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  • Phosphorus
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  • Electronic Resource  (256)
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  • 1985-1989
  • 1980-1984  (256)
  • 1960-1964
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  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Calcified tissue international 33 (1981), S. 477-484 
    ISSN: 1432-0827
    Keywords: 1,25-(OH)2-D ; Calcium ; Phosphorus ; Sex ; Age
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Medicine , Physics
    Notes: Summary Dietary phosphate deprivation in women, but not men, is accompanied by a fall in plasma PO4 and a rise in plasma 1,25-(OH)2-vitamin D concentrations. In contrast, young male rats exhibit a fall in plasma PO4 and a rise in plasma 1,25-(OH)2-D concentrations in response to PO4 deprivation. To evaluate whether age and sex influence basal plasma 1,25-(OH)2-D levels and their regulation by PO4 deprivation, plasma 1,25-(OH)2-D, PO4, and Ca levels were measured in male and female rats ranging in age from 6 weeks to 6 months while they were eating normal or low PO4 diets for 1 to 16 days. Similar observations were also made in 6-week-old castrated male and female rats, males replaced with testosterone, and females replaced with estradiol. Basal plasma 1,25-(OH)2-D levels were higher in 6-week-old males (228±76 pmol/l) than in 6-week-old females (148±62 pmol/l;P〈0.01) and declined by age 11 weeks to stable levels averaging about 100 pmol/l without sex difference. Dietary PO4 deprivation resulted in a three-to fourfold increase in plasma 1,25-(OH)2-D concentrations regardless of age and sex, accompanied by a correlated rise in serum Ca concentrations. Castration of 6-week-old males and females eliminated the sex difference in basal plasma 1,25-(OH)2-D levels and appeared to enhance the elevation of plasma 1,25-(OH)2-D concentrations in response to PO4 deprivation in females. Although gonadal hormones may modify basal plasma 1,25-(OH)2-D levels, they are not required for the augmentation of plasma 1,25-(OH)2-D levels in response to PO4 deprivation.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    Springer
    Calcified tissue international 33 (1981), S. 485-488 
    ISSN: 1432-0827
    Keywords: 1,25-(OH)2-D ; Hypophysectomy ; Calcium ; Phosphorus
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Medicine , Physics
    Notes: Summary The mechanism by which dietary phosphate deprivation elevates plasma 1,25-(OH)2-D levels is not known. To evaluate the role of the pituitary in regulating plasma 1,25-(OH)2-D concentrations, the responses of plasma 1,25-(OH)2-D to dietary phosphate deprivation and, separately, to dietary calcium deprivation were evaluated in intact and hypophysectomized male rats. Among intact and hypophysectomized rats eating normal diets, plasma 1,25-(OH)2-D levels averaged 228±76 and 148±62 pmol/1, respectively (P〈0.01). During dietary phosphate deprivation, plasma 1,25-(OH)2-D levels rose to 1160±260 in intact rats and fell to 90±26 pmol/l in hypophysectomized rats (P〈0.001). By contrast, during dietary calcium deprivation, plasma 1,25-(OH)2-D levels rose in both intact and hypophysectomized animals to 856±107 and 742±279 pmol/l, respectively (NS). In response to dietary phosphate deprivation, serum calcium concentrations rose as 1,25-(OH)2-D concentrations rose in intact rats but remained at control levels in hypophysectomized rats. These results support the hypothesis that a pituitary hormone acting either directly or indirectly on the kidney mediates the increase in plasma 1,25-(OH)2-D during dietary phosphate deprivation. The hypercalcemia that occurs in rats during dietary phosphate deprivation appears to depend on the elevation of plasma 1,25-(OH)2-D.
    Type of Medium: Electronic Resource
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  • 3
    ISSN: 1573-5036
    Keywords: Amino acid ; Deficiency ; Keto acid ; Peanut ; Phosphorus ; Potassium
    Source: Springer Online Journal Archives 1860-2000
    Topics: Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition
    Notes: Summary Lack of both phosphorus and potassuium results in accumulation of all the keto acids and amino acids in 30 days and 20 days old peanut leaves respectively. This is due to te sluggish metabolism of the tissue under P and K deficienty. Decrease of all the keto acids in 20 days old plants suggests that their synthesis might be affecte under P and K deficiency.
    Type of Medium: Electronic Resource
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  • 4
    Electronic Resource
    Electronic Resource
    Springer
    Plant and soil 60 (1981), S. 161-176 
    ISSN: 1573-5036
    Keywords: Aggregation ; Forests ; Land use ; Mycorrhiza ; Nitrogen ; Pasture ; Phosphorus ; Pine productivity
    Source: Springer Online Journal Archives 1860-2000
    Topics: Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition
    Notes: Summary Differences in the productivity of establishedP. radiata plantations on pasture and forest soils were found to be reproducible withP. radiata seedlings in a glasshouse environment. The growth of seedlings on pasture soil exceeded that of seedlings on native forest soil (the ‘primary pasture effect’). After a history of pine on both native and pasture soils a residual effect of pasture on seedling growth was evident (the ‘secondary pasture effect’). However, the effect of a history of pine plantation (the ‘pine effect’) was to decrease the productivity of both native and pasture soil as assessed by seedling growth. These effects were not related to changes due to land management in mycorrhizal infection or in soil structure. The analysis of seedling growth leads to the conclusion that soil fertility, particularly the availability of nitrogen and phosphorus, has changed.
    Type of Medium: Electronic Resource
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  • 5
    Electronic Resource
    Electronic Resource
    Springer
    Plant and soil 60 (1981), S. 187-193 
    ISSN: 1573-5036
    Keywords: Fertilizer ; Intensive cropping ; Lime ; Multiple cropping ; Manure ; Nutrient removal ; Nitrogen ; Phosphorus ; Potassium ; Weedicide
    Source: Springer Online Journal Archives 1860-2000
    Topics: Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition
    Notes: Summary The balance sheet of phosphorus and potassium were worked out from a long term manure and fertilizer experiment conducted for eight years and is still continuing at Ranchi Agricultural College, Kanke, Ranchi, India. Increasing levels of fertilizer combination with organic manure and lime give the highest yield as well as removed the highest amount of phosphorus and potassium from the soil and gave the positive gain of soil phosphorus and potassium in intensive cropping. The highest gains of 59.0 and 278.0 kg/ha of phosphorus and potassium respectively were recorded in 150% NPK application.
    Type of Medium: Electronic Resource
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  • 6
    Electronic Resource
    Electronic Resource
    Springer
    Plant and soil 62 (1981), S. 305-308 
    ISSN: 1573-5036
    Keywords: Liming ; Nitrogen ; Phosphorus ; Rice ; Tryptophan ; Zinc
    Source: Springer Online Journal Archives 1860-2000
    Topics: Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition
    Notes: Summary The effects of Zn, P, N and CaCO3 on tryptophan concentration in rice grain were studied in greenhouse at Haryana Agricultural University. Zinc application upto 20 ppm increased tryptophan concentration in rice grain. Zn-EDTA gave highest increase followed by ZnSO4 and then ZnO. Liming at the rate of 4 and 8 per cent decreased tryptophan concentration significantly. Phosphorus application upto 100 ppm also decreased tryptophan significantly but Zn in combination with P increased tryptophan and overcame negative effect of P. Nitrogen application upto 120 ppm increased tryptophan concentration. There was positive interaction between Zn and N. Ammonium sulphate gave highest tryptophan followed by ammonium nitrate and then urea. The tryptophan concentration ranged between 766 ppm and 2011 ppm in paddy grain. The lowest tryptophan concentration was in the plants treated with 8 per cent lime in absence of added Zn and highest with 10 ppm Zn through Zn-EDTA.
    Type of Medium: Electronic Resource
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  • 7
    ISSN: 1573-5036
    Keywords: Foliage age ; Nitrogen ; Phosphorus ; Potassium ; Red pine ; Tissue sampling
    Source: Springer Online Journal Archives 1860-2000
    Topics: Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition
    Notes: Summary The vertical distribution of inorganic nutrient concentrations in red pine were dependent on the foliage age. Older foliage did not show an average vertical gradient while younger foliage did show a significant gradient. Horizontal gradients across foliage age classes in a branch whorl were consistent for all branch whorls, but the relative difference between the concentration of the current foliage and foliage three years-old or older was dependent on crown position. Coefficients of variation (CV) did not show a variability gradient in the crown for nitrogen and phosphorus. Variability of potassium tended to decrease as foliage age increased.
    Type of Medium: Electronic Resource
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  • 8
    Electronic Resource
    Electronic Resource
    Springer
    Plant and soil 63 (1981), S. 491-495 
    ISSN: 1573-5036
    Keywords: Calcium ; Copper ; Flowers ; Iron ; Leaves ; Magnesium ; Nitrogen ; Nutrient uptake ; Phosphorus ; Potassium ; Koots ; Shoots ; Zinc
    Source: Springer Online Journal Archives 1860-2000
    Topics: Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition
    Notes: Summary Cucumber (Cucumis sativus) plants were grown in Hoagland solution to which 20 to 2000 ppm of a soil fulvic acid (FA) were added. The addition of 100 to 300 ppm of FA produced highly significant increases in the growth and development of above and below ground plant parts, in the uptake of nutrient elements (N, P, K, Ca, Mg, Cu, Fe and Zn), and in the formation of numbers of flowers per plant. Effects of adding 500 and more ppm of FA were less beneficial.
    Type of Medium: Electronic Resource
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  • 9
    Electronic Resource
    Electronic Resource
    Springer
    Hydrobiologia 77 (1981), S. 49-60 
    ISSN: 1573-5117
    Keywords: Phosphorus ; sediments ; isolation columns ; nutrient enrichment ; enclosures
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology
    Notes: Abstract Isolation columns positioned in approximately 3.5 m of water in Midmar Dam, were enriched with PO4-P and NO3-N, singly and in combination. Increased chlorophyll concentration resulted from all enrichment treatments. Responses showed marked seasonality and varied in intensity and duration. Despite the PO4-P fixing potential of the sediments, SRP concentrations increased markedly at times and possible reasons for this discussed. The marked response to addition of NO3-N alone suggested a flux of phosphorus from the sediment through the water to the algal component. The significance of periphyton within the columns is discussed.
    Type of Medium: Electronic Resource
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  • 10
    ISSN: 1573-5036
    Keywords: Availability ; Corn ; Extractability ; Heavy application ; Immobilization ; Phosphorus ; Plant parts ; Translocation ; Uptake ; Zinc
    Source: Springer Online Journal Archives 1860-2000
    Topics: Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition
    Notes: Summary The influence of heavy applications of P (100, 200 and 400 ppm P) and Zn (12.5 and 25 ppm) fertilizers on their extractabilities, availabilities and uptake by corn grown in highly calcareous soil was investigated. A significant increase was found in the levels of (NH4)2CO3-EDTA-extractable Zn either by Zn-applications alone or together with P. The amounts of NaHCO3-extractable P were also increased with P additions and the influence of Zn applications was not clear. Phosphorus application generally increased the plant dry weight. In the soils treated with P and Zn fertilizers, that increase was mostly related to P rather to Zn. In the soils not treated with Zn, P additions increased Zn uptake by the plants. On the other side, in the soils treated with Zn, P additions decreased Zn uptake. Phosphorus concentration in the whole plant and/or in the different plant parts was increased by P application without being significantly affected by Zn addition. The plants showed greater response to 12.5 ppm Zn application than to 25 ppm. Plants grown for 4 weeks contained lower amounts of Zn relative to those grown for 8 weeks. The influence of plant age on P content was not as clear as occurred with Zn.
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  • 11
    ISSN: 1573-5036
    Keywords: Accumulation ; Deficiency ; Grass ; Phosphorus ; Translocation ; Uptake ; Urea
    Source: Springer Online Journal Archives 1860-2000
    Topics: Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition
    Notes: Summary The effect of different phosphorus supplies on the uptake, translocation and accumulation of14C-urea by orchard grass was investigated. Phosphorus starvation inhibits the uptake, translocation and accumulation of the carbon of urea similarly to the nitrogen of urea. As compared with the uptake process the reduction of the accumulation is much more effected by the inhibition of the carbon translocation from roots to the aboveground parts. Lack of phosphorus also decreases the incorporation of the14C of urea into high-molecular compounds. The effect of phosphorus deficit on the accumulation of14C-urea increases with time of starvation.
    Type of Medium: Electronic Resource
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  • 12
    Electronic Resource
    Electronic Resource
    Springer
    Plant and soil 59 (1981), S. 465-471 
    ISSN: 1573-5036
    Keywords: Ectomycorrhiza ; Flooding ; Michigan ; Peat ; Phosphorus ; Salix
    Source: Springer Online Journal Archives 1860-2000
    Topics: Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition
    Notes: Summary Willows growing in a north central Michigan wetland were found to be ectomycorrhizal throughout the 1978 growing season on each of two sites (one water-saturated, one relatively drier). Each site was dominated by a mix of sedges (Carex spp.) and willows (Salix spp.). On both sites, phosphorus was added at two levels (20 or 200 kg P ha−1) to simulate potential inputs from the disposal of secondarily-treated municipal wastewater. The intensity of willow root infection was determined by scoring root tips on a 0 to 4 scale based on mantle-, intercellular hyphae-, and root epidermal cell characteristics. Infection on the wet site remained uniformly heavy in July and August when P was added, but it declined significantly during August for control plants at both sites. When water levels increased during September, the intensity of mycorrhizal infection increased on control plants on the wet site. On the drier site, mycorrhizal intensity decreased on controls and on plants exposed to the highest P levels. Between August and September samplings, mycorrhizal intensity increased considerably on dry-site controls but did not change on plants exposed to added P.
    Type of Medium: Electronic Resource
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  • 13
    Electronic Resource
    Electronic Resource
    Springer
    Plant and soil 61 (1981), S. 329-339 
    ISSN: 1573-5036
    Keywords: Availability ; Krasnozem ; Nitrogen ; Phosphorus ; Pinus radiata
    Source: Springer Online Journal Archives 1860-2000
    Topics: Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition
    Notes: Summary The improved growth of pine plantations on pasture soils compared with that on soils which previously supported native eucalypt forest is primarily explained in terms of soil phosphorus. Pasture development has resulted in a decrease in the P adsorption maximum of about 300 μg g−1 soil, a figure which agrees with the increase in total P due to the application of superphosphate. P adsorption isotherms were used to calculate additions of P to give comparable levels of soil solution P in eucalypt and pasture soils. The growth of pine seedlings in soils thus amended showed a strong N×P interaction. When P was non-limiting, addition of N raised productivity of the eucalypt soil above that of the pasture soil. It is postulated that the different nature of the N×P interaction in eucalypt and pasture soils results from differences in the nitrogen cycle in the two soils.
    Type of Medium: Electronic Resource
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  • 14
    Electronic Resource
    Electronic Resource
    Springer
    Plant and soil 62 (1981), S. 15-22 
    ISSN: 1573-5036
    Keywords: Growth ; Interactions ; Iron ; Manganese ; Phosphorus ; Sorghum ; Uptake
    Source: Springer Online Journal Archives 1860-2000
    Topics: Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition
    Notes: Summary The effects of P and Mn on growth response and uptake of Fe, Mn and P by grain sorghum were investigated using nutrient culture. High P and Mn concentrations in solution (greater than 40 and 1 mg/l for P and Mn, respectively) markedly reduced plant height and shoot and root dry weight of 4-week-old sorghum plants. High Mn concentrations in solution increased the concentrations of Mn and P in shoot tissue and uptake of Mn, but depressed the uptake of P. High levels of P enhanced Mn uptake by sorghum and accentuated Mn toxicity at low Mn levels. The tissue Fe and total uptake of Fe were both reduced markedly by the high levels of P and Mn concentrations in solution. The increases of P, Mn and Fe concentrations in root tissue with a concomitant decrease of Fe in shoots suggested that the translocation of Fe from roots to shoots was hindered under high P and Mn conditions. Since coating occurred on root surfaces and intensified with increasing Mn concentrations in the substrate, part of the reduction of Fe in shoots could be attributed to the formation of high valent manganese oxides on the root surfaces which may retain Fe and reduce its absorption by sorghum.
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  • 15
    Electronic Resource
    Electronic Resource
    Springer
    Hydrobiologia 78 (1981), S. 125-128 
    ISSN: 1573-5117
    Keywords: Phosphorus ; aluminum sulfate ; complex phosphorus ; phosphomonoesters
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology
    Notes: Abstract Application of aluminum sulfate to the hypolimnion of West Twin Lake, a hardwater eutrophic lake in northeastern Ohio, did not efficiently remove complex phosphorus compounds from the water column. The majority of the complex phosphorus compounds remaining after alum treatment released P04 following brief treatment with alkaline phosphatase.
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  • 16
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 17 (1981), S. 15-41 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The governing equations for large strain analysis of elastic-plastic problems are reconsidered. An improved form of these equations is derived, which is valid for small increments of strain and large increments of rotation. Special attention is paid to the integration procedures for these equations in the deformation history. It is shown that the tangent modulus procedure for integration of the constitutive equations is conditionally stable, and that implicit methods, such as the ‘mean normal’ method, are to be preferred. A novel procedure is introduced for the treatment of nonlinear geometric effects. The performance of various element types is examined, with specific attention to effects of ‘locking’ and distortion. Several applications are discussed to illustrate the various aspects of the formulation developed ein this paper.
    Additional Material: 24 Ill.
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  • 17
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 17 (1981), S. 97-112 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In this paper we analyse a simple but non-trivial steady-state creeping elasto visco-plastic (Maxwell fluid) radial flow problem, paying particular attention to the effects of the boundary conditions. Solutions are obtained by integration of a governing equation on stress, using the Runge-Kutta method for initial value problems and finite differences for boundary value problems. A more general approach by the finite element method, which solves for the velocity field rather than the stress field, and which is applicable to a wide range of problems, is presented and tested using the radial flow example.
    Additional Material: 9 Ill.
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  • 18
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 17 (1981), S. 133-139 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Some new formulae are presented for numerical integration over triangular regions. These formulae, which are triangularly symmetric, involve four, six, and seven integration points, respectively. They were derived by determining co-ordinates and weight factors for which polynomial functions of up to a certain degree are integrated exactly. The effectiveness of the formulae is demonstrated by applying them to the integration of five non-polynomial functions, two of which are singular within the region of integration. Results obtained with the new formulae are compared with results obtained with other, comparable formulae. It is seen that the new formulae are more accurate than some existing ones with the same numbers of points.
    Additional Material: 7 Ill.
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  • 19
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    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 17 (1981), S. 156-156 
    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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  • 20
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    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 17 (1981), S. 159-170 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A finite element anaylysis to predict the sloshing dislacements and hydrodynamic pressures in liquid-filled tanks subjected to earthquake ground motions is presented. Finite element equations were derived using the Galerkin formulation, and the predicted results were checked against the test data, showing a good agreement between the test and finite element results.
    Additional Material: 7 Ill.
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  • 21
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    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 17 (1981), S. 213-229 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Minimum cost design of a framed structure is considered by using the mini-mas dual method. Stress and/or displacement constraints are imposed as behavioural constraints. The minimum cost design problem has a discrete objective function and discrete design variables. A sequence of approximate optimization problems in created by using the first-order Taylor series expansion for displacements with respect to the reciprocals of cross-sectional areas and moments of inertia. Each approximate problem is solved in the dual space. Two simple structural examples are given to show the appropriateness and efficiency of the proposed procedure. Approximate solutions are obtained within five structural analysis.
    Additional Material: 5 Ill.
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  • 22
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 17 (1981), S. 123-132 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A kinematically nonlinear analysis of unbraced, rigid-jointed, portal frames, rotationally restrained at the base and subjected to eccentric concentrated and/or uniformly distributed loads, is presented. Through this analysis the complete behaviour, including the primary path and postbuckling path (whenever it exists), is evaluated. Moreover, through parametric studies, the effects of bar slenderness ratio, load eccentricity and amount of rotational restraint are assessed. Through this method it is also possible to assess the effect of member lengths and member lengths and member bending stiffnesses.
    Additional Material: 7 Ill.
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  • 23
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 17 (1981), S. 145-153 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Numerical evaluations of elliptic integral solutions of some large deflection beam and frame problems are presented. The values are given in tabular form with up to six significant figures. The numerical technique used for evaluating the elliptic integrals is described.
    Additional Material: 5 Ill.
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  • 24
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 17 (1981), S. 156-156 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
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  • 25
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 17 (1981), S. 187-198 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper presents the details of a unified numerical algorithm and the associated computer program developed for the efficient determination of natural frequencies and modes of free vibration of structures. Both spinning and nonspinning structures with or without viscous and/or structural damping may be solved by the current procedure; in a addition, the program is capable of solving static problems with multiple load cases as well as the quadratic matric eigenproblem associated with a finite dynamic element structural discretization. A special symmetric matrix decomposition scheme has been adopted for matrix triangularization, which renders the program rather efficient and economical. Also, a novel bisection scheme is described that further accelerates the solution convergence rate, particularly for the case of repeated roots.The associated computer program adopts and out-of-core solution strategy, thereby enabling effective solutions to be achieved for large, complex, practical structures. A complete listing of the program written in FORTRAN V, for the UNIVAC 1100/82 computer, along with the source deck is available for ready use.
    Additional Material: 1 Ill.
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  • 26
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 17 (1981), S. 271-279 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A FORTRAN subroutine is presented to integrate a function given only by a set of tabular values at unequal intervals. It uses the trapezoidal rule and a generalization of Simpson's rule, obtaining a conservative error estimate by comparing the two results.
    Additional Material: 5 Tab.
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  • 27
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 17 (1981), S. 301-305 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Additional Material: 3 Tab.
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  • 28
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 17 (1981), S. 309-309 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
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  • 29
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 17 (1981), S. 312-312 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
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  • 30
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 17 (1981), S. 335-346 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Splitting methods for time-dependent partial differential equations usually exhibit a drop in accuracy if boundary conditions become time-dependent. This phenomenon is investigated for a class of splitting methods for two-space dimensional parabolic partial differential equations. A boundary-value correction discussed in a paper by Fairweather and Mitchell for the Laplace equation with Dirichlet conditions, is generalized for a wide class of initial boundary-value problems. A numerical comparison is made for the ADI method of Peaceman-Rachford and the LOD method of Yanenko applied to problems with Dirichlet boundary conditions and non-Dirichlet boundary conditions.
    Additional Material: 6 Tab.
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  • 31
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    International Journal for Numerical Methods in Engineering 17 (1981), S. 357-365 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    International Journal for Numerical Methods in Engineering 17 (1981), S. 445-464 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A singular finite element is developed for direct calculation of combined modes I and II stress intensity factors for planar rectilinear anisotropic structures subject to arbitrary loading. Twelve-node conventional elements are used in conjunction with a linear elastic fracture mechanics enrichment of the same element which is formed into a four-element macro-element. Example problems show this formulation to be exceptionally accurate and results are presented for a variety of modern fibre-reinforced composites in simple mode I extension and in mixed mode I and II situations. In addition, it is shown that the meshes for accurate results are relatively coarse and thus calculations are quite economical.
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    International Journal for Numerical Methods in Engineering 17 (1981), S. 477-477 
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  • 34
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    International Journal for Numerical Methods in Engineering 17 (1981) 
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    Source: Wiley InterScience Backfile Collection 1832-2000
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  • 35
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    International Journal for Numerical Methods in Engineering 17 (1981), S. 527-541 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: This paper is concerned with conventional and mixed finite element analysis of large deflection bending and free vibration of axisymmetric circular plates including shear deformation. Conventional and mixed finite element formulations are presented. Numerical results are included for isotropic as well as orthotropic, circular and annular plates under various edge conditions and loadings.
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    International Journal for Numerical Methods in Engineering 17 (1981), S. 601-613 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: The general problem of optimum design of trusses composed of tubular elements requires the determination of cross-sectional dimensions for each element which satisfy a set of side constraints on those dimensions as well as Euler and local buckling constraints. A formulation is presented which eliminates the necessity to use mathematical programming methods for the determination of feasible cross-sectional dimensions. The minimization problem is shown to be expressible in terms of area variables only, with each area subject to bounds which are functions of truss stiffness but which may be obtained by explicit analysis of the element ‘desing space’ for any design. This‘direct’ formulation is completely general and compatible with any minimization algorithm. The formulation also leads to a simple and efficient recursive procedure for producing near-optimal fully-constrained designs. Several examples illustrate results obtained by both the direct and recursive procedures.
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    International Journal for Numerical Methods in Engineering 17 (1981) 
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    Source: Wiley InterScience Backfile Collection 1832-2000
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  • 38
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    International Journal for Numerical Methods in Engineering 17 (1981), S. 707-718 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The use of quasi-Newton methods is studied for the solution of the nonlinear finite element equations that arise in the analysis of incompressible fluid flow. An effective procedure for the use of Broyden's method in finite element analysis is presented. The quasi-Newton method is compared with the commonly employed successive substitution and Newton-Raphson procedures, and it is concluded that the use of Broyden's method can constitute an effective solution strategy.
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  • 39
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    International Journal for Numerical Methods in Engineering 17 (1981), S. 747-771 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: This paper discusses computational strategies for elastic-plastic-creep behaviour. These computational strategies, based on the tangent stiffness and initial strain techniques, include solution algorithms, modelling techniques and constitutive relations.A predictor-corrector iterative and non-iterative scheme is presented for combined plasticity and creep. This scheme has been incorporated into the three-dimensional, isoparametric element, module (HEX) of the Grumman PLANS finite element program for nonlinear analysis and used for the problems presented in this paper.The concept of modelling for inelastic behaviour is demonstrated by introducing a variable set of inelastic integration points within a finite element at which stresses and strains are monitored.In order to perform a meaningful analysis, one must understand and justify the employed constitutive relations. To this end, work at Oak Ridge National Laboratory in justifying constitutive relations for high-temperature nuclear reactor components is referred to.An analysis of a test model of a nuclear reactor inlet nozzle operating at high temperatures is presented to demonstrate some of the computational strategies discussed.
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  • 40
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    International Journal for Numerical Methods in Engineering 17 (1981), S. 1407-1426 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: The displacement and strain fields of thin-walled pretwisted beams are prescribed in terms of generalized displacements for extension, bending, torsion and warping. Differential equations and boundary conditions are obtained from the elastic potential energy functional without assuming coincidence of the beam axis with any of the structural axes. This procedure gives a unique consistent definition of sectional moments and generalized forces. Some simple explicit formulae are derived for homogeneous tension-torsion. For the general case a computer code is developed on the basis of discretized generalized displacements and a modified energy functional, devised to obtain consistent lengthwise variation of the stresses and a unique decomposition of the torsional moment. Examples show agreement with analytical results for cylindrical beams and illustrate the various coupling effects for beams with pretwist. They also demonstrate the usefulness of the explicit formulae for homogeneous tension-torsion.
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    International Journal for Numerical Methods in Engineering 17 (1981), S. 1443-1453 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: A computationally efficient and accurate solution technique for large-order eigenvalue problems with small to medium bandwidth is presented. The algorithm - called the Sub-Polynomial Iteration (SPI) method - solves for the eigenvalues and corresponding eigenvectors. directly without any transformation to the standard form. The method is an efficient combination of several separate techniques including Sturm sequence, Lagrangian polynomial interpolation, inverse iteration with shift and Gram-Schmidt orthogonalization. Computer run times for a set of sample solution indicate the efficiency of the SPI method.
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    International Journal for Numerical Methods in Engineering 17 (1981), S. 1647-1657 
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    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: A method for solving boundary value problems for thin plate flexure as described by Kirchhoff's theory is proposed. An integral formulation leads to a system of boundary integral equations involving values of deflection, slope, bending moment and transverse shear force along the edge. A discretization leading to a matrix formulation is proposed. To solve problems with inner conditions in the plate domain, an elimination of boundary unknowns proves successful. The degenerate case where the boundary is free (which leads to a non-invertible matrix) is investigated. Three examples illustrate the efficiency of the method.
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    International Journal for Numerical Methods in Engineering 17 (1981), S. 1740-1742 
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    Source: Wiley InterScience Backfile Collection 1832-2000
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    International Journal for Numerical Methods in Engineering 17 (1981), S. 1743-1748 
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    International Journal for Numerical Methods in Engineering 17 (1981), S. 1779-1789 
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    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: The following work proposes the use of a special description-language for producing input data of finite element programs. The programs now used require a detailed description of the structure to be analysed, and they require it in a form which is unfavourable to the user and which promotes errors. Therefore, a language was designed which allows a short and compact description of the structure. This description is then automatically transformed into the input data. In this paper, the design process and the characteristics of the language are presented. Some comments on its implementation, that is on the development of a special preprocessor, are made. As target system, the finite element program SAP IV has been chosen. Finally, we want to present an example of the improvements achieved by the use of this language and the SAP IV preprocessor, respectively.
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    International Journal for Numerical Methods in Engineering 17 (1981), S. 1791-1810 
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    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: Two alternative hybrid-stress-based functionals are examined for the incremental elastic-plastic static analysis of single layer plates. Material nonlinear effects are incorporated via the initial-stress approach so that an equivalent nodal force vector is defined and the stiffness remains constant throughout the incremental loading. The alternative functionals differ in the incremental stress which is assumed to satisfy equilibrium; in the first, it is the actual stress increment, and in the second it is the elastic stress increment. Results are presented for two example problems, and comparisons of the alternative functionals and plausible iteration schemes are given. The effects of variation of pertinent solution parameters are also shown. A 4-node hybrid-stress plate element based on a Mindlin-type displacement field is used for most cases; however, limited results are also presented using an 8-node plate element, thus permitting comparisons of the relative efficiencies of the two elements.
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    International Journal for Numerical Methods in Engineering 17 (1981), S. 1888-1889 
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    International Journal for Numerical Methods in Engineering 17 (1981), S. 43-52 
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    Notes: A parametric element is formulated which enables the economic modelling of ‘infinite domain’ type problmes. A typical problem is an opening in a stress field in an infinite medium, either in two or three dimensions. The strategy is to model around the opening with two or three layers of conventional isoparametric finite elements and surround these with a single layer of ‘infinite domain’ elements.Several sample problems has been analysed for circular, square and spherical openings in infinite media, and the results compared with either theoretical or boundary element solutions which include the ‘infinite’ boundary in their solution technique.
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    International Journal for Numerical Methods in Engineering 17 (1981), S. 113-121 
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    Notes: An approximation method is presented for the analysis for the interaction of a structure with a compressible linear fluid. The method uses the fact that the eigenvalues of the dry structure are higher than the corresponding eigenvalues of a structure in contact with an incompressible fluid, and the corresponding eigenvalues of a structure in contact with a compressible fluid are even lower. The proof of this theorem is given. It is shown that in both the compressible and incompressible cases the number of degress-of-freedom can be reduced to the number of boundary points which results in a substantial saving of core memory space and computing time. A sample problem is given to demonstrate the good results of the approximation methods for a low quotient of the eigenfrequencies divided by the square of the speed of sound.
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    International Journal for Numerical Methods in Engineering 17 (1981), S. 81-96 
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    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: A number of transport problems are complicated by the presence of physically important transition zones where quantities exhibit steep gradients and special numerical care is required. When the location of such a transition zone changes as the solution evolves through time, use of a deforming numerical mesh is appropriate in order to preserve the proper numerical features both within the transition zone and at its boundaries.A general finite element solution method is described wherein the elements are allowed to deform continuously, and the effects of this deformation are accounted for exactly. The method is based on the Galerkin approximation in space, and uses finite difference approximations for the time derivatives. In the absence of element deformation, the method reduces to the conventional Galerkin formulation.The method is applied to the two-phase Stefan problem associated with the melting and solidification of A substance. The interface between the solid and liquid phase form an internal moving boundary, and latent heat effects are accounted for in the associated boundary condition. By allowing continuous mesh deformation, as dictated by this boundary condition, the moving boundary always lies on element boundaries. This circumvents the difficulties inherent in interpolation of parameters and dependent variables across regions where those quantities change abruptly.Basis functions based on Hermite polynomials are used, to allow exact specification of the flux-latent heat balance condition at the phase boundary. Analytic solutions for special cases provide tests of the method.
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    International Journal for Numerical Methods in Engineering 17 (1981), S. 154-155 
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    International Journal for Numerical Methods in Engineering 17 (1981), S. 157-158 
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    International Journal for Numerical Methods in Engineering 17 (1981), S. 239-253 
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    Notes: A finite element formulation of laminar flow with finite rate chemical reaction and heat release is made. Results are presented for steady flow in a channel, a special case of which is solved analytically, and for transverse flow around a cylinder. These illustrate the power of the finite element method for the calculation of reacting flows in complex geometries.
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    International Journal for Numerical Methods in Engineering 17 (1981), S. 291-299 
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    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: The reduction of liner partial differential equations for boundary-value problems to ordinary differential equations by the Lanczos-Chebyshev method is discussed and illustrated by applications to linear stress analysis and heat conduction in axisymmetric cylinders. Numerical examples given include eigenvalues for self-equilibrating end load problems in hollow cylinders, and heat conduction in a semi-infinite cylinder. Heat conduction in an infinite half-space is treated by considering a large multi-annular cylinder. The simplicity of the Lanczos-Chebyshev reduction method and its speed and accuracy are demonstrated.
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    International Journal for Numerical Methods in Engineering 17 (1981), S. 310-311 
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    International Journal for Numerical Methods in Engineering 17 (1981), S. 312-314 
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    International Journal for Numerical Methods in Engineering 17 (1981) 
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    International Journal for Numerical Methods in Engineering 17 (1981), S. 347-355 
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    Notes: This paper presents a method of developing a family of 1/rn type infinite elements for the analysis of problems definite in unbounded media. The proposed method is a direct extension of the conventional finite element method. The resulting improper integrals are integrated exactly over the infinite element domains. Two numerical examples in elastic half-space static problems are investigated to illustrate the applicability and accuracy of the method. The use of the proposed infinite elements yields excellent results and preserves all the advantages of the finite element method.
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    International Journal for Numerical Methods in Engineering 17 (1981), S. 405-426 
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    Source: Wiley InterScience Backfile Collection 1832-2000
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    International Journal for Numerical Methods in Engineering 17 (1981), S. 465-470 
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    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: For the general quadrilateral isoparametric elements with 4(n-1) nodes (i.e. n nodes along each side), it is shown that the inverse square root singularity of the strain field at the crack tip can be obtained by a general but simple rule. This amounts to collapsing the quadrilateral elements into triangular elements around the crack tip and placing the (n-2) mid-side nodes at locations γ2/(n-1)2 (γ=1,2,…, n-2) times the length of side emanating from the crack tip. These locations are measured from the crack tip. The known results for n = 3 and n = 4 are thus obtained as special cases.
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    International Journal for Numerical Methods in Engineering 17 (1981), S. 478-478 
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    International Journal for Numerical Methods in Engineering 17 (1981), S. 503-526 
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    Source: Wiley InterScience Backfile Collection 1832-2000
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    International Journal for Numerical Methods in Engineering 17 (1981), S. 557-572 
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    Notes: Singular finite element displacement functions for linear elastic fracture mechanics applications are investigated. The displacement fields are expressed in terms of polynomials. These polynomials are expanded in varying degrees of r and θ in order to examine the effect of the number and type of terms on the solution to various problems with known solutions. Methods of estimating the stress intensity factors for mode 1 and mode 2 are presented. Numerical results evaluating the effect of various r and θ terms on the solutions are presented.
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    International Journal for Numerical Methods in Engineering 17 (1981), S. 645-647 
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    International Journal for Numerical Methods in Engineering 17 (1981), S. 649-662 
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    Notes: The nature of adaptive processes is reviewed using as an example a specific finite element problem. Several possible formulations for the objective of mesh refinement processes are given. For the most natural of these objectives the A*-algorithms of artificial intelligence turn out to provide a solution process which is known to be optimal in a certain sense. But practically, there is insufficient information and these processes tend to be inefficient. On the other hand, if the objective is replaced by a strictly local objective based on Pareto-optimality, the error estimates of the resulting mesh sequence are shown to exhibit the order of convergence which is known to be best possible for the type of elements used.
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    International Journal for Numerical Methods in Engineering 17 (1981), S. 735-745 
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    Notes: Recent finite element analysis of adaptive refinement has focused attention on high-order approximation within elements. High-order approximation may be attained over curved elements with either rational basis functions expressed directly in the global co-ordinates or with a particular class of isoparametric basis functions. Theory for construction of high-order rational bases yields modifications to the blending method for a special class of elements in order to achieve higher order approximation within these elements.
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    International Journal for Numerical Methods in Engineering 17 (1981), S. 790-795 
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    International Journal for Numerical Methods in Engineering 17 (1981), S. 797-800 
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    International Journal for Numerical Methods in Engineering 17 (1981), S. 957-974 
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    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: The calculation of the response of rotationally periodic structures to transient forces and prescribed motions is considered. The work extends the work previously described by Thomas1 in which only the free and harmonic forced vibration problems were considered. It is assumed that the finite element method is to be used, so that the equation of motion of the structure contains a finite number of degrees-of-freedom whose responses are governed by mass, stiffness and damping matrices. It is shown that an exact solution to the equation of motion of the idealized full structure can be obtained by solving the equation of motion of a single substructure for a number of different spatial Fourier harmonics of force (and hence response). A modal method of solving this equation is described. a brief description of the implementation of the method in a suite of computer programs, and the application of the programs to a practical problems, is also given.
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    International Journal for Numerical Methods in Engineering 17 (1981), S. 975-989 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Families of difference schemes are developed for both the linear and nonlinear inviscid Burger's equation and a system of shallow water equations. Single-step and two-step (Lax-Wendroff type) families are described and comparisons are made with other difference schemes.The schemes are developed using a very limited portion of a space-time continua, coupled with Galerkin's method applied over a few triangular elements. The elements are geometrically flexible as a function of a geometry factor α, creating the idea of difference families.Stability is commented on, including the continuous relationship between stability and the families of schemes as a function of α. Numerical results are presented and commented on for the system of shallow water equations and the inviscid Burger's equation. Several areas for future research are described.
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  • 71
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    International Journal for Numerical Methods in Engineering 17 (1981), S. 1069-1079 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper presents a series summation computation method for calculating temperatures arising from some geometries which commonly occur in microelectronics. The method, which is suitable for use with pocket calculators, involves an exchange of terms with those of a known series. At each stage of the summation a state of convergence (SOC) is calculated in terms of the maximum possible error, thus enabling the calculation to be terminated as soon as the required accuracy has been obtained.
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    International Journal for Numerical Methods in Engineering 17 (1981), S. 1103-1117 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper presents an algorithm and corresponding FORTRAN program for the solution of unsymmetric banded linear equation systems. The algorithm is based on the Crout method. A special technique, called double windowing, enables the solution of very large equation systems with a total equation number reaching 30,000 and a full bandwidth in excess of 1,000. Special attention was devoted to minimization of peripheral processor time (communication with backing disc memory). An appendix lists the complete program for Cyber series computers (CDC).
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  • 73
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    International Journal for Numerical Methods in Engineering 17 (1981), S. 1147-1159 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A triangular element is developed using a complete third-degree polynomial as the interpolation function. The nodal variables include the function and its first-order derivatives. A local continuity condition, which implements the conservation of the normal gradients of the interpolation function along the three boundaries of the element, is provided as a remedy for the nonconformity of the first-order derivatives in conventional C° elements. The element is applied to potential flow problems. Numerical results for the flow over a cylinder and the flow through a draft tube elbow of a hydraulic turbine confirm the validity and the accuracy of this new cubic element. A comparison of this element with a C° triangular element is made by checking their differences from an analytical solution for the flow over the cylinder. This element appears to be more accurate than the C° element.
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  • 74
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    International Journal for Numerical Methods in Engineering 17 (1981), S. 1233-1256 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Numerical integration of the system of governing equations which define a boundary value problem written down in the form of a coupled system of first-order ordinary differential equations is shown to be a powerful technique. After presenting the basic approach the paper critically examines the numerical schemes available for situations when the boundary value problem so defined has boundary layer characteristics. One such method which is originally due to Goldberg, Setlur and Alspaugh3 is described in detail, with documentation in the form of a flow diagram and a FORTRAN listing of a working subroutine. The method is shown to be computationally efficient and reliable for the solution of a class of problems in the field of solid mechanics. Potential use of the method for the solution of magnetostatic problems is indicated.
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    International Journal for Numerical Methods in Engineering 17 (1981), S. 1273-1278 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: We present two self-contained programs which have given excellent results for uniform approximation of functions (or discrete data) by generalized rational functions. The first program is an extension of a program published in 1975 which uses a linear programming approach known as the differential correction algorithm. The present version is more robust, and allows for the use of a multiplicative weight function and restrictions on the values of the approximating function. These features make the program more suitable for applications such as digital filter approximation. The second program uses a combination of the Remes and differential correction algorithms which combines some of the good features of both algorithms. Given here is a discussion of the algorithms together with several examples. A FORTRAN listing can be obtained from the first author.
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    International Journal for Numerical Methods in Engineering 17 (1981), S. 1281-1282 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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  • 77
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    International Journal for Numerical Methods in Engineering 17 (1981), S. 1385-1395 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A finite difference solution of a system of first-order partial differential equations, using a central difference scheme, is presented. The equations describe the linear elastic behaviour of a thick rectangular plate resting on an elastic foundation and carrying an arbitrary transverse load. The lateral edges of the plate are unstressed. The main deflections and stresses predicted by the method for a particular case are given, together for purposes of comparison, with results from a finite element analysis.
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    International Journal for Numerical Methods in Engineering 17 (1981), S. 1427-1429 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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  • 79
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    International Journal for Numerical Methods in Engineering 17 (1981) 
    ISSN: 0029-5981
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    Source: Wiley InterScience Backfile Collection 1832-2000
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  • 80
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    International Journal for Numerical Methods in Engineering 17 (1981), S. 1469-1496 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Formulation and applications of the hybrid-stress finite element model to plane elasticity problems are examined. Conditions for invariance of the element stiffness are established for two-dimensional problems, the results of which are easily extended to three-dimensional cases. Next, the hybrid-stress functional for a 3-D continuum is manipulated into a more convenient form in which the location of optimal stress/strain sampling points can be identified. To illustrate these concepts, 4- and 8-node plane isoparametric hybrid-stress elements which are invariant and of correct rank are developed and compared with existing hybrid-stress elements. For a 4-node element, lack of invariance is shown to lead to spurious zero energy modes under appropriate element rotation. Alternative 8-node elements are considered, and the best invariant element is shown to be one in which the stress compatibility equations are invoked. Results are also presented which demonstrate the validity of the optimal sampling points, the effects of reduced orders of numerical integration, and the behaviour of the elements for nearly incompressible materials.
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    International Journal for Numerical Methods in Engineering 17 (1981), S. 1571-1575 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Two-dimensional distributions and three-dimensional element meshes are usually plotted in axonometric projection. Stereo decomposition can make the plots of complicated functions and structures more synoptical; the object appears in three dimensions. The method can be useful for the display of displacements and model shapes of three-dimensional structures as well.
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  • 82
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    International Journal for Numerical Methods in Engineering 17 (1981) 
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    Source: Wiley InterScience Backfile Collection 1832-2000
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    International Journal for Numerical Methods in Engineering 17 (1981), S. 1631-1646 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper deals with an application of the boundary element method to the analysis of nonlinear sloshing problems, namely nonlinear oscillations of a liquid in a container subjected to forced oscillations. First, the problem is formulated mathematically as a nonlinear initial-boundary value problem by the use of a governing differential equation and boundary conditions, assuming the fluid to be inviscid and incompressible and the flow to be irrotational. Next, the governing equation (Laplace equation) and boundary conditions, except the dynamic boundary condition on the free surface, are transformed into an integral equation by employing the Galerkin method. Two dynamic boundary condition is reduced to a weighted residual equation by employing the Galerkin method. Two equations thus obtained are discretized by the use of the finite element method spacewise and the finite difference method timewise. Collocation method is employed for the discretization of the integral equation. Due to the nonlinearity of the problem, the incremental method is used for the numerical analysis.Numerical results obtained by the present boundary element method are compared with those obtained by the conventional finite element method and also with existing analytical solutions of the nonlinear theory. Good agreements are obtained, and this indicates the availability of the boundary element method as a numerical technique for nonlinear free surface fluid problems.
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    International Journal for Numerical Methods in Engineering 17 (1981), S. 1735-1739 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A numerical approximation for the two-dimensional Laplacian operator at a point is derived for the general case in which the point is surrounded by an arbitrary number of arbitrarily located coplanar nodes. The expression obtained is shown to generalize the usual Cartesian finite difference expression.
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    International Journal for Numerical Methods in Engineering 17 (1981), S. 1743-1743 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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  • 86
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    International Journal for Numerical Methods in Engineering 17 (1981), S. 1763-1778 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Two explicit representation of a C1 quintic interpolant over triangles are given. These representations are derived by generalization of Coons' methods and Bernstein-Bézier methods, respectively.
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    International Journal for Numerical Methods in Engineering 17 (1981), S. 1823-1833 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The nonlinear elastic problem involving the indentation of a slightly compressible rubber-like layer bonded to a rigid cylinder and indented by another rigid cylinder is analysed by the finite element method. Both the geometric and material nonlinearities are accounted for. The finite element formulation of the problem is based upon a variational principle recently proposed by Cescotto and Fonder, and is valid for both slightly compressible and incompressible materials. The results computed and presented graphically include the shape of the indented surface, the pressure distribution over the contact surface, and the stress distribution at the bond surface. For the same contact width, the results for the compressible material are found to differ significantly from those for the case when the rubber-like layer is assumed to be incompressible.
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    International Journal for Numerical Methods in Engineering 17 (1981), S. 1877-1881 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Additional Material: 3 Ill.
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    International Journal for Numerical Methods in Engineering 17 (1981), S. 1890-1890 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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  • 90
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    International Journal for Numerical Methods in Engineering 17 (1981), S. 71-80 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Techniques for computing the sensitivity of temperatures to changes in design variables needed for designing thermal protection systems are considered. It is shown that the choice of the most efficient technique depends on the ratio of number of temperature constraints to the number of design variabies, as well as on the thermal analysis method employed. The analysis is specialized to the case of a structure modelled by finite elements, and an example of an insulation panel is used demonstrate the techniques.
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    International Journal for Numerical Methods in Engineering 17 (1981), S. 471-476 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper describes how general-purpose finite element structural analysis computer programs can be used, without modification, to solve various scalar field equations such as the wave equation, the Helmholtz equation, Laplace's equation, Poisson's equation, the heat equation and the telegraph equation, as well as mixed field problems (such as coupled structural-acoustic problems) which involve these equations.
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    International Journal for Numerical Methods in Engineering 17 (1981), S. 480-482 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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  • 93
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    International Journal for Numerical Methods in Engineering 17 (1981), S. 427-444 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A finite difference method for the large deformation elastic-plastic analysis of spherical caps is applied to predict the collapse strength of initially imperfect deep spherical shells. Twelve uniformly loaded hemispherical shell models with flat spots at their apex are analysed. For each model, a number of shallow spherical regions containing the flat spot are selected from its domain. One of these selected shallow regions yields a minimum buckling pressure; this minimum value is taken as the theoretical buckling load for the shell model under consideration. Present solutions are in good agreement with existing experimental and empirical results. The good comparison suggests that initially imperfect deep spherical shells may be analysed by using a much simpler mathematical model - the spherical cap - and thus the analytical cost may be greatly reduced. This also demonstrates that the collapse of imperfect spherical shells is primarily a local phenomenon and therefore dependent on local geometry. Consequently, the presence of initial imperfections must be fully taken into consideration in any large deformation inelastic buckling analysis before such analysis can be expected to quantitatively predict the collapse strength of practical shell structures.
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    International Journal for Numerical Methods in Engineering 17 (1981), S. 478-478 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    International Journal for Numerical Methods in Engineering 17 (1981), S. 615-631 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Simple mixed models are developed for the geometrically nonlinear analysis of deep arches. A total Lagrangian description of the arch deformation is used and the analytical formulation is based on a form of the nonlinear deep arch theory with the effects of transverse shear deformation included. The fundamental unknowns consist of the six internal forces and generalized displacements of the arch, and the element characteristic arrays are obtained by using Hellinger-Reissner mixed variational principle. The polynomial interpolation functions used in approximating the forces are one degree lower than those used for approximating the displacements, and the forces are discontinuous at the interelement boundaries.The equivalence between the mixed models developed herein and displacement models based on reduced integration of both the transverse shear and extensional energy terms is discussed. The advantages of mixed models over equivalent displacement models are outlined. Numerical results are presented to demonstrate the high accuracy and effectiveness of the mixed models developed, and compare their performance with other mixed models reported in the literature.
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    International Journal for Numerical Methods in Engineering 17 (1981), S. 679-706 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The treatment of zero energy modes which arise due to one-point integration of first-order isoparametric finite elements is addressed. A method for precisely isolating these modes for arbitrary geometry is developed. Two hourglass control schemes, viscous and elastic, are presented and examined. In addition, a convenient one-point integration scheme which analytically integrates the element volume and uniform strain modes is presented.
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    International Journal for Numerical Methods in Engineering 17 (1981), S. 633-644 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Often, finite element solutions of thin plate/shell elements become very stiff and the displacement field solutions diverge from those predicted by Kirchhoff's theory. This phenomenon is known as the locking phenomenon. A theoretical fomulation demonstrating its existence is developed, and results of finite element analysis of a single element and mesh are discussed. This leads to a sufficient and necessary criterion which must be satisfied to avoid the locking phenomenon.
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    International Journal for Numerical Methods in Engineering 17 (1981), S. 663-678 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper deals with constructing finite difference formulaes for approximating ordinary derivatives in a uniform or non-uniform mesh. The corresponding order of truncation error is also established. The accuracy and versatility of the proposed formulae are illustrated through numerical solution to two-point boundary value problems.
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    International Journal for Numerical Methods in Engineering 17 (1981), S. 923-930 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper presented an efficient computational algorithm for the eigensolution for real symmetric positive definite matrices. The algorithm is based on the Cholesky decomposition and will be referred to as the Cholesky algorithm. The efficiency of the algorithm is due to the combination of several iteration cycles into one, as well as to a judicious choice of shifts. The latter is accomplished by combining an approach based on Sturm's theorem for the initial stages of the process with another approach based on Gersch-gorin's theorem for the subsequent and final stages of the process. The efficiency of the proposed algorithm was tested against that of the QL method and was found to be superior. Moreover, its superiority increases with an increase in the order of the eigenvalue problem. For an eigenvalue problem of order 100, the proposed algorithm produced a solution in about one-half the time required by the QL method.
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    International Journal for Numerical Methods in Engineering 17 (1981), S. i 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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