Library

Notes: In continuation of our earlier work on the electrochemical behaviour of amino acids and their metal complexes [1-3], the present investigation reports the polarographic behaviour of Cd(II) and Pb(II) in presence of DL-norleucine, formation and composition of their complexes, determination of stability constants by DEFORD and HUME'S method [4] and MIHALLOV'S mathematical approach [5] at 20° and 30°C and also thermodynamic parameters accompanying complexation reactions at 20°C.

Notes: Reactions of Cyclanyl Radicals in the Gas Phase. II. Cyclohexyl Radicals from Mixtures of Azomethane and CyclohexaneCyclohexane-azomethane mixtures in argon as diluent were converted by temperatures between 400 and 480°C in a stirred flow system. All products were analytically determined in a comprehensive way. In this way not only isomeric C6H11-radicals, which were already known from former investigations, but also hitherto unknown C6H11-radicals, especially the 3-methylcyclopentyl radical, could be detected as a recombination product with methyl radicals or as the corresponding olefinic compounds. From the results the stationary concentrations of important radical species were estimated and mechanistic consequences discussed.

Notes: 1H-Nuclear Magnetic Resonance Spectra of PhenylfulgidesThe 1H-chemical shifts are determined in a series of phenylfulgides in order to investigate the steric influences of substituents. The magnetic anisotropy of the carbonyl and the phenyl groups is used for a qualitative discussion of the steric effects introducing different substituents in the fulgide framework. The benzene induced solvent shift supports the conclusions about the bond angle alterations between the different compounds.

Notes: Investigations on the Bromination/Dehydrobromination of 17α-Cyanomethyl-17β-hydroxy-estr-5(10)-en-3-oneBromination/dehydrobromination of 17α-Cyanomethyl-17β-hydroxy-estr-5(10)-en-3-one 1a in the presence of pyridine leads to 17α-cyanomethyl-17β-hydroxy-estra-4, 9-dien-3-one 2a. The reaction was studied in various solvents with several bromination agents. Intermediates and byproducts of the reaction were isolated and their structures elucidated.

Notes: Peptides. XXX. Synthesis of Bradykinin Analogs Designed for the Tritium LabellingThe synthesis of three bradykinin analogs is described: [5-(Cl)Phe,8-βPhabu]-bradykinin, [5-(I)Phe, 6-Gly]-bradykinin, and [2-ΔPro, 4γAbu,6-Gly]-bradykininNomenklatur und Abkürzungen nach den Regeln der IUPAC-IUB: Hoppe-Seylers Z. Physio l. Chem. 348, 245 (1967) und Methoden der Organischen Chemie (HOUBEN-WEYL), 4.Auflage, XV/1 und 2, Georg Thieme Verlag Stuttgart 1974.(Cl)Phe = para-Chlorphenylalanin, (J)Phe = para-Jodphenylalanin, ΔPro = L-3,4-Dehydroprolin, βPhabu = L-erythro-α-Amino-β-phenylbuttersäure, BZL(NO2) = p-Nitrobenzyl, TCP = 2,4,5-Trichlorphenyl, PCP = Pentachlorphenyl, AdOC = Adamantyl-(1)-oxycarbonyl.DMF = Dimethylformamid, THF = Tetrahydrofuran, TFE = Trifluoressigsäure, BOC-N3 = tert.-Butyl-oxycarbonylazidThe syntheses has been accomplished in different ways with conventional methods of peptide chemistry. The analogs are designed to obtain tritium labelled compounds.Bradykinin spielt neben anderen Substanzen eine wichtige Rolle bei der Regulation des Blutdrucks. Für die Charakterisierung seines enzymatischen Abbaues und der Bradykininrezeptoren sowohl unter physiologischen als auch unter pathophysiologischen Bedingungen ist der Einsatz radioaktiv markierter Verbindungen notwendig. Diese müssen eine hohe spezifische Radioaktivität und sogleich eine hohe biologische Aktivität besitzen. Außerdem erscheint es wünschenswert, eine Reihe markierter Verbindungen mit abgestufter biologischer Aktivität einsetzen zu können. Die bisher in der Literatur beschriebenen Markierungsversuche sind entweder nur am Bradykinin selbst durchgeführt worden [2,3], wobei durch Chlor-Tritium-Austausch am p-substituierten Phenylalanin Verbindungen mit ausreichender spezifischer Radioaktivität und voller biologischer Aktivität entstanden, oder aber sie gingen von Tyrosin-Analoga des Bradykinins aus, die nach bekannten Methoden mit 125J markiert wurden, was zu hochmarkierten Verbindungen mit veränderter biologischer Aktivität führte [4]. Als mögliche tritiierbare Vorstufen sind bisher Bradykininanaloga mit p-Chlorphenylalanin [5], Dehydroprolin [6] und auch Dehydrophenylalanin [7] hergestellt worden.Auf Grund der angeführten Überlegungen haben wir drei Analoga des Bradykinins synthetisiert, die als Vorstufen für eine nachfolgende Einführung von Tritium geeignet sind: 1[5-(Cl)Phe,8-βPhabu]-Bradykinin, das nach Tritiierung in das marierte [8-βPhabu]-Bradykinin übergeht, ein abbaustabiles Analogon mit hoher biologischer Aktivität [8, 9].2Aus [5-(J)Phe, 6-Gly]-Bradykinin wird markiertes [6-Gly]-Bradykinin erhalten, das ebenfalls eine hohe biologische Aktivität aufweist [8].Es sollte sich außerdem als ein gutes Modell für das Studium der Effektivität des Halogen-Tritium-Austausches im Vergleich zwischen Jod- und Chlorverbindung eignen.3Das dritte Analogon [2-ΔPro, 4-γAbu, 6-Gly]-Bradykinin liefert nach der Tritiierung das markierte [4-γAbu, 6-Gly]-Bradykinin, das trotz Erhalts aller wichtigen funktionellen Seitenketten durch die Veränderung am Peptiddrückgrat biologisch nahezu inaktiv [10] ist und deshalb die Bestimmung der unspezifischen Bindung erlauben sollte.

Notes: Synthesis of 5-Butyl-2-methyl-pyridine by Electrocyclic Ring Closure

Notes: Untersuchungen an heterocyclisch-kationischen Farbstoffen. I. Kationische Farbstoffe mit 2-Amino-6-(hydroxyethoxy)benzothiazol als Diazokomponente

Notes: Acylation of Heterocycles with Carbonic Acid Derivatives. VII. Synthesis of Benzimidazolo [2, 1-b] (1,3,5,)-thiadiazines

Notes: Development of a ESR-Spectra Simulation Program and its Application for the Spectra-Simulation of 33Sulfur-labeled 1,2,3-Dithiazolyls

Notes: A Rapid Leu-Enkephaline Synthesis in Solution

Notes: Photochemistry of Aminoketones. V. Diastereoselective Synthesis of 3-Aryl-azetidin-3-ols via Photocyclization of Aryl-α-amidoalkyl-ketonesN-Acyl-azetidin-3-ols 3 and 4 are formed by diastereoselective cyclization of n,π*-excited N-benzyl-N-phenacyl-amides 1 and 2 in ether solution. Dependent on the nature of the p-and α-substituents of the phenacyl part and especially of the N-acylgroups in the amides 1 and 2 competing reactions occur, particularly the NORRISH II cleavage and an oxydative cleavage of the intermediate hydroxybiradicals A. N-Acylgroups with low energy barrier ΔG≠ of internal rotation favour the diastereoselective photocyclization by intramolecular interaction between the amide oxygen atom and the n,π*-CO-group in 1*, 2* and the OH group in the biradicals A, respectively. An intramolecular hydrogen bonding enables the N-tosyl-azetidinols 3 to rearrange to the N-tosylamino-methyl-benzhydryl-ketones 6 by 1-sensitized photoreaction.

Notes: Mass Spectrometry of Natural Products. XV. Comparative Positive-Negative Ion Mass Spectrometry of AzidogibberellinsThe fragmentation behaviour of 1-azido-3-hydroxy-gibberellin derivatives has been studied by means of positive and negative ion mass spectrometry, high resolution and metastable transitions. The results obtained allow a mass spectrometric distinction to be made between epimers with different stereochemistry of the ring A substituents.

Notes: Insektenwachstumsregulatoren. XIII. Juvenoide mit dem Cyclopentenring. Synthese von Alkyl-ω-(2,2,3-Trimethyl-cyclopent-3-en-1-yl)-2-alkenoaten und ω-(2,2,3-Trimethyl-cyclopent-3-en-1-yl)alkylphenylethernNeue Analoga, der Insektenjuvenilhormone mit dem Cyclopentenring wurden aus dem (2,2,3-Trimethyl-cyclopent-3-en- 1-yl)acetonitril (1) durch eine mehrstufige Synthese erhalten. Die Ether 7 a-c, 8a, b, 15 a-c und 34a, b wurden durch Alkylierung der 4-substituierten Phenolate mit entsprechenden Tosylaten oder Bromiden synthetisiert. Die Ester 11 a-c, 12a, b, 21 a-c, 23 a-c, 28a, b, 29, 27 und 33 a, b mit unterschiedlicher Kettenlänge wurden durch die WADSWORTH-EMMONS-Reaktion der Ketone 11, 12, 19, 26, 27, 32 bzw. des Aldehydes 16 mit entsprechenden Phosphonsäurealkylestern erhalten.

Notes: Insektenwachstumsregulatoren. XIV. Juvenoide mit dem Cyclopentenring. Synthese von 3,7-Dimethyl-10-(2,2,3-trimethyl-cyclopent-3-en-1-yl)-deca-2,8-dien-und -deca-2,4,8-triensäure-isopropylesternNeue Analoga von Insektenjuvenilhormonen wurden aus [(R)-2,2,3-Trimethylcyclopent-3-en-l-yl]acetonitril (1) durch cine Mehrstufensynthese erhalten. Die als Schlüsselverbindung anzusehende Verbindung (1S,3RS)-(E)-3-Methyl-6-(2′, 2′, 3′-trimethyl-cyclopent-3′-en-1′-yl)-hex-4-en-l-ol (6a) entsteht durch Reduktion des entsprechenden Esters 5 mittels LiAlH4, der aus (1′R,2RS)-(E)-1-(2′, 2′, 3′-Trimethyl-cyclopent-3′-en-1′-yl)-pent-3-en-2-ol (4) nach der Orthoacetatmethode nach Claisen erhalten wurde.Die Alkylierung von sub. Phenolen mit dem Tosylat des Alkohols la ergibt die Ether 11 a-h. Durch Wadsworth-Emmons-Reaktion des Ketones 7 bzw. des Aldehydes 9 mit entsprechenden Phosphoryliden entstehen die Carbonsäureester 8 bzw. 10.

Notes: 13C-N.M.R. Spectroscopic Investigation of 2-Bromo-cholest-5-en-3-onesThe 13C-n.m.r. spectra of the 2-epimeric 2-bromocholest-5-en-3-ones have been measured and the substituent effects are determined. The substituent effects of 2-Br and Δ5 double bond follow the rules known from literature.

Notes: The Use of Dimethyl Sulfide as a Reductant of Ozonization Products Synthesis of 1,1-Dimethoxy-alkan-4-ones and 4-Oxo-alkanals by Ozonization of Alk-1-en-5-ones

Notes: Peptides. XXIX. Synthesis of the Protected Insulin Sequence B 1-8

Notes: Protonation and Solvation of Weak Organic Bases. I. Basicity of ω-ChloroacetophenonesThe protonation equilibria of ω-chloroacetophenone and some p-substituted derivates have been studied in the acid system H2O/H2SO4/SO3 by u.v. and 1H-n.m.r. spectroscopy. From the determined H0 values for half-protonation pKBH+ values were calculated by means of the solvation parameters m of YATES and McCLELLAND. The (H0)1/2 and the pKBH+ values were successfully correlated with σp and σp+ substituent constants.

Notes: Ring Opening and Substitution Reactions of 4,4-Dihalo-pyrazolin-5-ones with Nucleophiles1-Aryl-4,4-dihalo-3-methyl-pyrazolin-5-ones (1a-c) undergo ring opening with alkoxides and form alkyl 3-arylazo-2-halo-2-butenoats (2a-d). Analogous reactions take place with ammonia and amines.4-Nitro-phenoxide reacts with substitution of both halogens to the 4,4-bis(4-nitro-phenyl)-compound (5).Phenols are selectively orthobrominated by the title compounds 1a and b.

Notes: Tetrathiafulvalenes. XXI. Syntheses of Tetrathiafulvalenes from 2-Alkylthio-, 2-Arylthio- and 2-Alkylseleno-1,3-dithiolium SaltsIn the reaction of 2-alkylthio-, 2-arylthio- or 2-alkylseleno-1, 3-dithiolium salts with trivalent phosphorus compounds in acetonitril tetrathiafulvalenes 2 are formed. As an intermediate we suppose a phosphorane, which reacts with further 1,3-dithiolium salt to provide the tetrathiafulvalene. By the application of a 2-alkylthio-1,3-dithiolium salt a monomethin dye is formed in a side reaction. When the reaction is carried out in methanol, the phosphorane is trapped by the solvent and a 2H-1,3-dithiolium salt is obtained.

Notes: Synthesis of 6-Acetyl-3-alkyl-2-phenyl-chromen-4-ones by Phasetransfer Catalysed Baker-Venkataraman ReactionThree of the five partial steps of the Baker-Venkataraman xssynthesis of flavones (scheme 1) can be favoured by PTC conditions. In the intermolecular O-acylations of the 4-hydroxyacetophenone 1 (A) and the 5-acetyl-2-hydroxy-acylophenones 3 (C), respectively, the nucleophilicity of the phenolat anions is increased by the PT catalysator. The steric and electronic effects of the substituents in the 5-acetyl-2-benzoyloxy-acylophenones 4 cause the formation of the 6-acetyl-flavones 6 in the phasetransfer catalysed Baker-Venkataraman rearrangement (D) in one step and in good yields. The over-all yields of the 1 → 6 reactions are not higher than 30% because of the limiting step (B). This Fries rearrangement of 4-acyloxy-acetophenones 2 affords only 32-62% of 3 under drastically enhanced conditions.

Notes: 1,4-Benzoquinones and 1,4-naphthoquinones bearing 2′-methyloxiranyl substituents have been synthesized as new bioreductive alkylating agents. The method presented here involved the synthesis of 2-acetyl-1,4-dimethoxybenzenes 6a, b, d and -naphthalenes 6c, e, f, conversion of the acetyl group into 2′-methyloxirane ring using trimethylsulfonium chloride and sodium hydroxide in anhydrous medium, and oxidative demethylation of these intermediates 7a-f to quinones 8a, c, e, f with silver(II) dipicolinate.

Notes: Determination of Configurations by the Aid of Sterically Corresponding Epoxides. XI. Glycidic Nitriles. IV. Synthesis of 1α-Methyl-2α-aryl-cyclohexane-1ß-carboxylic Acids from 4α-Aryl-2-methyl-1α-oxaspiro[2, 5]octane-2-nitrilesThe opening of an epoxide ring of the C-2-isomeric glycidic nitriles 1a-b with anhydrous HCl in dry Et2O yields the corresponding chlorocyanohydrines 2a-b. Treatment of these chlorocyanohydrines with diluted NaOH does not give the expected α-chloroketones 3a-b, but only the original glycidic nitriles. Dehydrocyanation of the chlorocyanohydrines 2a-b is carried out by column chromatography on silica or neutral Al2O3. Favorskii rearrangement of the resulting α-chloroketones 3a-b gives the angular methylated carboxylic acid methyl esters 4a-b, which are converted to the acids 5a-b by saponification with NaOH in quantitative yield.Better reaction conditions for the Favorskii rearrangement of 1-acetyl-1-chloro-cyclohexanes are described.

Notes: Pyrylium Compounds. XXII. 1H-N.M.R. and U.V. Spectroscopic Investigations on the Isomerization of Pseudobases of Unsymmetrically Substituted 2, 4, 6-Triarylpyrylium SaltsThe kinetics and mechanism of the isomerization of the title compounds, the pentene 1,5-diones 2 and 3, were studied by 1H-n.m.r. and u.v. spectroscopy. The equilibrium constants measured vary little near 1, indicating the small influence of substituents on the equilibrium position. The mutual rearrangement 2⇄3 proved to be a base-catalized reaction which is characterized by strictly linear Hammett correlation between 1g k and Σσp. The results obtained suggest resonance-stabilized anions of type4 as intermediates. - Pseudobases of 3-alkyl-2, 4, 6-triarylsubstituted pyrylium salts do not undergo a reversible isomerization.

Notes: Pyrylium Compounds. XXIII. 2-Dialkylamino-2H-pyrans from Tetra- and Pentasubstituted Pyrylium Salts.Tetra- and pentasubstituted pyrylium salts of type 6 react with secondary alkyl amines to give stable crystalline 2-dialkylamino-2h-pyrans 7. In the case of tetrasubstituted pyrylium salts 6, R′ = Me, R″ = H the reaction occurs regioselectively leading to 2H-pyrans with Me at C-3 of the heterocyclic ring. The structure of the reaction products was established by n.m.r., i.r., u.v. and mass spectroscopic methods. Electrophilic agents like protons, carboxylic acid chlorides or methyl iodide regenerate the original pyrylium cations from 7. In refluxing methanol 7a is converted into the 2-methoxy-2H-pyran derivative 8, whereas in aqueous acetone the pseudobase 9 and with ammonia the pyridine 10 are formed. Reaction of 7a with nitromethane or ethyl cyanoacetate provides the benzene derivatives 11 and 12, respectively.

Notes: Synthesis of 4H-Pyrazolo[1,5-a]benzimidazoles

Notes: A New Method of the Introduction of CF3- and C2F5-Groups into Pyrimidine Derivatives and their Antiherpes ActivityA new method of the perfluoroalkylation of uracil derivatives is described. The irradiation of aqueous solutions of uracil and uracilnucleosides with bis-(perfluoroalkyl) mercury (CnF2n+1)2Hg n = 1, 2 under the exclusion of oxygen in the presence of catalytic amounts of azo-bis-isobutyronitril at 254 nm for several hours gave new 5-perfluoroalkylated compounds. In this way we obtained 5-trifluoromethyluracil (5a), 5-pentafluoroethyluracil (5b), 5-trifluoromethyl-2′-deoxyuridine (6a), 5-pentafluoroethyl-2′-deoxyuridine (6b) and 1-(ß-D-arabinofuranosyl)-5-trifluoromethyluracil (7a) in different yields. The perfluoroalkylated compounds were tested against HSV-1 and HSV-2 viruses on human lungefibroblasts. The compounds are markedly less potent than other known nonfluorinated compounds.

Notes: The tautomerism of the nucleic acid bases cytosine and adenine and some of their derivatives is investigated by means of semiempirical MO methods. The influence of the solvent is estimated using various versions of the reaction field model. In the cases under investigation here, the medium influence does not favour “rare” tautomeric forms having other coding properties in DNA replication process than the “normal” nucleic acid base tautomers. Thus, the probability of their participation in spontaneous mutations seems to be very low.

Notes: Synthesis and Characterization of Polychlorinated IsobutenesThe preparation of polychlorinated methallylic chlorides by continuous chlorination of isobutene with different ratios of chlorine and following HCl-elimination is described. The structure is proved by reaction of the polychlorinated isobutenes with sodium thiolacetate and potassium thiocyanate and by spectroscopic methods.

Notes: [N + 1]π-polymethine radicals with nitrogen containing terminal groups (violenes) display electron transfer reactions. Modification of the simple chain structures results in distinct changes of the molecular electronegativity and, consequently, of the redox properties. Based on the formerly defined non-bonding singly occupied MO (SOMO) of ideal polymethines, the various polymethine derivatives are classed into electrono-dative and electrono-captive polymethine radicals. Electrono-dative radicals are prone to release electrons, whereas electrono-captive radicals are prone to accept electrons. This classification reflects experimental results presented by HÜNIG and coworkers, which have been formerly discussed in terms of aromaticity rather than of MO theory. A third class of radicals embraces compounds in which the redox properties of the simple chain polymethine radicals are less changed upon structural modification. These radicals have been termed as electrono-ambident radicals because they are both inclined to release and to accept an electron. HÜNIG and coworkers obviously found the first representatives of this series of radicals. Electronoambident radicals also encounter in VIEHE-type radicals suggesting a more general definition of the latter ones.

Notes: A Novel Synthesis of Organic Tellurium Compounds by the Use of Electrochemically Generated Polytelluride-ionsThe cathodic polarisation of a tellurium electrode in aprotic solutions gives rise to polytelluride anions, which react with alkylhalides to the corresponding disubstituted ditellurides. By this method of electrosynthesis a number of organic ditellurides can be simply prepared and without danger. Dialkylditellurides of the general formula R-Te-Te-R (2a-r) can be produced with high yields. The reaction with α,ω-dihalides gives heterocycles, which involve one or two tellurium atoms in the ring (5a-d, 6-8). The electrochemical reduction of tellurium in the presence of methyliodid yields trimethyltelluroniumiodid (9).

Notes: Quantum Chemical Studies on Colour and Stereodynamics of Acyclic Azines. XIV. On the Chromophoric System of the Isomeric Anthraldazines in the Lowest Sp (ππ*) StatesThe chromophoric system of the isomeric anthraldazines have been studied quantumchemically by means of the PPP-CA and LHM-CI methods. On the basis of a definite substructure being in analogy to the molecular geometries the electronic Sp(ππ*) states of the isomers can be characterized through the corresponding configurations. Taking into account these results an interpretation of the electronic absorption spectra is presented. The conclusions with respect to the chromophoric system are generalized for this class of compounds.

Notes: Influence of the Z/E configuration on the 15N-13C Coupling constants 2,3J(15N-13C) of Aromatic Azo and Diazo Compounds

Notes: Synthesis of 2-Aminoalkan-(1)-oles and 2-Dimethylaminoalkan-(1)-oles

Notes: Prostaglandins and Prostaglandin Intermediates. Synthetic Approach to 8-Methyl Prostanoic Acid DerivativesStarting from the chiral key-product 1 the 8-methyl prostanoic acid derivative 13 was prepared within 10 steps. Construction of the α-side chain involves DIBAH-reduction of the lacton moiety of 1 followed by Wittig-olefination with a C5-ylide. C1-Homologation of the oxo group of 1 via cyanhydrin synthesis and Wittig-olefination with a C7-ylide are important steps to form the ß-side chain of compound 13.

Notes: Direct and Sensitized Photoisomerization of α,δ-PhenylfulgidesThe photoreactions starting from the E- and E-E-isomers of mono-, di-, tri- and tetra-(substituted-)phenylfulgides are investigated. The phenylfulgides show strong steric interactions in the molecular framework. For that reason internal conversion is the main deactivation process which increases in the series of mono-, tri- and tetraphenylfulgides. The α,δ-di-(substituted-)-phenylfulgides show the highest photoreactivity. At room temperature in no case luminescence is observed from any E(E-E)-, Z(E-Z, Z-E)- or Z-Z-phenylfulgid isomer of the substances under study. Intersystem crossing cannot compete neither with thermal deactivation nor can it be observed by applying both the internal and external heavy atom effect. The phenylfulgides show typical ππ*-photoreactivity: in the singlet state E-Z-isomerization about one double bond competes with electrocyclic ring closure; in the triplet state only simultaneous E-Z-isomerization about the two double bonds is observed. The steric and electronic substituent influences on the photoreactivity are interpreted. A first qualitative model of the isomerization reactions of the fulgides in the excited states is established.

Notes: The present paper attempts to evaluate the fracture mechanics parameters, the stress intensity factor (K) and Rice's energy integral (J) in plane strain conditions for three-point bend specimens. Both the parameters have been evaluated by the FEM using higher order isoparametric elements (i.e. quadratic elements). The crack tip elastic singularity (1/√r) has been taken into account by the use of the special crack tip elements of degenerate triangular element type as well as the fine eight-noded isoparametric plane elements. The stress distribution has been compared with the Westergaard solution in the vicinity of the crack. The K and J values have also been-compared with the theoretical results.

Notes: A generalized boundary integral equation method for the solution of the Laplace equation is developed based on the Cauchy integral theorem for analytical complex variable functions. Although the approach is complicated by the utilization of complex variable theory, the resulting model involves direct integration along straight-line boundary segments (elements) rather than using quadrature formulae that are required in current real variable boundary element formulations. Previously published boundary integral equation methods based on the Cauchy integral theorem are shown to be a subset of the generalized model theory developed in this paper.

Notes: An optimum design sensitivity analysis capability is reported which exploits the approximation concepts-dual method formulation of the minimum weight structural sizing problem. An efficient iterative solution technique is used to facilitate determination of sensitivity derivatives for both primal and dual variables. Estimates on the useful range of parameter perturbations, over which the optimum design sensitivity projections can be expected to yield satisfactory revised optimum designs, are also obtained. Numerical results for several example problems will be presented to illustrate the effectiveness of the capability reported.

Notes: An optimal control finite element approximation of the penalization type for the solution of incompressible viscous Navier-Stokes equations is presented. This paper has proved the convergence of its minimizing sequence and the existence of the solution for the optimal control problem corresponding to the penalty variational problem of the Navier-Stokes equations. Based on this method and the conjugate gradient algorithm, the program for solving the three-dimensional Navier-Stokes problem has been developed, and some numerical results have also been provided.

Notes: We present numerical solutions for the following Stefan problems. The half-space z 〉 0 is initially filled with liquid at its fusion temperature. The boundary z = 0, taken to be the x axis, is maintained at a constant temperature, less than the fusion temperature, for x 〈 0. For x 〉 0, the first problem considers the case of an insulated boundary, and the second problem considers the case of the boundary maintained at the fusion temperature. This gives rise to a solid-liquid interface curved in the (x, z) plane.

Notes: For the semi-infinite crack propagating quasi-statically in a porous-elastic medium, the boundary integral equation method (BIEM), based on a reciprocal principle, is formulated for the governing equations of the Biot model of linear porous-elasticity. The resulting numerical scheme is efficient since the discretization of the solution unknowns is required only along the axis of symmetry of a fracture. Fracture propagation criteria based on both elastic and plastic constitutive relations are investigated. Practical applications of the model are expected in the failure of overconsolidated clay, earthquake prediction and underground hydraulic fracturing for energy exploration.

Notes: Recently developed computer aided design systems for the design and modification of complex physical solids using interactive computer graphics offer the exciting possibility of an integrated design/analysis system. Called geometric modellers, these systems build complex solids from primitive solids (cubes, cylinders, spheres, etc.) and macro solids (combinations of primitives). To provide an effective finite element analysis capability for these systems, methods must be devised to ease the burden of discretizing the solid geometry into a user controlled finite element mesh. In this paper we describe a new class of transitional blended finite elements which make substantially simpler the task of finite element mesh generation and local mesh refinement. Computational experience indicates that numerical accuracy is not compromised by use of these flexible elements.

Notes: A non-iterative method is presented for solving a system of algebraic equations forming a banded matrix with each diagonal submatrix being tridiagonal and all other submatrices being diagonal. A recursion relation is assumed between successive elements of the solution vector. This relation is determined by equating a linearly combined form of it with the original set of equations also being linearly combined. The solution vector is determined by back-substitution of elements in the recursion relation. Since the method takes advantage of the banded structure of the matrix, it is more efficient than the conventional methods. A FORTRAN program that incorporates the present method is included.

Notes: A finite element model that is suitable for the analysis of shells of revolution with arbitrary local deviations is presented. The model employs three types of shell elements: rotational, general and transitional. The rotational shell elements, which are most efficient, are used in the region where the shell is axisymmetric. The general shell elements, which can simulate almost any shell geometry, are used in the local region of the deviation. The transitional shell elements connect these two distinctively different types of elements and make it possible to combine them in a single analysis.The form of the global stiffness matrix is somewhat unique in the new model. Non-zero terms are not confined to a narrow band along the diagonal, but occur throughout the matrix. This is due to the following: (1) two different types of nodes, ring nodes and point nodes, are combined in a single analysis; and (2) a locally non-axisymmetric geometry creates a coupling of the Fourier harmonic coefficients of the rotational elements. Yet, the matrix still contains many scattered zero terms that should be considered for numerical efficiency. In this paper an efficient solution procedure that is effective for this situation is developed. The steps include the use of a substructuring technique and separate partial harmonic analysis. A numerical example is presented and compared with existing solutions to demonstrate the capabilities and the efficiency of the new model.

Notes: Viscoplastic constitutive models typically lead to compliance (strain-stress) relationships, which must be inverted for use in the finite element displacement method. Computational requirements can be increased significantly for models of practical size due to the large number of matrix inversions which are necessary. This paper describes a method of obtaining the required stress-strain relations analytically, thus eliminating the need for numerous matrix inversions in the solution. The technique is applicable to a number of commonly-used viscoplastic models, as demonstrated in the examples.

Notes: Higher order implicit integration techniques for solving dynamic response equations are derived utilizing Padé approximations. In an effort to minimize the disadvantages of using these higher order formulae to obtain solutions to systems with large numbers of degrees-of-freedom, the conjugate gradient method is employed to solve for the displacements. The accuracy and efficiency of the techniques are evaluated by making comparisons between known analytical and calculated results.

Notes: Further insight into the functional consistent displacement correlation method to calculate the stress-intensity factor for elliptical cracks will be presented. The method will be modified to account for the actual crack face shape in pure opening mode.

Notes: Special quadrature rules are described for elastic finite elements that have rq behaviour (0 〈 q 〈 1) directly induced in natural element co-ordinates. In general, the quadrature points and weights can vary with the exponent q. For two-dimensional problems with a square-root singularity (q = 1/2), the use of special quadrature results in significant improvements over regular Gauss quadrature. The development of special quadrature rules for three-dimensional elements is shown to be a difficult task. Several special case rules are developed and tested for a line-type singular element, and a precise rule is given for a point-type singular element in three dimensions.

Notes: A lowest order difference scheme has been developed for a spatially non-uniform grid such that the integrated square error is a minimum. This algorithm accommodates grid asymmetry and maintains reasonable accuracy without recourse to higher order approximations. Numerical experiments and computations of the Fourier response factor confirm the performance of the optimized asymmetric algorithm.

Notes: A transfer-matrix analysis is presented for determining the static behaviour of thick beams of ‘multimodular materials’ (i.e. materials which have different elastic behaviour in tension and compression, with nonlinear stress-strain curves approximated as piecewise linear, with four or more segments). To validate the transfer-matrix method results, a closed-form solution is also presented for cases in which the neutral-surface location is constant along the beam axis. Numerical results for axial displacement, transverse deflection, bending slope, bending moment, transverse shear, axial force and location of neutral surface are presented for multimodular and bimodular models of unidirectional aramid cordrubber. The transfer-matrix method results agree very well with the closed-form solutions.

Notes: An effective surface integral and finite element hybrid (SIFEH) method has been developed to model fracture problems in finite plane domains. This hybridization by (incrementally) linear superposition combines the best features of both component methods. Finite elements are used to model the finite domain (and eventually nonlinearity), while continuous distributions of dislocations (resulting in surface integral equations) are used to model the fracture (i.e. displacement discontinuity). This method has been implemented in a computer program and results of representative problems are presented: these compare very well with known solutions and they demonstrate the computational advantages of SIFEH over other numerical methods (including the individual components).

Notes: A unified simple 6 degrees-of-freedom beam finite element and the associated computational procedures have been developed for the fast and efficient solution of a wide class of static and dynamic response problems of the beam type with material and/or geometrical nonlinearities.The material nonlinearity is treated by including its effect in the governing equations by forming the stiffness matrix of each element using a two-dimensional grid of Gauss points and using the material properties at each point corresponding to the uniaxial strain at that point. Examples are provided for metal and reinforced concrete beams.A powerful yet straightforward method for the solution of elastica problems of beams and frames, using the beam element developed by the senior author, has been extended for determining the dynamic response of beams undergoing large displacements, including large rotations.The solution procedure involves piecewise linearization of response equations and iterations at each incremental step to achieve equilibrium. The solution procedure is simple and easy to apply. A variety of problems is solved to determine the applicability of the proposed simple formulations. Excellent agreement with existing analytical solutions which employ higher order elements demonstrates the efficiency and versatility of the present simple beam element in nonlinear analysis.

Notes: A concise survey of formulation methods of geometric and material nonlinearity problems is given. Differences between existing formulations in the literature are discussed. A consistent Lagrangian and updated Lagrangian formulations are derived from the energy balance equation transformed to the proper reference configuration. Differences between the existing formulations and similar ones in the literature are found to be in specific geometric nonlinear terms in the final incremental equation as well as in the definition of the load increment vector. Specific forms of constitutive equations for elastic and elastoplastic materials are presented. Some of the forms used by other authors in application to elastoplastic materials are shown to be inconsistent. Sample numerical examples intended for checking some particular points in the formulation are presented.

Notes: Two numerical methods for solving two-point boundary-value problems associated with systems of first-order nonlinear ordinary differential equations are described. The first method, which is based on Lobatto quadrature, requires four internal function evaluations for each subinterval. It does not need derivatives and is of order h7, where h is the space chop. The second method, which is similar to the first but is based on Lobatto-Hermite quadrature, makes the additional use of derivatives to achieve O(h9) accuracy. Results of computational experiments comparing these methods with other known methods are given.

Notes: An almost linear optimization problem of importance in vibration isolation has been identified and algorithms were developed to minimize the forced vibrational response of structural systems. The constraints can be either displacements or accelerations. These algorithms have been studied for transient response, frequency response and stationary random using the direct dynamic solution. Multiple response points and loading conditions may be used.

Notes: When applied to large sparse sets of simultaneous equations, classical iterative methods may yield very poor convergence rates. This paper gives an incomplete Choleski-conjugate gradient algorithm (ICCG) which has reliably good convergence rates at the expense of computing and using at each iteration an incomplete Choleski factor of the coefficient matrix. The method is applicable to any problems in which the coefficient matrix is symmetric positive definite and is likely to be advantageous with respect to elimination when it is not possible to represent the equations in a dense band form.

Notes: A method is presented for performing efficient and stable finite element calculations of heat conduction with quadrilaterals using one-point quadrature. The stability in space is obtained by using a stabilization matrix which is orthogonal to all linear fields and its magnitude is determined by a stabilization parameter. It is shown that the accuracy is almost independent of the value of the stabilization parameter over a wide range of values; in fact, the values 3, 2 and 1 for the normalized stabilization parameter lead to the 5-point finite difference, 9-point finite difference and fully integrated finite element operators, respectively, for rectangular meshes; numerical experiments reported here show that the three have identical rates of convergence in the L2 norm. Eigenvalues of the element matrices, which are needed for stability limits, are also given. Numerical applications are used to show that the method yields accurate solutions with large increases in efficiency, particularly in nonlinear problems.

Notes: A set of path independent integrals is constructed for the calculation of the generalized stress intensity factors occurring in elastic plates having sharp re-entrant corners or notches with stress-free faces and subjected to Mode I, II or III type loading. The Mode I integral is then demonstrated to enjoy a reasonable degree of numerical path independence in a finite element analysis of a test problem having an exact solution. Finally, this integral is used on the same problem in conjunction with a regularizing, finite element, procedure or superposition method. The results indicate that sufficiently accurate estimates of these stress intensity factors for engineering purposes can be achieved with little computational effort.

Notes: Hybrid analysis techniques based on the combined use of finite elements and the classical Bubnov-Galerkin approximation are presented for predicting nonlinear steady-state temperature distributions in structures and solids. In these hybrid techniques the modelling versatility of the finite element method is preserved and a substantial reduction in the number of degrees-of-freedom is achieved by expressing the vector of nodal temperatures as a linear combination of a small number of global-temperature modes, or basis vectors. The Bubnov-Galerkin technique is then used to compute the coefficients of the linear combination (i.e. the amplitudes of the global-temperature modes).The basis vectors chosen are the path derivatives commonly used in perturbation techniques, namely, the derivatives of the nodal-temperature vector with respect to a preselected control (or path) parameter(s). The vectors are generated by using the finite element model of the initial discretization. Also, the performance of alternate sets of basis vectors is investigated. In the alternate sets, only a few path derivatives are generated, and they are augmented by a constant vector representing a uniform temperature rise (or drop), and by reciprocal vectors with nonzero components equal to the reciprocals of the nonzero components of the path derivatives. A problem-adaptive computational algorithm is presented for efficient evaluation of global approximation vectors and generation of the reduced system of equations and for monitoring the accuracy of the reduced system of equations.The potential of the proposed reduction methods for the solution of large-scale, nonlinear steady-state thermal problems is also discussed. The effectiveness of these methods is demonstrated by means of four numerical examples, including conduction, convection and radiation modes of heat transfer.This study shows that the use of the uniform-temperature mode and the path derivatives as global approximation vectors significantly increases the accuracy of the solutions obtained by reduction methods, thereby enhancing the effectiveness of these methods for the solution of large-scale, nonlinear thermal problems.

Notes: Formulae are derived for exact inextensional bending solutions for arbitrary quadrilateral shell finite elements of bilinear parametric representation. It is found that the polynomial degree of parametric representation of the rectangular components of displacement requires to be at least cubic in order to describe any inextensional bending modes.

Notes: A simply-supported rhombic plate with obtuse angle equal to 150 degrees is analysed by the finite element method, using both the h-version and the newer p-version. Results obtained using the computer code CONE (C1-continuity) for plate bending problems are compared with theoretical predictions and with computational results reported in the literature. If accuracy in terms of the number of degrees-of-freedom is used as a criterion, the solutions presented here are the most efficient that have been published to date.

Notes: Stiffness matrices for three-dimensional beam elements that include the effect of warping restraint on elastic torsional response have been derived by various investigators. Using one of the available stiffness matrices and assuming that the warping boundary conditions can be specified on a member-by-member basis, an elastic ‘warping’ support is introduced to represent conditions of partial warping restraint at the member ends. The concept of a ‘warping indicator’ is then introduced to facilitate use of warping springs. Following this, static condensation is used to eliminate the restrained warping degrees-of-freedom. The condensed stiffness matrices for the elements can then be assembled to yield a global stiffness matrix. In the global matrix, continuous warping degrees-of-freedom, that is, those internal to a member represented by several elements, are expressed in local co-ordinates. The remainder are expressed in global co-ordinates. In the force recovery phase, it is shown that an ‘indirect’ method yields most accurate results for the bimoment and warping torsion when the twist function is represented by a cubic polynomial. Solutions to examples of linear elastic analysis are compared with well-known analytical solutions to demonstrate the application of the method.

Notes: The paper describes the development of an eight-node plane rectangular finite dynamic element and presents detailed descriptions of the associated numerical formulation involving the higher order dynamic correction terms pertaining to the related stiffness and inertia matrices. Numerical test results of free vibration analyses are presented in detail for the newly developed eight-node element and also the corresponding four-node element in order to make a clear comparison of the relative efficiencies of the corresponding finite element and dynamic element procedures. Such results indicate a superior pattern of solution convergence of the presently developed dynamic element.

Notes: A computational strategy for the evaluation of delamination stresses in multilayered fibre-reinforced composites is presented. The approach uses special inter-laminar shear elements and an iterative procedure in the calculation of out-of-plane stresses. Both regular and singular elements for the free edge are presented. The solutions are carried on by switching between direct matrix solution methods of small systems of equations and an iterative conjugate gradient method. The proposed discretization avoids ill-conditioning problems, modelling difficulties and large computational cost associated with three-dimensional analysis of delamination of holes, cut-outs, joints and areas of complex stress states.

Notes: In this work, the plastic stress-strain relation and the incremental elastoplastic stiffness matrix for materials obeying the principal stress yield criterion are derived in the context of the associated theory of plasticity. Particular attention is paid to the treatment of the singularity conditions associated with this yield criterion.

Notes: It is demonstrated that the residual in a compatible (displacement) finite element solution can be partitioned into local self-equilibrating systems on each element. An a posteriori error analysis is then based on a complementary approach and examples indicate that the guaranteed upper bound on the energy of the error is preserved.

Notes: The paper develops a new discrete transform pair which economizes on the number of samples of F(s) and f(t) compared with the standard pair. Whereas the standard pair used uniform sampling along the Bromwich contour, the new method allows a progressive increase in the sampling interval, thereby reducing the number of samples required to meet a specified bandwidth requirement. In the case of the computation of transient responses of physical systems, a reduction by a factor of 10 is not unrealistic. The new transform pair is based on the generalization of fundamental sampling principles. In particular, this leads to an integration contour different from the Bromwich contour.

Notes: The paper presents results obtained by the implementation of a new method of Laplace transformation and inversion developed by the authors. Test functions are used to show that basic accuracy is comparable to that obtainable by uniform sampling along the Bromwich contour. The advantage of the new method is seen to be that it generally requires far fewer samples of F(s). It is clarified that the new method does have certain limitations so far as general application is concerned. However, given results indicate that very satisfactory performance may be expected whenever the method is specifically applied to the calculation of transient responses of damped physical systems.

Notes: Simple solutions are extracted from the exact compatibility equations of inextensional bending for a special class of shell shapes, and it is speculated that these solutions provide useful criteria towards evaluating finite elements for these and closely related shapes. Curved finite elements of a quadratic parametric representation, which do not belong to the special class, are then studied. By using a series of exact inextensional bending displacements, it is concluded from numerical evidence that the criteria apply to finite element shapes in this representation when they are shallow, as is usually the case in practice. Criteria for homogeneous membrane actions follow from Gol'denveizer's static-geometric analogue.