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  • 1983  (298)
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  • Bone
  • 1
    ISSN: 1432-0827
    Keywords: Vitamin D ; Bone ; Osteoblasts ; Receptors ; 1,25-dihydroxyvitamin D3
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Medicine , Physics
    Notes: Summary Thaw-mount autoradiographic studies after injection of3H-1,25-D3 were conducted on 18-and 20-day-old rat fetuses. In maxillary bones, ribs, and tibia, nuclear concentration of radioactivity was found in osteoprogenitor cells and osteoblasts. Osteocytes and chondrocytes in epiphyseal plates were either unlabeled or weakly labeled. In competition experiments, nuclear concentration of radioactivity was blocked by the injection of a high dose of nonradioactive 1,25-D3 prior to the administration of the labeled hormone, but not by a similar dose of nonradioactive 25-D3. The results are interpreted as indicating that osteoprogenitor cells and osteoblasts are target cells for the direct action of 1,25-D3 on fetal bone.
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  • 2
    ISSN: 1432-0827
    Keywords: Vitamin D ; Vitamin D deficiency ; Bone ; Cartilage ; Bone development
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Medicine , Physics
    Notes: Summary The role of vitamin D in early skeletal development was studied by measuring serum calcium and phosphorus, osseous tissue quantity and mineralization, and endochondral bone elongation in rat fetuses and pups from vitamin D-replete and vitamin D-deficient mothers. At the 20th day of pregnancy there was a slight, yet significant, increase in the amount of osteoid on trabecular bone surfaces in fetuses from vitamin D-deficient mothers. The fetal bones otherwise appeared normal in spite of severe skeletal changes in the vitamin D-deficient mothers. After parturition, the importance of vitamin D in skeletal development becomes progressively more obvious. Serum calcium levels were slightly, yet significantly, lower in vitamin D-deficient than in vitamin D-replete pups and these levels continued to fall in the vitamin D-deficient pups through lactation and after weaning. At 3 days postpartum, there was a small, yet significant, increase in the amount of osteoid on bone surfaces of the vitamin D-deficient pups. The relative amounts of osteoid in the vitamin D-deficient pups continued to increase through lactation and after weaning when compared with vitamin D-replete pups. By the 14th day of lactation and at later periods, there were significant reductions in metaphyseal mineralized tissues in the vitamin D-deficient pups when compared with the vitamin D-replete pups. At weaning and after weaning, there were substantial increases in growth plate thickness and decreases in longitudinal bone growth in the vitamin D-deficient pups when compared with the vitamin D-replete pups. The results from this study indicate that vitamin D does not appear to play a major role in fetal skeletal development. However, after birth, vitamin D becomes progressively more important with age for normal bone development, mineralization, and endochondral growth.
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  • 3
    Electronic Resource
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    Springer
    Calcified tissue international 35 (1983), S. 481-485 
    ISSN: 1432-0827
    Keywords: Chemotaxis ; Bone ; Osteoblasts ; Bone proteins
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Medicine , Physics
    Notes: Summary When demineralized bone matrix powder is implanted subcutaneously in the rat, the early responses involve the appearance and proliferation of mesenchymal cells at the site of implantation, followed by cartilage and bone formation. The ability of cells to migrate to the implant suggests that chemotaxis may be a critical event in this process. Therefore, using the modified Boyden chamber assay, we tested extracts of demineralized bone matrix for chemotactic activity. We have identified and partially purified, on molecular sieve chromatography, a heat labile and trypsin-sensitive protein (Mr=60,000–70,000) that is a potent chemoattractant for mouse calvaria, osteoblast-like cells (MMB-1), but not for monocytes (putative osteoclast precursors). These findings suggest that chemotactic protein(s) have a significant role in the recruitment of osteoprogenitor cells to a site of bone repair.
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  • 4
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    Springer
    Calcified tissue international 35 (1983), S. 762-766 
    ISSN: 1432-0827
    Keywords: Enamel ; Maturation cycles ; Tetracycline ; Dentine ; Bone
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Medicine , Physics
    Notes: Summary Uptake of tetracycline by enamel in the short-term was studied at an advanced stage of crown formation and after completion of crown formation in deciduous molars in the cat. Both secretory phase enamel and bands of postsecretory, maturation phase enamel labeled rapidly. The pattern of labeling mimicked that seen in the continuously growing, rootless incisor teeth of the rat, with narrow doublets fusing to form narrow bands with wide unlabeled intervals in the short term. This is a physiological demonstration which indicates that cyclical activity and changes may occurin vivo during the maturation phase of amelogenesis in rooted teeth. It is also noted that dentine did not, and that some circumscribed patches of bone did label in the same animals in the same time interval. Short-term tetracycline labels are lost following conventional histological processing, but are retained after freeze-drying or air-drying.
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  • 5
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    Springer
    Calcified tissue international 35 (1983), S. 148-152 
    ISSN: 1432-0827
    Keywords: Bone ; Computed tomography ; Densitometry ; Osteoporosis ; Osteomalacia
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Medicine , Physics
    Notes: Summary The linear attenuation coefficient (μ in cm1) of trabecular bone was modeled for different conditions of bone and marrow composition in order to assess their influence on computed tomography (CT) quantitation. A large relative change (10% of TBV at 15% TBV) of bone concentration resulted in small changes of μ: 2.3% at 60 keV, 3.4% at 44 keV, 5.2% at 29 keV. Relative changes of trabecular bone volume (TBV) on the order of 3% could be detectedin vivo by CT were it not for errors of relocation and for compositional influences on accuracy. The μ (and density) depended critically not only on amounts of bone substance and marrow but on their compositions. Normal variation in the composition of bone substance produced an uncertainty in μ equivalent to 0.5 to 1% TBV. Increases of yellow marrow produced a decrease of μ which could be mistaken for a decrease of bone concentration. The biological variation (90% confidence limit) of marrow composition gives an uncertainty at 15% TBV of about 2.4% TBV at 60 keV, 1.7% at 44 keV, and 1.3% at 29 keV. These correspond to relative uncertainities of 16, 11, and 9% respectively. These factors help explain the large accuracy errors (30%) observed in all studies of trabecular bone where single-energy CT was used. Marrow composition also can affect precision of bone measurement. Systematic shifts of red and yellow marrow could mask biological changes such as those occurring with aging or treatment.
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  • 6
    ISSN: 1432-0827
    Keywords: Bone ; Calcium metabolism ; Whole-body counting
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Medicine , Physics
    Notes: Summary A whole-body counter was used to measure the retention and distribution of radioactivity along the longitudinal axis of the body during 10 days after the intravenous injection of 50 µCi of47Ca. These data and the simultaneous measurements of the serum specific activity allowed us to calculate, by the Bauer-Carlsson-Lindquist (BCL) formulas generalized by Marshall, the calcium accretion rate and exchangeable pool in 7 areas: skull, thorax, pelvis, thighs, knees, legs, and ankles and feet. For the whole body, the accretion rate was 336±115 mg/24 h, and the exchangeable pool 5668±1221 mg, in 26 subjects without bone disease. Both parameters were significantly correlated with body height; the exchangeable pool was significantly higher in men than in women. The accretion rate and exchangeable pool expressed on a basis of bone content varied widely from one area to another, reflecting the ratio of spongy to compact bone: the thorax, pelvis, and arms, which contain 49% of the skeletal mass, accounted for 57% of the total accretion rate and 53% of the exchangeable pool; the skull, 18% of the skeletal mass, accounted for 14% of the accretion and 11% of the pool.
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  • 7
    ISSN: 1432-0827
    Keywords: Dentin ; Bone ; Apposition rate ; Parathyroid hormone
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Medicine , Physics
    Notes: Summary The dose-dependency of the effects of parathyroid hormone (PTH) on bone and dentin apposition after both intermittent and continuous administration of the hormone was investigated. The purpose was to compare the sensitivity of these two mineralizing tissues to parathyroid hormone and to provide additional information regarding the direct effect of PTH on mineralized tissue formation. Adult rats were thyroparathyroidectomized and 5 groups of 4 or 5 rats each were given daily subcutaneous injections with different doses of bovine parathyroid hormone. Five more groups of 4 rats each were administered equivalent dosages by means of a continuous infusion pump implanted subcutaneously. An additional group of 4 rats served as controls. All animals were labeled with tetracycline injected on days 7, 9, and 11. The animals were killed on day 12 and blood samples were collected for serum calcium determination. The lower metaphysis of the femur and the left and right mandibles were dissected out, and undecalcified sections of plastic-embedded tissues were prepared. The distances between the three tetracycline bands were measured to determine the amount of bone or dentin formation. Results indicated that both dentin and bone apposition increased with higher dosages of hormone. No overall effect of the method of administration was evident. For both methods, bone apposition showed a more pronounced increase over the control levels than dentin apposition. This suggests that, although both osteoblasts and odontoblasts appear to respond directly to PTH, differences do exist in the magnitude and dose-dependency of the response. No causal relationship was found between increases in serum calcium levels and either bone or dentin apposition at the lower dose levels.
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  • 8
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    Springer
    Calcified tissue international 35 (1983), S. 728-731 
    ISSN: 1432-0827
    Keywords: Bone ; Bioelectricity
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Medicine , Physics
    Notes: Summary The origin of the bioelectric potentials in unstressed living bones is still an open question. Blood-flow in vessels, stationary potentials on peripheral nerves, muscle injury potentials, and viability of bone cells are claimed to be possible sites of origin of the electric potentials recorded on bone surface. The present data show that the topographic quantitative distribution of tetracycline labeling at sequential levels of rabbit tibia and the distribution pattern of the bioelectric potentials in this bone are significantly superimposable. This coincidence of bone formation rates and bioelectric potentials seems to support the view that the latter are in some way linked with the laying down of new bone.
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  • 9
    ISSN: 1432-0827
    Keywords: Bone ; Osteosarcoma ; Matrix vesicles ; Alkaline phosphatase ; Aminopeptidase ; Naphthylamidase
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Medicine , Physics
    Notes: Summary Extracellular matrix vesicles from bovine fetal alveolar bone and from a dog osteosarcoma were isolated by differential centrifugation and then fractionated on a discontinuous sucrose density gradient. The fractions were examined by electron microscopy and were analyzed for protein, alkaline phosphatase, aminotripeptidase, and four different β-naphthylamidase activities. The low-density peak of enzyme activities was shown by electron microscopy to be much more homogeneous than the crude matrix vesicle fraction. Two major peaks of protein and enzyme activities were present, one in the high and one in the low density layers. There was good correlation between the activities of alkaline phosphatase and the various peptidases in the fractions from the sucrose density gradient. These results indicate a coexistence of peptidase and alkaline phosphatase in matrix vesicles. On the other hand, there was generally no correlation between the peptidase and alkaline phosphatase activities in vesicular specimens from bovine liver obtained in the same way. Most of the peptidase activity and about half of the alkaline phosphatase activity were solubilized from bone matrix vesicles by detergents. The extracted alkaline phosphatase and alanyl β-naphthylamidase activities were separated from each other on a DEAE-cellulose column.
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  • 10
    ISSN: 1432-0827
    Keywords: Bone ; Mineral ; Crystallinity ; Maturation ; Age
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Medicine , Physics
    Notes: Summary The crystallinity of bone mineral at different stages of maturation has been measured by quantitative X-ray diffraction methods. Crystallinity measurements were made on tibial middiaphyses from 17-day embryonic chicks, newlyformed periosteal bone from embryonic chicks, and density-fractionated bone from post-hatch chickens from 5 weeks to 2 years of age. For a given animal age and degree of mineralization, crystallinity increases with animal age, indicating that changes in bone mineral occur even after mineralization is complete or nearly complete.
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  • 11
    ISSN: 1432-0827
    Keywords: ADP ; Bisphosphonate ; Bone ; Resorption ; Formation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Medicine , Physics
    Notes: Summary The effects of 1.5–2 years oral administration of disodium (3-amino-1-hydroxypropylidene)-1,1-bisphosphonate (APD) on bone metabolism were studied in male and female rats. APD was mixed in the food at levels of 500, 2,000 and 10,000 ppm. A dose-dependent increase in metaphyseal bone was found, indicative of continued inhibition of bone and cartilage resorption. APD did not affect mineralization of bone and cartilage, primary bone formation, or periosteal apposition. A short-term metabolic balance study was performed to compare the effects of oral with subcutaneous APD. Absorption of APD was in the order of 0.2%. Oral APD increased absorption of phosphate, probably by complexation of calcium with APD. The excess absorbed phosphate increased phosphaturia and decreased urinary calcium.
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  • 12
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    International orthopaedics 7 (1983), S. 105-111 
    ISSN: 1432-5195
    Keywords: Malignant fibrous histiocytoma ; Bone ; Prosthesis ; Resection
    Source: Springer Online Journal Archives 1860-2000
    Topics: Medicine
    Description / Table of Contents: Résumé Chez une malade de 50 ans un histiocytome osseux fibreux malin, localisé à la métaphyse distale du fémur droit, a été reconnu par l'histologie et confirmé par la microscopie électronique. Elle a été traitée par résection «en bloc» et mise en place d'une prothèse de polyméthylacrylate faite sur mesure et comportant une articulation du genou type Waldius. La malade a été revue deux ans après, sans récidive.
    Notes: Summary This is a case report of a fifty-year old female patient with malignant fibrous histiocytoma of bone well localised in the distal metaphysis of the right femur. It was treated by ‘en bloc’ resection and replacement with a purpose-made polymethylmethacrylate prosthesis and a Waldius-type knee replacement. The diagnosis was confirmed by electron microscopy. The patient had good function of the limb and was symptom free two years later.
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  • 13
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    Virchows Archiv 400 (1983), S. 287-295 
    ISSN: 1432-2307
    Keywords: Breast neoplasms ; Cartilage ; Bone ; Mesenchymoma ; Pleomorphic adenoma
    Source: Springer Online Journal Archives 1860-2000
    Topics: Medicine
    Notes: Summary A total of 307 breast neoplasms and tumour-like conditions were reviewed to assess the frequency with which bone and/or cartilage occurred. Of 90 fibroadenomas, 1 (1.1%) and 2 of 158 breast carcinomas (1.3%) contained bone, one benign mesenchymoma contained cartilage, and one benign “mixed” tumour (pleomorphic adenoma) displayed cartilage and bone. Twenty-two papillomas and 34 cases of gynaecomastia did not contain any cartilage or bone. This study confirms the impression that the occurrence of bone or cartilage in human breast neoplasms is rare. These lesions are briefly discussed with reference to the pertinent literature.
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  • 14
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    Cell & tissue research 233 (1983), S. 689-691 
    ISSN: 1432-0878
    Keywords: Fluoride ; Progeny ; Bone ; Rat
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Medicine
    Notes: Summary Femurs of weanling rats from third-pregnancy litters of dams given 150 ppm fluoride in the drinking water were examined by light- and scanning-electron microscopy. Under the conditions of the experimental procedure, no pathological changes were seen in the femurs as a result of maternal ingestion of fluoride. These results indicate that the amount of fluoride crossing the placenta and mammary gland was insufficient to produce significant morphological changes in the bones of 3-week-old rats.
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  • 15
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    Annals of biomedical engineering 11 (1983), S. 263-295 
    ISSN: 1573-9686
    Keywords: Bone ; Mechanical bone properties ; Functional adaptation of bone tissue ; Mathematical models of Hooke's law
    Source: Springer Online Journal Archives 1860-2000
    Topics: Medicine , Technology
    Notes: Abstract The properties of bone tissue as a material and bones as the structural elements of the skeleton are reviewed and summarized. The first half of this work describes bone tissue microstructure, the stress-strain relations, and the strength and fracture of bone. The second and slightly larger half concerns the adaptation of living bone tissue to its load environment. Some observations and experiments of bone remodeling due to applied stress are described and continuum models for this process are formulated. An example of bone remodeling leading to shape changes in the bone is described as well as an example of bone remodeling leading to changes in the bulk density of the bone tissue.
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  • 16
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 19 (1983), S. i 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
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  • 17
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 19 (1983), S. 17-26 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A simple two-step corrective technique is presented in this paper for evaluating stress intensity factors in crack problems. In the first step an approximate evaluation of the stress intensity factor was made by considering the cracked plate to be of infinite size. The stresses of the problem were relaxed by the stresses of the infinite body which corresponds to the approximate value of the stress intensity factor. The expected discrepancy in the value of SIF by the infinite plate approximation was corrected in the second step where the existing residual stresses are equilibrated at the cracked plate by using any of the conventional finite element techniques and the corrective value of the stress intensity factor is calculated by using an appropriate collocation formula. The method was applied to three typical plane problems of cracked plates with satisfactory results.
    Additional Material: 6 Ill.
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  • 18
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 19 (1983), S. 73-91 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In this study, three boundary element method approaches are compared by solving a typical problem in linear elastodynamics. The first approach formulates and solves the problem in the real time domain in conjunction with a time-stepping algorithm. The other two approaches formulate and solve the problem in the Laplace and the Fourier transformed domains, which necessitates a numerical inversion of the results to the time domain. The results obtained compare favourably with available analytic solutions. A detailed tabulation of the computer time and memory requirements of each approach is presented.
    Additional Material: 6 Ill.
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  • 19
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 19 (1983) 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
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  • 20
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 19 (1983), S. 185-215 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: It is well known that one way to treat nonlinear periodic dynamical systems governed by ordinary differential equations is to find first the corresponding point mappings. This approach has many advantages but it has a main obstacle in that it is difficult to obtain the exact mapping except in very special cases. Presented in this paper is a procedure which allows us to determine the point mapping in a polynomial form up to any specific degree of accuracy. The procedure when applied to linear periodic systems reduces to the one proposed by Friedmann et al.22 After presenting the algorithm for finding the point mappings, the method is applied to several problems in order to study the dynamical properties of the systems and to demonstrate the usefulness of the method.
    Additional Material: 15 Ill.
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  • 21
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 19 (1983), S. 281-291 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The inclusion principle provides a qualitative characterization of the eigenvalues of a matrix. The principle has been shown to apply to systems described by a single Hermitian matrix, the most important of which being the real symmetric matrix. Self-adjoint distributed systems, when discretized by either the classical Rayleigh-Ritz method or by the finite element method, lead to algebraic eigenvalue problems described in terms of two real symmetric matrices. The algebraic eigenvalues problem derived by the classical Rayleigh-Ritz method possesses the embedding feature required by the inclusion principle, but that derived by the finite element method in general does not. This paper demonstrates that the inclusion principle can be extended to discretized systems derived by the hierarchical finite element method.
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  • 22
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 19 (1983), S. 310-310 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
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  • 23
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 19 (1983), S. 315-329 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Two kinds of techniques for solving a shape determination problem are proposed. The determination of the interface boundary between two domains governed by Poisson and Laplace equations under the compatible and constraint condition is considered. Influence coefficient and inverse variational approaches are examined by using the iterative finite element procedure. A two-dimensional model of a junction-type field effect transistor is a test example. The determination of its interface boundary and the prediction of the potential distribution and static characteristic are demonstrated.
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  • 24
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 19 (1983), S. 393-404 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A new, improved infinite element based on mapping is proposed for modelling unbounded domain problems. Mapping has previously been used in such problems, not only for the entire domain, but also for the infinite element itself. The novelty of the present approach is the simplicity of the mapping, and the retention of standard integration abscissae and weights. The implementation of these elements is very straightforward, and they are ideally suited for the analysis of infinite domain static problems in two and three dimensions.
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  • 25
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    International Journal for Numerical Methods in Engineering 19 (1983), S. 431-449 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A uniform linear beam in a uniform linear ambient medium is studied. The beam performs stationary harmonic damped nonsynchronous space vibration in simultaneous tension, torsion, bending and shear in the presence of a large static axial load. Hysteretic and viscous dampings of the beam material and ambient medium are considered. Generalized complex Koloušek functions are derived. A 12 × 12 complex symmetric stiffness matrix is established for a supported beam member excited at its ends by prescribed harmonic translations and rotations which have the same frequency but may be out of phase. This matrix allows for an exact analysis of nonproportionally damped built-up beam structures, thus avoiding assumed mode shapes and lumped or consistent masses. A general notation is suggested. Numerical examples are given, including applications of the computer program SFVIBAT-DAMP.
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  • 26
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    International Journal for Numerical Methods in Engineering 19 (1983), S. 468-472 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
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  • 27
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    International Journal for Numerical Methods in Engineering 19 (1983), S. 467-468 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Additional Material: 1 Tab.
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  • 28
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 19 (1983), S. 451-465 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In this paper we extend predictor-corrector methods, commonly used for the numerical solution of ordinary differential equations (o.d.e.s), to parabolic partial differential equations (p.d.e.s), typically of the form ut = auxx + ƒ(u, ux, x, t).We describe linear multistep methods for p.d.e.s, the nonlinear algebraic equations arising from implicit formulae being solved using a corrector analogous to those used for o.d.e.s. A sufficient condition for convergence of the iteration is then derived and is found, in most cases, to be far less restrictive than that obtained from the usual method of lines approach. Numerical results are presented to investigate the necessity of this condition. They also indicate that we can accelerate convergence by reducing the time increment. This allows us to achieve convergence within a prescribed number of iterations and so to construct PCm methods corresponding to P(EC)m methods for o.d.e.s. Numerical results are also given to test the absolute stability of the Crank-Nicolson corrector for various predictors P, and iterations, m.
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  • 29
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    International Journal for Numerical Methods in Engineering 19 (1983), S. 626-630 
    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 19 (1983), S. 647-664 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A Fortran computer program is described which calculates physical quantities for a class of shell triangular elements undergoing inextensional bending. These elements are in quadratic parametric representation and may have positive, zero or negative Gaussian curvature.The exact inextensional bending solutions for the rectangular displacement components are cubic in the surface co-ordinates and the curvature changes are relatively slowly varying.
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  • 31
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    International Journal for Numerical Methods in Engineering 19 (1983), S. 757-764 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An algorithm based on a new formulation of problem is used in generating the co-ordinates of the meridian of the drop-shaped tank. The stresses and moments of this form, due to the varying hydrostatic pressure head, are obtained by a finite element simulation and the usefulness of this approach is assessed.
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  • 32
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    International Journal for Numerical Methods in Engineering 19 (1983) 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
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  • 33
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    International Journal for Numerical Methods in Engineering 19 (1983), S. 803-810 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Universal serendipity elements (USE) are defined as isoparametric elements having linear, quadratic and cubic node configurations at their edges in an arbitrary manner. Formulation of shape functions and their derivatives for USE is presented. A computer algorithm which allows the efficient application of USE is explained. Only corner nodes are kept transparent to the user. Changing the order of USE is fully automated. It is concluded that the USE concept allows interactive mesh refinement in an efficient manner and eliminates the difficulties encountered in the use of higher order isoparametric serendipity elements.
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  • 34
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    International Journal for Numerical Methods in Engineering 19 (1983), S. 859-871 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In this paper we consider solution of the eigen problem in structural analysis using a recent version of the Lanczos method and the subspace method. The two methods are applied to examples and we conclude that the Lanczos method has advantages which are too good to overlook.
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  • 35
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    International Journal for Numerical Methods in Engineering 19 (1983), S. 145-151 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In many commercial finite element method systems, the formulation of constraint equations from rigid elements is based entirely on rigid body mechanics. However, when initial (thermal) strains exist, a more general approach is required for rigidizing the element. This new approach also opens up a more versatile generation scheme of constraint equations for rigid or partially rigid elements.
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  • 36
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    International Journal for Numerical Methods in Engineering 19 (1983), S. 169-184 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A class of mixed finite element discretizations of the problem of limit analysis for plastic plates is analysed. For the discrete problem we discuss a linear programming approach based on linearization of the yield condition and a convex programming approach based on the exact Mises condition. Applying the method to rectangular plates with uniform load and concentrated loads we get improved and new results partly in disagreement with one of our references.
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  • 37
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    International Journal for Numerical Methods in Engineering 19 (1983), S. 237-255 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A shear-flexible finite element is employed to investigate the transient response of isotropic, orthotropic and layered anisotropic composite plates. Numerical convergence and stability of the element is established using Newmark's direct integration technique. Numerical results for deflections and stresses are presented for rectangular plates under various boundary conditions and loadings. The parametric effects of the time step, finite element mesh, lamination scheme and orthotropy on the transient response are investigated. The present results agree very closely with the results available in the literature for isotropic plates, and the results for composite plates should serve as bench marks for future comparisons by other investigators.
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  • 38
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    International Journal for Numerical Methods in Engineering 19 (1983), S. 305-309 
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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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  • 39
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    International Journal for Numerical Methods in Engineering 19 (1983), S. 311-311 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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  • 40
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    International Journal for Numerical Methods in Engineering 19 (1983), S. 355-371 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper contains numerical considerations on, and the results of the problem of a fluid filtering through a porous, isotropic, homogeneous, three-dimensional dam with variable cross-section. The numerical solution is obtained by the finite element method using cylindrical elements that exactly match the curved part of the boundary.Furthermore, a lower and an upper numerical enclosure of the free boundary are considered, together with a description of the procedure of calculations performed by an IBM 370/158 computer.
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  • 41
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    International Journal for Numerical Methods in Engineering 19 (1983), S. 421-430 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A new technique for the solution of singular integral equations is proposed, where the unknown function may have a particular singular behaviour, different from the one defined by the dominant part of the singular integral equation. In this case the integral equation may be discretized by two different quadratures defined in such a way that the collocation points of the one correspond to the integration points of the other. In this manner the system is reduced to a n × n system of discrete equations and the method preserves, for the same number of equations, the same polynomial accuracy. The main advantage of the method is that it can proceed without using special collocation points. This new technique was tested in a series of typical examples and yielded results which are in good agreement with already existing solutions.
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  • 42
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    International Journal for Numerical Methods in Engineering 19 (1983), S. 479-493 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A uniform linearly elastic beam element with non-coinciding centres of geometry, shear and mass is studied under stationary harmonic end excitation. The Euler-Bernoulli-Saint Venant theory is applied. Thus the effect of warping is not taken into account. The frequency-dependent 12 × 12 element stiffness matrix is established by use of an exact method. The translational and rotational displacement functions are represented as sums (real) of complex exponential terms where the complex exponents are numerically found. Built-up structures containing beam elements of the described type can be analysed with ease and certainty using existing library subroutines.
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  • 43
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    International Journal for Numerical Methods in Engineering 19 (1983), S. 567-580 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The implementation of a combined boundary element-finite element analysis capability is discussed. A comparison is then made between the finite element, boundary element and coupled method as applied to unbounded problems in elasticity and plasticity.
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  • 44
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    International Journal for Numerical Methods in Engineering 19 (1983) 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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  • 45
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    International Journal for Numerical Methods in Engineering 19 (1983), S. 37-47 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An examination is made of displacement trial functions found in the quadratic isoparametric representation of an arc. Special attention is given to the quality of curvature change description and to effective manipulation of the trial functions. Various interpolation formulae are derived which have relevance to curved shell finite element design under Love-Kirchhoff assumptions.
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  • 46
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    International Journal for Numerical Methods in Engineering 19 (1983), S. 59-71 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Thin-walled members subject to generalized loading may be modelled by using a finite element approach with conventional stress and strain parameters. A solution method for a class of problems that would use these elements is described. A numberical example of an elastic beam is given.
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  • 47
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    International Journal for Numerical Methods in Engineering 19 (1983), S. 125-140 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The computational methods used to predict and optimize the thermal-structural behaviour of aerospace vehicle structures are reviewed. In general, two classes of algorithms, implicit and explicit, are used in transient thermal analysis of structures. Each of these two methods has its own merits. Due to the different time scales of the mechanical and thermal responses, the selection of a time integration method can be a difficult yet critical factor in the efficient solution of such problems.Therefore mixed time integration methods for transient thermal analysis of structures are being developed. This proposed methodology would be readily adaptable to existing computer programs for structural thermal analysis.
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  • 48
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    International Journal for Numerical Methods in Engineering 19 (1983), S. 141-144 
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    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: In this paper the application of the theorems of structural variation to finite element problems is presented and a simplified procedure for constant strain triangular elements is developed. Applications for these techniques are discussed.
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  • 49
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    International Journal for Numerical Methods in Engineering 19 (1983), S. 152-156 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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  • 50
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    International Journal for Numerical Methods in Engineering 19 (1983), S. 217-235 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The mini-max dual method ia applied for solving the material selection structural optimization problems. A somewhat general objective function is introduced to consider structural weight and material cost simultaneously. It is expressed by the sum of scaled structural weight and material cost. The present formulation can yield minimum cost and minimum weight designs as two distinct special cases. It is shown that practically useful intermediate optimal designs can exist between the two extremes. Only truss structures are considered as a representative example. One numerical example is provided to illustrate the change in optimal material distribution when various objective functions are employed. A particular advantage in using the dual method for the material selection problem is also described.
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    International Journal for Numerical Methods in Engineering 19 (1983), S. 271-280 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The finite element reduced scalar potential method of calculating magnetic fields is investigated by comparing it with a classical series method. Both methods are applied to two problems having a current band surrounding a ferromagnetic shell. The magnetic field distributions obtained by both methods are shown to be in generally good agreement.
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  • 52
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    International Journal for Numerical Methods in Engineering 19 (1983), S. 310-310 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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  • 53
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    International Journal for Numerical Methods in Engineering 19 (1983), S. 312-314 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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  • 54
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    International Journal for Numerical Methods in Engineering 19 (1983), S. 331-340 
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    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: A finite strip method is presented for the geometrically nonlinear analysis of prismatic structures under arbitrary loading. The method employs an iterative finite element approach but replaces numerical integration by an explicit formulation. A computer program has been developed and is described in the paper; a numerical example is given.
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  • 55
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    International Journal for Numerical Methods in Engineering 19 (1983), S. 405-419 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A stabilization procedure is developed for controlling the kinematic modes of the four-node, bilinear quadrilateral element when single-point quadrature is used. These kinematic modes manifest themselves by spatial oscillations or singularity of the total stiffness. In this stabilization procedure, additional generalized strains are defined which are activated by the kinematic modes; these generalized modes are furthermore not activated by rigid body motions regardless of the shape of the quadrilateral. By using a scaling law developed in an earlier paper, the stabilization parameters are defined so they do not adversely affect the element's performance. Several problems which are subject to kinematic modes are presented to illustrate the performance of this stabilization procedure for linear problems.
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  • 56
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    International Journal for Numerical Methods in Engineering 19 (1983), S. 473-478 
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    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: A method is developed which basically concerns how to reduce the necessary storage and cost of solving a set of algebraic equations arising from applying the initial stress technique to the analysis of a uniformly layered elastic-plastic soil. Advantage is taken of the geometrical symmetry of the problem and the consequent symmetry of the stiffness matrix. The nodal values are expanded in a discrete Fourier series so that a two-dimensional problem is reduced to a number of one-dimensional problems.
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  • 57
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    International Journal for Numerical Methods in Engineering 19 (1983), S. 495-503 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: We consider numerical methods for initial value problems for second-order systems of ordinary differential equations, analysing them by applying them to the test equation We discuss conditions which ensure an oscillatory numerical solution and the desirability of such a property. We also use a slightly more general test equation to derive conditions which ensure that the numerical forced oscillation is in phase with the true forced oscillation.To illustrate the theory, we consider the damping and phase properties of some frequently used methods.
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  • 58
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    International Journal for Numerical Methods in Engineering 19 (1983), S. 541-566 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An elasto-plastic analysis of anisotropic plates and shells is undertaken by means of the finite element displacement method. A thick shell formulation accounting for shear deformation is considered, which is based on a degenerate three-dimensional continuum element. The accommodation of variable material properties, not only along the surface of the structure but also through the thickness, is made possible by a discrete layered approach. Although isoparametric elements of the Serendipity family give satisfactory solutions for thick and moderately thin shells the results exhibit ‘locking’ for an increasing ratio of span to thickness. To develop a numerical model which is applicable to thick or thin plates and shells, the nine-node Lagrangian element and the Heterosis element are also introduced into the present model. Plastic yielding is based on the Huber-Mises yield surface extended by Hill for anisotropic materials. The yield function is generalized by introducing anisotropic parameters of plasticity which are updated during the material strain hardening history. Numerical examples are presented and compared with available solutions. The effects of anisotropy on these solutions are also discussed.
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  • 59
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    International Journal for Numerical Methods in Engineering 19 (1983), S. 625-625 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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  • 60
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    International Journal for Numerical Methods in Engineering 19 (1983), S. i 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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  • 61
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    International Journal for Numerical Methods in Engineering 19 (1983), S. 631-646 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: When a homogeneous elastic continuum is modelled by a non-uniform finite element grid, the differences in the size of adjacent finite elements can cause a spurious wave reflection which does not exist in the continuum. Extending previous studies in which the spurious wave reflection was investigated for the case of two uniform grids with a sudden element size change from one grid to the other, the present study deals with the case when the two uniform grids of different element sizes are separated by a transition zone through which the element size varies gradually, either by a geometric progression or by an arithmetic progression. The solution is carried out in complex variables and numerical plots of the results are given. When the ratio of wavelength to the largest element size is as low as 4 : 1, the spurious wave reflection is very significant, while for the ratios over 10 : 1 it is insignificant. Inserting a transition zone with gradually varying element size between the two uniform parts of the grid somewhat mitigates the phenomenon of spurious reflection, but this is significant only when the ratio of element sizes in the uniform grids is small (less than about 1·5 : 1). Varying the element size throughout the transition zone in an arithmetic progression seems slightly better than in a geometric progression. The spurious wave reflection is less pronounced for higher-order elements, in particular for linear strain elements as compared to constant strain elements. The spurious reflection is also less severe for consistent mass than for lumped mass.
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    International Journal for Numerical Methods in Engineering 19 (1983), S. 725-737 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: We have assessed the accuracy of a commercially available computer software package for finite element method calculations of magnetostatic fields. The computer program, MSC/NASTRAN,Available from the MacNeal-Schwendler Corporation, Los Angeles, CA 90041, U.S.A. is well known for its wide applicability in structural analysis and heat transfer problems. We exploit the fact that the differential equations of magnetostatics are identical to those for heat transfer if the magnetic field problem is formulated with the reduced scalar potential.1 Consequently, the powerful, optimized numerical routines of NASTRAN can immediately be applied to two- and three-dimensional linear magneto-statics problems. Application of the NASTRAN reduced scalar potential approach to a ‘worst case’ two-dimensional problem for which an analytic solution is available has yielded much better accuracy than was recently reported2 for a reduced scalar potential calculation using a different finite element program. Furthermore, our method exhibits completely satisfactory performance with regard to computational expense and accuracy for a linear electromagnet with an air gap. Our analysis opens the way for large three-dimensional magnetostatics calculations at far greater economy than is possible with the more commonly used vector potential and boundary integral methods.
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    International Journal for Numerical Methods in Engineering 19 (1983), S. 789-802 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper presents an algorithm which determines the invertibility of any planar, triangular quadratic isoparametric finite element transformation. Extensions of the algorithm to three-dimensional isoparametric finite element transformations yield conditions which guarantee invertibility of 10-node tetrahedra and 8-node bricks. The mathematical basis for the algorithm focuses on the Jacobian as a continuous function defined over a compact set where the Jacobian attains a maximum and a minimum value. The algorithm then determines whether these values are of opposite sign.
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    International Journal for Numerical Methods in Engineering 19 (1983), S. 825-829 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The pulse-spectrum technique (PST), an iterative numerical algorithm, is presented and extended to solve the inverse problems arising from the dynamic structural identification and structural design problems. A simple one-dimensional shear beam model is used to demonstrate the applicability of PST. Numerical simulations are carried out to test the feasibility and to study the general characteristics of this technique without the real measurement and design data. It is found that the PST is not only quite robust in providing accurate results but also an excellent numerical method according to the four practical criteria for evaluating numerical methods.
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    International Journal for Numerical Methods in Engineering 19 (1983), S. 891-911 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: A two-step approach to finite element ordering is introduced. The scheme involves ordering of the finite elements first, based on their adjacency, followed by a local numbering of the nodal variables. The ordering of the elements is performed by the Cuthill-McKee algorithm. This approach takes into consideration the underlying structure of the finite element mesh, and may be regarded as a ‘natural’ finite element ordering scheme. The experimental results show that this two-step scheme is more efficient than the reverse Cuthill-McKee algorithm applied directly to the nodes, in terms of both execution time and the number of fill-in entries, particularly when higher order finite elements are used. In addition to its efficiency, the two-step approach increases modularity and flexibility in finite element programs, and possesses potential application to a number of finite element solution methods.
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    International Journal for Numerical Methods in Engineering 19 (1983), S. 943-948 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The matrix N(λ) whose elements are functions of a parameter λ is called the λ-matrix. Those values of λ that make the matrix singular are of great interest in many applied fields. An efficient method for those eigenvalues of a λ-matrix is presented. A simple explicit convergence criterion is given, as well as the algorithm and two numerical examples.
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    International Journal for Numerical Methods in Engineering 19 (1983) 
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    International Journal for Numerical Methods in Engineering 19 (1983), S. 950-950 
    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 19 (1983), S. 951-952 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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  • 70
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    International Journal for Numerical Methods in Engineering 19 (1983), S. 953-970 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A new boundary element technique based on Green's formula is applied to the analysis of nonlinear water wave problems. The problems are formulated mathematically as two-dimensional nonlinear initial-boundary value problems in terms of a velocity potential, assuming the fluid to be inviscid and incompressible, and the flow to be irrotational.In the present paper, two kinds of wave-making problems are analysed: (1) a tsunami generated by sea bed elevation; (2) generation, propagation and run-up on a vertical wall of a solitary wave. Numerical results obtained by the present method are compared with available experimental data and analytical solutions. Excellent agreements are obtained.
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    International Journal for Numerical Methods in Engineering 19 (1983), S. 985-993 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: In Reference 1 a series of general formulae for evaluating the total number of non-zero blocks in the stiffness matrix, both of two-dimensional and three-dimensional (arbitrary polygonal/polyhedral) finite element networks, was presented. In this paper, an alternative, more direct and efficient method for deriving such formulae is presented. In addition, this new method can be used for more complex situations. In fact, it may be used for almost all kinds of finite element networks.
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    International Journal for Numerical Methods in Engineering 19 (1983), S. 1005-1032 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A technique is developed for the numerical analysis of wave motion in layered strata. Semidiscrete particular solutions satisfying inhomogeneous boundary conditions are calculated by the finite element method. These solutions are combined with semidiscrete modes of an appropriate eigenvalue problem. The boundary conditions corresponding to rigid and rough footings on a layered stratum are treated in detail. Applications are considered which demonstrate the validity of the technique.
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    International Journal for Numerical Methods in Engineering 19 (1983), S. 1033-1045 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The nonlinear diffusion equation as applied to two-dimensional time-dependent magnetic fields is solved with a finite element algorithm. This algorithm permits the analysis of problems possessing complex geometries, induced eddy currents, permanent magnets, and nonperiodic excitation currents. The numerical procedure utilizes implicit time stepping with an iterative scheme to solve the resulting set of equations. Two examples of applications of this program are presented.
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    International Journal for Numerical Methods in Engineering 19 (1983), S. 995-1004 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper describes a new contouring algorithm for isoparametric elements which can be used to map three-dimensional scalar fields. The contours are generated on arbitrary planes intersecting finite element structures. Tracing element contour lines is accomplished by an accurate predictor-corrector technique. A method of finding starting points for the algorithm on the boundary of the elements is also given.
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    International Journal for Numerical Methods in Engineering 19 (1983), S. 971-984 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Finite element models for linear elastic plane stress problems which provide, alternatively, a completely compatible displacement field or a precisely equilibrated stress field are developed. The basis for both models is a biquintic interpolation polynomial representing Airy's stress function over a triangular region. The polynomial coefficients are modified and grouped to establish compatibility while retaining equilibrium within each element. Nodal kinematic parameters are selected and matched to the stress function for the compatible (modified stiffness) model, while nodal stress function parameters are chosen for the equilibrium (modified flexibility) model. Constraints on the global freedoms, enforced by Lagrange multipliers, are introduced to augment nodal connectivity in establishing interelement compatibility in the ‘stiffness’ model and uniform stress transmission in the ‘flexibility’ model. Appropriate boundary conditions are formed for each model. Numerical solutions are obtained and assessed.
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    International Journal for Numerical Methods in Engineering 19 (1983), S. 1063-1072 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Earlier formulations of the finite element approach to cylindrical (rz) field problems led initially to variational expressions containing a simple term in 1/r and consequent attempts to remove it by appropriate choice of interpolation functions. The present paper uses new interpolation functions which ensure that the field behaviour near the axis is correctly modelled. High-order finite elements up to order four are derived and tested on a special cylindrical geometry to confirm, in a practical case, the theoretical claims of improved rates of convergence in solving problems of engineering significance.
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    International Journal for Numerical Methods in Engineering 19 (1983), S. 1047-1052 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An improved bisection strategy is presented to determine the eigenvalues of a real symmetric tridiagonal matrix which occurs in a simple column buckling problem. The new strategy, which involves only a minor modification, utilizes incomplete Sturm sequences only as long as relevant information on the next and following eigenvalues is obtained resulting in a minimization of the computational work. The strategy is particularly effective if only a few eigenvalues are required. The technique can be used for a wider class of eigenvalue problems than the illustrative one presented here.
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    International Journal for Numerical Methods in Engineering 19 (1983), S. 1073-1077 
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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 19 (1983), S. 1105-1107 
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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 19 (1983), S. 1107-1109 
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    Keywords: Engineering ; Engineering General
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    International Journal for Numerical Methods in Engineering 19 (1983), S. 1079-1103 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A general method is presented for the isothermal mechanical analysis of incompressible material solids in which a small-amplitude time harmonic oscillation is superposed on a static finite deformation field. Material behaviour is assumed to be of the ‘fading memory’ type describable by the finite linear viscoelasticity theory of Coleman and Noll.4 Existing finite element codes, that treat finite elasticity material behaviour, can be extended with minor modifications to treat the subject problem. A specialized form of the finite linear viscoelasticity constitutive equations proposed by Morman8 has been implemented in the MARC nonlinear finite element program for predicting the response of statically deformed elastomeric components to small amplitude vibrations. Numerical results obtained with MARC for the static force-deflection behaviour and dynamic (complex) stiffness for a viscoelastic cylinder subject to combined axial and twisting pre-loads, are in excellent agreement with corresponding analytical results.
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    International Journal for Numerical Methods in Engineering 19 (1983) 
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    International Journal for Numerical Methods in Engineering 19 (1983), S. 1139-1152 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An automatic algorithm is presented for reducing the bandwidth of symmetric interconnectivity matrices. The technique takes an arbitrary input scheme and reorders the nodes so as to reduce the bandwidth. A large number of examples is presented to illustrate the reliability and cost-effectiveness of the method.
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    International Journal for Numerical Methods in Engineering 19 (1983), S. 1131-1138 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: A new method for solving structural dynamics problems has been proposed by the author in a separate paper.1 This method of solution produces a high order real symmetric eigenvalue problem of the form (A - λ B - λ2C - λ3D…)U = 0. An algorithm for solving such an eigenvalue problem using simultaneous iteration is presented in this paper. Methods of accelerating the convergence and reducing the amount of computation are also described. A numerical example is given in which the algorithm is used to calculate the eigenvalues and eigenvectors of a framed structure.
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    International Journal for Numerical Methods in Engineering 19 (1983), S. 1193-1207 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A boundary element method for the solution of problems of elastic and elasto-plastic torsion of solids of revolution is proposed. The displacement and stress field produced by a circumferential ring load in an infinite elastic body are derived and used as the fundamental solution to establish the governing integral equations. For the elasto-plastic case, linear boundary elements and bilinear quadrilateral internal cells are used for discretization of these equations. In order to carry out Gaussian integrations along boundary elements and over internal cells, a method ensuring sufficient accuracy for the calculation of singular integrals is proposed. Numerical results for several problems are given.
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    International Journal for Numerical Methods in Engineering 19 (1983), S. 1183-1192 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The results of the finite element analysis of 3-ply laminated conical shells with light core for linear panel flutter are presented and certain advantages of such shells discussed.
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    International Journal for Numerical Methods in Engineering 19 (1983), S. 1111-1129 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The dynamic analysis of structures by the standard finite element method introduces additional inaccuracies into the solution which are not present when the method is used for static analyses. These inaccuracies can arise from two sources: (i) the element formulation and (ii) the reduction of the size of the matrices by a static condensation (i.e. using the Guyan method1,2). The errors in both cases are caused by neglecting frequency-dependent terms in the functions relating the displacements at any point in the structure to the displacements at certain fixed points (i.e. nodes in the element formulation and ‘masters’ in the condensation). A new method of solution is proposed in this paper in which the frequency-dependent terms are retained implicitly by using dynamic stiffness matrices defined at a number of fixed frequencies. The dynamic stiffness matrices may be condensed efficiently to a relatively small number of master degrees-of-freedom using a front solution algorithm. The final stage in the solution uses these matrices to synthesize a high-order eigenvalue problem. A method of solving such an eigenvalue problem, of arbitrary order, is described in a separate paper.3 Numerical examples are given to show the accuracy and efficiency of the proposed method compared with conventional methods of solution.
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    International Journal for Numerical Methods in Engineering 19 (1983), S. 1153-1181 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper describes an element reordering algorithm which is suitable for use with a frontal solution package. The procedure is shown to generate efficient element numberings for a wide variety of test examples. In an effort to obtain an optimum elimination order, the algorithm first renumbers the nodes, and then uses this result to resequence the elements. This intermediate step is necessary because of the nature of the frontal solution procedure, which assembles variables on an element-by-element basis but eliminates them node by node. To renumber the nodes, a modified version of the King1 algorithm is used. In order to minimize the number of nodal numbering schemes that need to be considered, the starting nodes are selected automatically by using some concepts from graph theory. Once the optimum numbering sequence has been ascertained, the elements are then reordered in an ascending sequence of their lowest-numbered nodes. This ensures that the new elimination order is preserved as closely as possible.For meshes that are composed of a single type of high-order element, it is only necessary to consider the vertex nodes in the renumbering process. This follows from the fact that mesh numberings which are optimal for low-order elements are also optimal for high-order elements. Significant economies in the reordering strategy may thus be achieved. A computer implementation of the algorithm, written in FORTRAN IV, is given.
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    International Journal for Numerical Methods in Engineering 19 (1983), S. 1209-1226 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A general approach for using infinite elements within the context of the finite element method is presented. Based upon Gauss-Laguerre quadrature, a scheme for numerically computing the infinite element characteristic matrices is proposed. The general formulation of the element shape functions is outlined, including that for infinite elements that model the far field of hyperbolic systems. The technique is illustrated with a classical example in elasticity: a vertically loaded circular rigid plate.
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    International Journal for Numerical Methods in Engineering 19 (1983), S. 1235-1241 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A general expression for finite difference approximations for all derivatives up to the (N - 1)th order on a finite difference mesh with N-nodes is established. The mesh may be non-uniform and the derivative evaluated at any of the N-nodes. An estimate for the truncation error is obtained and shown to depend on the nonlinearity of the mesh as well as on the mesh diameter. Specific formulae for first- and second-order derivatives are given as examples.
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    International Journal for Numerical Methods in Engineering 19 (1983), S. 1227-1233 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Any segment between two points on a Bézier curve is itself a Bézier curve whose Bézier polygon is expressed explicitly in terms of the sides of the Bézier polygon associated with the original curve.
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    International Journal for Numerical Methods in Engineering 19 (1983), S. 1243-1251 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: This paper shows that the ‘streamline upwinding’ proposed by Hughes and Brooks1 is particularly simple to implement with the coupled nonlinear equations of the problem of salt water intrusion in a coastal aquifer. Because the mechanical dispersion effect is far larger than the molecular diffusion, the notorious spurious oscillations can be controlled by limiting the ratio of grid size to the streamline mixing length. The method is demonstrated on an example of a typical aquifer by giving the diagnostic variation of concentration and various salt profiles for different values of the key parameter.
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    International Journal for Numerical Methods in Engineering 19 (1983), S. 1266-1268 
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    Keywords: Engineering ; Engineering General
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    International Journal for Numerical Methods in Engineering 19 (1983), S. 1253-1264 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An analysis is presented for the stability of an initial and boundary value difference scheme arising from the solution of a two-dimensional hyperbolic equation by the Lax-Wendroff method. The positive and negative characteristic speeds of the linear equation are not necessarily equal in magnitude. Supplementary boundary conditions required for the finite difference solution are obtained using extrapolation for a linear combination of the dependent variables. The analysis produces stability intervals for the parameter which describes this linear combination of variables. Numerical experiments are described which support the theoretical analysis.
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    International Journal for Numerical Methods in Engineering 19 (1983), S. 1265-1265 
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    International Journal for Numerical Methods in Engineering 19 (1983), S. 1319-1330 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The authors' aim was the development of a suitable procedure for the structural design of railway vehicles within an existing general purpose finite element package. A previous application to railway vehicles was based on the use of a sequence of linear programming steps incorporating move limits on the design variables. This approach was slow and in other fields mathematical programming techniques tended to give way to methods based on optimality criteria.Nevertheless because of its simplicity of concept, and because some apparently successful alternatives to the move limit idea were available, the use of linear programming was returned to and the method is now incorporated in the British Rail finite element program NEWPAC. Couched in terms of inverse variables and using linearized forms of the stress constraints, the linear programming approach converges with the optimality criteria method. Details of the implementation and of some standard examples are given.
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    International Journal for Numerical Methods in Engineering 19 (1983), S. 1291-1317 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: A family of high-order, conforming triangles for the finite element analysis of plate bending problems is developed, using the displacement method of formulation.The development proceeds in two steps. A family of non-conforming triangles, based on polynomial expansions of order 〉4 is first generated, and its performance found to be unacceptable. Nodal variables for the non-conforming family are selected from the set w, wx, wy, wn. The elements are then made to conform, by adding a twist nodal variable wnt at the mid-side nodes. Rational functions define the three additional degrees-of-freedom. Simple and very accurate procedures solve the problems associated with the use of such functions.Numerical results are presented for the conforming triangles of order 4 and 7, following a brief description of the two elements. A listing of the explicit shape functions for the quartic triangle is included.The numerical results are very good. In particular, they are superior per degree-of-freedom to the results predicted by the various non-conforming and conforming, cubic and related elements at present used in computer packages. Together with a similar performance by the quintic member10 of the family, they validate the proposed theoretical solution.
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    Notes: This paper describes a method for introducing line searches into the arc-length solution procedure. Such line searches may be used at each iteration to calculate an optimum scalar step-length which scales the normal iterative vector. In practice, a loose tolerance is provided so that on many iterations the line searches are avoided. However on ‘difficult iterations’, the line searches are shown to lead to a substantial improvement in the convergence characteristics. A simple single-parameter acceleration is also developed using line search concepts. The new arc-length method is applied to both the geometrically nonlinear analysis of shallow shells and the materially nonlinear analysis of reinforced concrete beams and slabs. Significant improvements are demonstrated in relation to the standard arc-length method.
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