional convergence test in determining the order of the processes and in finding sufficient conditions for convergence. Numerical results are presented.
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    International Journal for Numerical Methods in Engineering 11 (1977), S. 194-198 
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    Notes: This paper contains an algorithm for the ordering of elements in the finite element method, which can be utilized in the Non-assembly Method of the author and in the Frontal Solution Method of B. M. Irons.
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    International Journal for Numerical Methods in Engineering 11 (1977), S. 231-246 
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    Notes: Based on a generalized complementary energy principle the derivation of the element matrices is presented for calculation of natural frequencies. The degrees-of-freedom are not defined on nodal points but in an abstract way. No restrictions about the number of interpolation functions in the interior and at the boundaries of the element have been introduced. The exact solution of the discretized element equations leads to the dynamic stiffness matrix while the approximate solution results in a linear eigenvalue problem. Plate bending problems are used to study the convergence of frequencies depending on the degrees of interpolation functions within the element and on its boundaries and on the number of elements.
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    International Journal for Numerical Methods in Engineering 11 (1977), S. 247-267 
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    Notes: A Block-Stodola eigensolution method is presented for large algebraic eigensystems of the form AU = λBU where A is real but non-symmetric. The steps in this method parallel those of a previous technique for the case when both A and B were real and symmetric. The essence of the technique is simultaneous iteration using a group of trial vectors instead of only one vector as is the case in the classical Stodola-Vianello iteration method. The problem is then transformed into a subspace where a direct solution of the reduced algebraic eigenvalue problem is sought. The main advantage is the significant reduction of computational effort in extracting a subset of eigenvalues and corresponding eigenvectors. Theorems from linear algebra serve to underlie the basis of the present technique. Complex eigendata that emerge during iteration can be handled without doubling the size of the problem. Higher order eigenvalue problems are reducible to first order form for which this technique is applicable. The treatment of the quadratic eigenvalue problem illustrates the details of this extension.
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    International Journal for Numerical Methods in Engineering 11 (1977), S. 377-382 
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    International Journal for Numerical Methods in Engineering 11 (1977), S. 393-395 
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    International Journal for Numerical Methods in Engineering 11 (1977), S. 404-405 
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    International Journal for Numerical Methods in Engineering 11 (1977), S. 411-417 
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    Notes: We suggest an exercise which illustrates many of the fundamental ideas of finite elements, and is nevertheless easily programmed and quickly solved. It is governed by a partial differential equation on a circular region, but by maintaining symmetry the stiffness matrix becomes small and tridiagonal. The accuracy of linear elements can be studied in detail, and a straightforward extension leads to the eigenvalue problem, elements of higher degree, numerical integration, isoparametric elements, and a simple example in plasticity.
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    International Journal for Numerical Methods in Engineering 11 (1977), S. 469-480 
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    Notes: A novel method is proposed for the numerical computation of Fourier coefficients in the range of higher frequencies for which hitherto no practical method was available. The accuracy of the results obtained by application of this method is discussed, and bounds of a correction term are determined accordingly. An example from the field of Diesel engine research is given, and the computed spectrum is compared with the spectrum recorded by an electronic harmonic analyzer.
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    International Journal for Numerical Methods in Engineering 11 (1977), S. 185-190 
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    International Journal for Numerical Methods in Engineering 11 (1977), S. 204-207 
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    International Journal for Numerical Methods in Engineering 11 (1977), S. 269-287 
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    Notes: Finite element formulations based on the Galerkin and variational principles have been developed for the self-adjoint and non-self-adjoint problems represented respectively by the flow and convective-dispersion equations in the cylindrical polar system of co-ordinates. The formulation based on the variational principle is shown to be restricted to dispersion-dominant transports only. The Galerkin method is demonstrated to be more versatile and free from convergence and stability problems. The computational scheme based on the Galerkin principle is shown to be equally valid for both convection and dispersion dominant transports. The numerical results obtained are verified with known analytical solutions. It is concluded that the suggested scheme can be used in solving a variety of field problems involving groundwater dispersion.
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    International Journal for Numerical Methods in Engineering 11 (1977), S. 579-591 
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    Notes: The indirect design problem for compressible fluid flow in a channel determines the physical shape of the channel from the prescribed flow on the channel boundary. In this paper, a global variational method for the solution of this problem is described.The non-linear equations are solved by iteration; at each step of this iteration the solution to the equations (which are now linear) is found by a global variational method. The variational method differs from conventional methods in that the trial function does not satisfy the prescribed boundary conditions, but the method reproduces the conditions on the boundary.Results are presented for various physical quantities associated with the channel.Some comments are made on the extensions of these methods to supersonic flow and to the realistic cascade design problem.
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    International Journal for Numerical Methods in Engineering 11 (1977), S. 605-605 
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    International Journal for Numerical Methods in Engineering 11 (1977), S. 611-622 
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    Notes: A complete analytical analysis of three-dimensional, quadratic displacement tetrahedron elements is presented. The results show that the element stiffness can readily be obtained from the much simpler stiffness matrix of the linear displacement element. Thus, the task of obtaining the matrix of the quadratic displacement element is, in effect, reduced to finding that of the linear displacement element.The analysis has been made possible only by using a symbolic manipulation language (PL/I-FORMAC) on a computer. A rather general program for computer-aided basic element analysis is presented. It seems that the extremely effective tool of symbolic manipulation has hardly been used until now in mechanics.
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    International Journal for Numerical Methods in Engineering 11 (1977), S. 407-407 
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    International Journal for Numerical Methods in Engineering 11 (1977), S. 431-438 
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    Notes: A direct numerical method is presented for the solution of classes of non-linear, singular Volterra integral and integro-differential equations of the types where y is the unknown and the Fs and Gs are given but to a large extent arbitrary functions of their arguments. The adaptation of the method to other equations, in particular with different kernels, is immediate.
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    International Journal for Numerical Methods in Engineering 11 (1977), S. 817-832 
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    Keywords: Engineering ; Engineering General
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    Notes: An interative approach is proposed for the numerical analysis of elastic-plastic continua. This approach gives after convergence an implicit scheme of integration of the evolution problem, and is concerned with elastic-perfectly plastic materials and with hardening standard materials. Under a generalized assumption of positive hardening, the proof of convergence of the iterative solutions is given. Some numerical examples by the finite element method are also discussed.
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    International Journal for Numerical Methods in Engineering 11 (1977), S. 875-881 
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    Notes: An elasto-plastic finite element small displacement procedure to predict the behaviour of structures under cyclic loads is presented. The solution combines incremental procedure with correction for equilibrium and iterative scheme. Applications are made for a rectangular strip and a notched bar under cyclic axial loads. Flow theory of plasticity with either isotropic hardening or kinematic linear hardening is used.
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    International Journal for Numerical Methods in Engineering 11 (1977), S. 771-796 
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    Notes: The objective of the paper is a survey and classification of available numerical methods for boundary value problems with an emphasis on two point boundary value problems. In the paper a general two point boundary value problem is stated first and later available numerical methods are classified into five main groups according to their approach in numerical solution. In the next sections of the paper, each of these main groups are described and appropriate subgroups are defined and discussed.
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    International Journal for Numerical Methods in Engineering 11 (1977), S. 945-962 
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    Notes: A two-dimensional isoparametric Hermitian element is investigated for use in potential field problems with irregular geometry. Nodal degrees-of-freedom are the potential, the gradients in the directions normal and tangential to the element sides, and the twist. In applying the isoparametric principle a simple approximation is used which in general guarantees C1 continuity only at the element corners. The present version is restricted to 90-degree interior angles.The element is applied in the Galerkin solution of the steady-state continuity equation and several examples are presented. It is found that in cases where the potential field is simple but the element is strongly distorted, gradients obtained from the Hermite are not as accurate as those from the Lagrange-type cubic element having the same number of degrees-of-freedom. When the potential field is complex and the distortion is small, the Hermitian gradients are comparable to those of the Lagrange cubic; with increasing distortion they are comparable at the boundaries but less so in the interior. The errors in the potentials themselves are very similar, both elements giving a high degree of accuracy.Since all of its degrees-of-freedom are shared by four elements in the interior of a grid, the Hermite element is approximately 20 per cent more efficient than the Lagrange cubic for all but the smallest grids. Also, since the Hermite uses fewer nodes, data handling is greatly reduced. The element appears to be attractive at least in the area of groundwater flow.
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    International Journal for Numerical Methods in Engineering 11 (1977), S. 1005-1027 
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    Keywords: Engineering ; Engineering General
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    Notes: Optimization techniques are applied to the design of both hydrodynamic journal and tilting pad thrust bearings. Fletcher's adaptation of Davidon's gradient search method is further modified to deal with non-linear constraints in journal bearing design. A form of the Sequential Simplex is used for tilting pad thrust bearings. Penalty functions and variable transformations are used in both cases. Composite objective functions are included and the effect of weighting on each component of the composite function is investigated.
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    International Journal for Numerical Methods in Engineering 11 (1977), S. 623-640 
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    Keywords: Engineering ; Engineering General
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    Notes: A method is presented for the minimum weight optimum design of laminated fibre composite plates, subject to multiple inplane loading conditions, which includes stiffness, strength and elastic stability constraints. The buckling analysis is based on an equivalent orthotropic plate approach leading to two uncoupled eigenproblems per load condition. Overall computational efficiency is achieved by using constraint deletion techniques in conjunction with Taylor series approximations for the constraints retained. The optimization algorithm used, namely the method of inscribed hyperspheres, is a sequence of linear programs technique which exhibits rapid convergence in this application. Several example problems are given to demonstrate that the method presented offers an efficient and practical optimum design procedure for the fundamental and recurring problem treated.
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    International Journal for Numerical Methods in Engineering 11 (1977), S. 709-728 
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    Notes: The penalty function approach has been recently formalized as a general technique for adjoining constraint conditions to algebraic equation systems resulting from variational discretization of boundary value problems by finite difference or finite element techniques. This paper studies the numerical behaviour of the penalty function method for the special case of individual equation constraints imposed on a symmetric system of linear algebraic equations. Constraint representation and computational roundoff error components are distinguished and asymptotically characterized in terms of the penalty function weight coefficients. On the basis of this study, practical rules for the automatic assignment of values to those coefficients within the linear equation solver are proposed. Numerical problems encountered in the case of more general constraints are briefly discussed, and procedures for circumventing such difficulties are suggested.
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    International Journal for Numerical Methods in Engineering 11 (1977), S. 756-758 
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    International Journal for Numerical Methods in Engineering 11 (1977), S. 766-767 
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    International Journal for Numerical Methods in Engineering 11 (1977), S. 770-770 
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    International Journal for Numerical Methods in Engineering 11 (1977), S. 1107-1115 
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    Notes: Based on the Lagrange multiplier's concept, a superposition method of analytical and finite element solutions has been developed to solve efficiently various non-linear and/or time-dependent problems in structural mechanics. According to the theory, the transient creep behaviour of a cantilever beam is analysed as an expository example.
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    International Journal for Numerical Methods in Engineering 11 (1977), S. 1198-1198 
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    International Journal for Numerical Methods in Engineering 11 (1977), S. 883-895 
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    Notes: The analysis of stresses and deformations in concrete structures subjected to temperature gradients is described. As a result of the spatial variation of temperature, the creep compliance is a function of position. Previous work has shown that the constitutive equations for concrete creep can be expressed in a form which is invariable although ageing is included in the analysis. Thus viscoelastic methods can be used and correspondence principles can be developed; emphasis is placed in the present work on those which are based on the Laplace transform. A particular form is described, in which replacement of the elastic modulus by a function of the transformed creep compliance gives transformed values of stress; these values are easily obtained numerically by the finite element method using elastic analyses. The transformed values of stress are then expressed as approximate functions of the transformed creep compliance; inversion of the ensuing functions gives the stress as an approximate function of time. Two applications are given; the first considers a simple axially loaded column with reinforcement and the second deals with a thick cylinder subjected to a temperature gradient.
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    International Journal for Numerical Methods in Engineering 11 (1977), S. 908-910 
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    International Journal for Numerical Methods in Engineering 11 (1977), S. 933-943 
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    Notes: The problem of heat conduction in a multiphase medium is a free boundary problem in which the free boundary is the phase transition line. The solution to this problem is highly irregular in that the temperature gradient is discontinuous at the free boundary. Two-dimensional, discontinuous, space-time finite elements are introduced to obtain a finite element, free boundary formulation for this problem. The jump in heat flux and position of the phase transition line become dependent variables in the finite element model. The resulting models give accurate results while allowing the calculation of free boundary problems with a fixed finite element mesh.
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    International Journal for Numerical Methods in Engineering 11 (1977), S. 975-993 
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    Notes: Formulated in the hodograph plane, the bi-dimensional flow of a perfect fluid past a symmetric body leads to an elliptic variational inequality. By this way we show the existence of a one-parameter family of solutions. Furthermore the study gives us a simple and effective method for calculating the solutions. The results obtained with some typical profiles are given and compared with previous works.
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    International Journal for Numerical Methods in Engineering 11 (1977), S. 995-1003 
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    Notes: In this paper the geometric stiffness matrices of a 12 degree-of-freedom rectangular element based on a fully compatible displacement field are developed for the first time and used to solve the elastic stability problem of rectangular plates under combined in-plane forces.The rapid convergence of buckling solutions based on the derived geometric stiffness matrices is demonstrated for plates with various boundary and loading conditions. Comparison of results shows that the present conforming element gives in all cases better results than the well known 12 degree-of-freedom non-conforming rectangular element.
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    International Journal for Numerical Methods in Engineering 11 (1977), S. 1044-1048 
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    Notes: A finite difference approximation for the equilibrium equation of a thin, laterally loaded, elastic plate of variable stiffness is developed; it uses plate stiffnesses at node points and at points midway between the nodes of the rectangular grids. Displacement and moment results using this operator and an alternate one are compared.
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    International Journal for Numerical Methods in Engineering 11 (1977), S. 1056-1056 
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    International Journal for Numerical Methods in Engineering 11 (1977), S. 1067-1081 
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    Notes: Existing theory is assembled to give a method which needs only the core of a mini-computer to calculate the eigenvalues of large rigidly jointed plane frames with certainty, the eigenvalues being natural frequencies and critical load factors in free vibration and buckling problems, respectively. The method is illustrated by annotated listings of vibration and buckling programs, each involving under two hundred Fortran statements and with low number storage requirements (see Table I). The use of the programs as ‘black boxes’ is fully explained, with illustrative examples.The member theory used is the ‘exact’ classical Bernoulli-Euler uniform member theory. Possible applications include: evaluation of answers from approximate methods; calculation of critical loads for substitution in the modified Merchant-Rankine formula to estimate collapse loads of frames; and calculation of shifts in natural frequencies caused by structural damage, in connection with structural integrity monitoring of inaccessible structures.
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    International Journal for Numerical Methods in Engineering 11 (1977), S. 1155-1174 
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    Notes: The convergence properties of several non-linear solution procedures were examined with respect to the accelerated flow of a fluid in a converging channel (the Hamel problem), using two different finite element computer programs with different elemental construction. The Reynolds number varied from that for creeping flow to 1088 without exceeding the radius of convergence. Special attention was given to the successive substitution and Newton-Raphson solution algorithms, with a significant advantage in rate of convergence noted for the latter.
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    International Journal for Numerical Methods in Engineering 11 (1977), S. 1579-1592 
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    Notes: This paper presents an unconditionally stable explicit algorithm for the direct integration of the structural dynamic equations of motion. The algorithm is restricted to a diagonal mass matrix and positive definite symmetric stiffness and damping matrices. The algorithm is based on splitting the stiffness and damping matrices into strictly lower and upper trangular form. Unconditional stability is proven, but only for the undamped case and a completely symmetric splitting of the stiffness matrix. An alternate splitting method is also presented and numerical examples indicate superior performance over the symmetric splitting, but only a conditional stability. A spring-mass-dashpot model is used to illustrate the algorithm.
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    International Journal for Numerical Methods in Engineering 11 (1977), S. 1627-1630 
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    Keywords: Engineering ; Engineering General
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    International Journal for Numerical Methods in Engineering 11 (1977), S. 1621-1626 
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    Notes: Using a finite element method, a value of 13.2 per cent is obtained for the die swell of a highly-viscous Newtonian fluid flowing at very low Reynolds number from a circular tube of constant radius. The same method is then used to obtain die swell values for a variety of axisymmetric tube exits. It is found that, in general, conical constrictions at or near the tube exit result in a decrease in die swell, while conical expansions increase the die swell.
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    International Journal for Numerical Methods in Engineering 11 (1977), S. 1261-1269 
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    Notes: The non-linear steady state response of structures with curvature is investigated through the expository example of a shallow circular arch. A consistent mass finite element formulation is employed to derive the governing non-linear differential equations.These equations are solved by assuming a single mode expansion reducing the governing equations to the single degree-of-freedom Duffing's equation with a quadratic term. The non-symmetric amplitude-frequency curve is derived and compared with results previously obtained by direct integration of the equations of motion.
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    International Journal for Numerical Methods in Engineering 11 (1977), S. 1329-1333 
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    Notes: Temperature load on a shell is usually represented as initial strains in the tangent plane directions of the shell, since strains in shell surface normal directions are neglected. It is shown, however, that this simplification may give rise to significant errors for thick curved shell elements. A procedure to overcome this problem is presented. In particular the eight-node subparametric thick shell element is considered.
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    International Journal for Numerical Methods in Engineering 11 (1977), S. 1879-1892 
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    Notes: An iterative method for numerically solving the time independent Navier-Stokes equations for viscous compressible flows is presented. The method is based upon partial application of the Gauss-Seidel principle in block form to the systems of the non-linear algebraic equations which arise in construction of finite element (Galerkin) models approximating solutions of fluid dynamic problems. The C0-cubic element on triangles is employed for function approximation. Computational results for a free shear flow at Re = 1000 indicate significant achievement of economy in iterative convergence rate over finite element and finite difference models which employ the customary time dependent equations and symptotic time marching procedure to steady solution. Numerical results are in excellent agreement with those obtained for the same test problem employing time marching finite element and finite difference solution techniques.
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    International Journal for Numerical Methods in Engineering 12 (1978), S. 59-65 
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    Notes: This note presents the closed form equations for the stiffness terms in the elastic-plastic stiffness matrix for axisymmetric finite elements. The element considered is a triangular ring element characterized by linear displacement relationships and an averaged state of stress. The physical law is modelled by the incremental theory of plasticity utilizing the Prandtl-Reuss flow rule and von-Mises Yield Criterion. Results are presented comparing stiffness terms as computed by numerical integration to those computed from the closed form equations. Significant errors in stiffness terms arising from numerical integration are observed for axisymmetric elements located near the line of axial symmetry as a result of the logarithmic nature of some of the stiffness terms.
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    International Journal for Numerical Methods in Engineering 12 (1978), S. 85-92 
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    Notes: The compressible potential flow on a blade-to-blade surface of a turbomachine is analysed using the Thomas algorithm. The numerical properties of resulting non-linear simultaneous equations are studied with respect to grid aspect ratios and convergence. The heuristic approach has established which are the important factors that affect the flow solution in typical blade-to-blade configurations.
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    International Journal for Numerical Methods in Engineering 12 (1978), S. 93-99 
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    Notes: This note describes improvements to the Suhara-Fukuda method for generating a triangular finite element network. These are based on the use of a node generation procedure which distributes nodes is a regular pattern across the network area and is sufficiently flexible to permit any variation in element density. Because of the regular node distribution, poorly shaped elements will not arise and so the procedure for connecting the nodes to form elements can be simplified. Examples of networks generaed in this way are given.
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    International Journal for Numerical Methods in Engineering 12 (1978), S. 183-185 
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    Notes: In a recent paper, Dr. Frind has formulated a two-dimensional isoparametric finite element based upon the Hermite bicubic interpolation scheme. The present discussion focuses upon certain simplifications in the derivation which appear to have diminished the accuracy of the resulting element, and suggests a simpler approach to the element formulation. This author agrees strongly with Dr. Frind's recommendation of the Hermite parametric element as an efficient and useful tool for general field problems; the present comments are offered to point out that, in fact, the accuracy comparisons presented by Dr. Frind are biased against the Hermite finite element.
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    International Journal for Numerical Methods in Engineering 12 (1978) 
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    International Journal for Numerical Methods in Engineering 12 (1978), S. 1-10 
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    Notes: A numerical technique for solving unsteady gas dynamic equations is presented. The technique is based on least squares finite element concepts with elements that are constructed in both space and time. Both linear and quadratic interpolation is used on individual elements. The technique is tested against a problem whose solution is known so that numerical accuracy can be ascertained.
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    International Journal for Numerical Methods in Engineering 12 (1978), S. 47-57 
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    Notes: A viscous approximation for steady creeping flow is extended to include the effect of elastic strains. Two examples are presented which illustrate both the method and the need for including elastic strains in the analysis of steady-state visco-plastic flows.
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    International Journal for Numerical Methods in Engineering 12 (1978), S. 101-114 
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    Notes: A finite element formulation for large elasto-plastic deformation of polycrystalline materials is proposed in incremental form. The effect of rotation of crystal axes besides usual element rotaion is taken into account. Some numerical considerations on polycrystalline plasticity (i.e. stress-strain curves for several proportional loadings, effect of change of loading path on stress-strain curve, subsequent yield loci for uniaxial and equi-biaxial loadings and so forth) are given for the case of small deformation by using a plate model which consists of 121 square FCC crystals.
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    International Journal for Numerical Methods in Engineering 12 (1978), S. 382-383 
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    International Journal for Numerical Methods in Engineering 12 (1978), S. 405-414 
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    International Journal for Numerical Methods in Engineering 12 (1978), S. 453-469 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A least squares method is presented for computing approximate solutions of indefinite partial differential equations of the mixed type such as those that arise in connection with transonic flutter analysis. The mehod retains the advantages of finite difference schemes namely simplicity and sparsity of the resulting matrix system. However, it offers some great advantages over finite difference schemes. First, the method is insensitive to the value of the forcing frequency i.e., the resulting matrix system is always symmetric and positive definite,. As a result, iterative methods may be successfully employed to solve the matrix system, thus taking full advantage of the sparsity. Furthermore, the method is insensitive to the type of the partial differential equation, i.e., the computational algorithm is the same in elliptic and hyperbolic regions. In this work the method is formulated and numerical results for model problems are presented. Some theoretical aspects of least squares approximations are also discussed.
    Additional Material: 12 Ill.
    Type of Medium: Electronic Resource
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  • 98
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 14 (1979), S. 1851-1863 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The boundary control problem of optimal heating of an infinitely long slab with tempertue-dependent thermal conductivity, subjected to a convection and radiation boundary condition, is analysed by numerical methods.In order to reformulate the optimal control problem of distributed parameter systems as a mathematical programming problem of finite dimension, a space, co-ordinate is discretized by use of the finite element method, while the Runge-Kutta method is utilized for time integrations. Finally, the performance index of the optimal control problem is minimized by the conjugate gradient method of optimization.
    Additional Material: 9 Ill.
    Type of Medium: Electronic Resource
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  • 99
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 14 (1979), S. 1879-1879 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
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  • 100
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 12 (1978), S. 1375-1382 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An optimal steady-state control problem governed by an elliptic state equation is solved by several finite element methods. Finite element discretizations are applied to different variational formulations of the problem yielding accurate numerical results as compared with the given analytical solution. It is sated that, for minimum computational effort and high accuracy, ‘mixed’ finite elements requiring only C° continuity, and approximating the control and state functions simultaneously are better suited to similar ‘fourth order’ problems.
    Additional Material: 3 Ill.
    Type of Medium: Electronic Resource
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