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  • Articles: DFG German National Licenses  (853)
  • 1990-1994  (853)
  • 1992  (853)
  • Engineering General  (725)
  • crystal structure  (128)
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  • Articles: DFG German National Licenses  (853)
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  • 1990-1994  (853)
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  • 1
    ISSN: 1572-8862
    Keywords: Manganese ; agostic ; crystal structure ; CH activation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Abstract Agostic interactions of CH bonds with metal atoms are currently of great interest. UV irradiation of Mn2(CO)8 (PMe2Ph)2 in the presence of the HC≡COEt yielded the new compound Mn2(CO)6(PMe2Ph)2 [μ-C(OEt)=C(H)C=C(H)C=O(OEt)],1 that contains a strong agostic interaction of an olefinic CH bond to one of the managanese atoms, Mn...C=2.349(5), Mn...H=2.01(4). This interaction can be removed (reversibly) by CO addition (25°C/1000 psi) to1 to yield the new complex Mn2(CO)7(PMe2Ph)2[μ-C(OEt)=C(H)C=C(H)C=O(OEt)],2.
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  • 2
    Electronic Resource
    Electronic Resource
    Springer
    Journal of cluster science 3 (1992), S. 123-144 
    ISSN: 1572-8862
    Keywords: Molybdenum ; tungsten ; crystal structure ; reduction ; acetate
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Abstract Four new compounds having nine cluster electrons and cores of the types Mo3OCl3, Mo3OBr3, and W3OCl3 are reported. Compound (1) prepared by reduction of [Bu4N][Mo3OCl6(OAc)3] in THF with metallic zinc, was shown by X-ray crystallography to be Mo3OCl4(OAc)3 (THF)2 (1). It forms crystals in space groupP21 with unit cell dimensionsa=9.472(2) Å,b=13.546(4) Å,c=9.652(2) Å, β=101.70(2)°,V=1201(1) Å3,Z=2. The [Mo3(μ3-O)(μ-Cl)3]4+ core is surrounded by three μ-O2CCH3 anions, one Cl−, and two THF and has Mo-Mo distances of 2.620(1) Å, 2.613(1) Å, and 2.530(1) Å, with the shortest bond between the two Mo atoms to which the THF molecules are coordinated. Compounds [Bu4N]2 [Mo3OBr6(O2CCH3)3] · Me2CO, (2) and [Mo3OBr3(O2CCH3)3(PMe3)3]3 · BF4, (3) are the first two nine-electron Mo3 species with a [Mo3(μ3-O) Br3]4+ core. Both were obtained by zinc reduction of [Mo3OBr6(O2CCH3)3]− in the presence of (NBu4) Br (2) or PMe3 and NaBF4 (3), and each was characterized crystallographically. Compound (2) crystallized in space group Cc with unit cell dimensionsa=25.037(5) Å,b=12.827(2) Å,c=21.484(4) Å, β=122.96(1)0,V=5790(3) Å3,Z=4. While the anion has no crystallographically required symmetry, its virtual symmetry is C3v . The Mo-Mo distances are 2.619(2) Å, 2.610(3) Å, 2.644(2) Å, with a mean value of 2.624[14] Å. Compound (3) crystallized in space groupP21/c with unit cell dimensionsa=10.846(2) Å,b=25.033(5) Å,c=12.641(5) Å, β=94.74(2)0,V=3420(2) Å3,Z=4. The cation occupies a general position but has virtual C3v symmetry, with Mo-Mo distances of 2.601(2) Å, 2.610(2) Å, 2.627(2) Å, with a mean value of 2.613[14] Å. Thus the anionic and cationic Mo3 clusters in (2) and (3), respectively, have average Mo-Mo distances that are equal within experimental error. Compound (4), [NEt4]2 [W3OCl6(O2CCH3)3] is the first 9-electron compound of this type containing tungsten. It was prepared by reduction of [Et4N][W3OCl6(OAc)3] in benzene with Na/Hg. It crystallized in space groupP212121 with unit cell dimensionsa=11.076(2) Å,b=14.345(2) Å,c=21.026(3) Å,V=3574(1) Å3,Z=4. The anion resides on a general position but has virtual C3v symmetry, with W-W distances of 2.577(1) Å, 2.612(1) Å, 2.584(1) Å and a mean value of 2.591[15] Å.
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  • 3
    ISSN: 1572-8862
    Keywords: Heterometallic-heterobridging cubane-type tetranuclear cluster ; preparation ; crystal structure ; molecular orbital calculation ; quasi-aromaticity ; copper ; molybdenum
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Abstract By the reaction of cluster [Mo3OS3](dtp)4(H2O) used as starting material with CuI using [3+1] mode, two novel heterometallic-heterobridging cubane-type tetranuclear cluster compounds [CuMo3OS3]·I·(μ-OAc)[S2P(OC2H5)2]3·L [(I)L=py, (II)L=DMF] [dtp=S2P(OC2H5)2; OAc=OOCCH3] containing [CuMo3OS3] core have been obtained. Compounds (I) and (II) have been characterized by IR, EPR, UV-VIS, electrochemistry and X-ray crystallography. By comparison of these two compounds with the analogous [CuMo3S4] series in the structure and molecular orbital calculation, the influence of mixed S/O bridging on the structure is discussed. It is demonstrated that the {Mo3S3} cluster ring in [Mo3OS3]4+ possesses a similar quasi-aromaticity to [Mo3S4]4+. Crystal data: for (I), space group= $$P\overline 1 $$ ,a=13.781(8)Å,b=14.523(6)Å,c=12.098(6)Å, α=98.37(4)°, β=109.41(5)°, γ=105.00(5)°,V=2133(2)Å3,Z=2,R=0.058; for (II), space group= $$P\overline 1 $$ ,a=13.215(4)Å,b=17.818(8)Å,c=9.873(4)Å, α=106.06(4)°, β=109.78(3)°, γ=82.00(3)°,V=2100(2)Å3,Z=2,R=0.045.
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  • 4
    ISSN: 1572-8951
    Keywords: Non-topochemical reaction ; crystal structure ; lattice energy calculations ; thermal motion analysis ; disorder
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract The molecular and crystal structure of 2,5-dibenzylidenecyclopent-3-ene-1-one has been studied in detail to explain the formation of a non-topochemical pseudo-mirror-symmetric dimer upon photoirradiation. Packing energy calculations, analysis of the thermal motion, and lattice energy calculations are employed to analyse and understand the observed dimerization reaction, crystal structure, and crystal properties.
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  • 5
    Electronic Resource
    Electronic Resource
    Springer
    Russian chemical bulletin 41 (1992), S. 1076-1079 
    ISSN: 1573-9171
    Keywords: X-ray crystallographic analysis ; 1,1′-divinyl-2,2′-biimidazolyl ; crystal structure ; molecular structure
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract The crystal and molecular structures of 1,1′-divinyl-2,2′-biimidazolyl (L) were determined by x-ray crystallographic analysis. It was established that the molecule of L has crystallographic symmetry 2 and a cisoid conformation with an angle of rotation of 128° between the imidazole rings. The length of the C2-C2′ bond is increased to 1.485(11) Å compared with the length of the analogous bond in unsubstituted 2,2′-biimidazolyl (1.423 Å). Localization of the N=C multiple bond is observed [1.297(9) Å]. The other N-C bonds of the ring are almost equalized (1.374 Å) and are close to the standard values for bonds of the C sp 2-N type in imidazoles. The angle between the plane of the heterocycle and the plane passing through the atoms of the vinyl group amounts to 7°.
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  • 6
    ISSN: 1573-9171
    Keywords: synthesis ; crystal structure ; UV spectra ; 2,6-di-tert-butyl-4-[α-(2-hydroxy-1-naphthyl)methyl]phenol ; 2,6-di-tert-butyl-4-[α-morpholino-α-(2-hydroxy-6-bromo-1-naphthyl)methyl]phenol ; 2,6-di-tert-butyl-4-α-(2-hydroxy-1-naphthyl)-1,4-methylenequinone ; 2,6-di-tert-butyl-4-α-(2-acetyloxy-1-naphthyl)-1,4-methylenequinone
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract Mannich bases exhibiting photo- and thermochromic properties in solutions were synthesized from 3,5-di-tert-butyl-4-hydroxybenzaldehyde and 2-naphthols. An investigation of an acetyl derivative of methylenequinone, modeling a product of photo- and thermochromic transformations, proved that the color change of solutions of the Mannich bases is due to reversible dissociation into colored methylenequinones and morpholine. On the basis of data of x-ray diffraction analysis of one of the Mannich bases, characteristics of their molecular structure were determined, and reasons were stated for their effect on the dissociation mechanism.
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  • 7
    Electronic Resource
    Electronic Resource
    Springer
    Russian chemical bulletin 41 (1992), S. 1950-1956 
    ISSN: 1573-9171
    Keywords: hexafluorotitanates ; synthesis ; crystal structure ; 19F NMR ; IR spectroscopy
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract Mixed alkali hexafluorotitanates of the composition LiMTiF6 are synthesized, which crystallize with the orthorhombic symmetry. The lattice parameters of these materials are determined. It is shown that substitution of the Li+ cation in Li2TiF6 by Na+, K+, Rb+, and Cs+ leads to various degrees of distortion of the hexafluoroion. It is determined (19F NMR data) that the change in the dynamic state of the octahedral [TiF6]2− ions is related to their transition from the hindered-rotational to the isotropic state.
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  • 8
    ISSN: 1573-9171
    Keywords: macrocyclic polyethers ; crystal structure ; biological activity ; IR spectra ; complex with calcium thiocyanate
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract The antihypoxic and anticonvulsant activity of eight new amidophosphoryl derivatives of crown ethers was investigated. It was found that some of them exhibit pronounced antihypoxic activity. The results of an x-ray structural and IR spectroscopic study of dibenzo-N-phenylphosphonyl-14-crown-5 (a=9.818,b=16.062,c=15.925 Å; γ=124.90°;V=2072 Å3;M=417.2;d=1.33 g/cm3 forZ=4, 1955 independent reflections [I〉3σ(I)] in a DAR-UM inCuK α radiation,P2 1/b space group,R=5.2%) and dibenzo-N-adamantylphosphonyl-14-crown-5 compounds (a=11.077,b=15.936,c=16.771 Å; γ=56.05°;V=2456 Å3;M=486.3;d=1.31 g/cm3 forZ=4, 2164 independent reflections [I〉3σ(I)] in a DAR-UM inCuK α radiation,P21/b space group,R=5.1%) are reported. Some details of the structure of the dibenzo-N-phenylphosphonyl-14-crown-5-complex with calcium thiocyanate and water are discussed; a polyhedron with a coordination number of six was found for the first time for calcium complexes with macrocyclic ligands. The combined examination of the results of the biological, x-ray structural, and IR spectroscopic study of macrocyclic, 14-member ligands suggested that the nature of the substituents at phosphorus affect the conformational state of the macrocycle, which remains unchanged in complexation in the investigated conditions.
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  • 9
    ISSN: 1573-9171
    Keywords: crystal structure ; molecular complexes ; phosphinimines ; protonation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract X-ray diffraction analysis has been used to determine the crystal structures of the 1:1-composition products of protonation by perchloric acid of isomeric triphenyl-N-(4-methylpyridyl-2)phosphinimine (1) and triphenyl-N-(3-methylpyridyl-2)phosphinimine (2). The structures were refined toR=0.048 andR=0.052, respectively, using 2274 (1) and 2647 (2) reflections. The protonation centers are located at the sites of N atoms of the pyridine ring (1) and the phosphinimino group (2). The distribution of the bond lengths in the cations suggests that a significant contribution is made by a phosphonic structure with positive charges localized on the P atoms. N-H...O hydrogen bonds, with lengths of 2.890(4) and 3.020(3) Å, connect cations and anions in both structures.
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  • 10
    ISSN: 1573-9171
    Keywords: synthesis ; crystal structure ; 1,12-difluoro-1,1,3,5,5,8,8,10,12,12-decanitro-3,10-diazadodecane-6,7-diol dinitrate
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract A two-step synthesis has been proposed to obtain 1,12-difluoro-1,1,3,5,5,8,8,10,12,12-decanitro-3,10-diazadodecane-6,7-diol dinitrate, starting from 1,1,4,4-tetranitrobutane-2,3-diol and N-(methoxymethyl)-2-fluoro-2,2-dinitroethyl-amine, followed by nitration of the Mannich base formed. An x-ray-diffraction investigation of the dinitrate obtained was carried out.
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  • 11
    ISSN: 1573-9171
    Keywords: organic metals ; radical-cation salts ; bis(ethylenedithio)tetrathiafulvalene = ET ; crystal structure
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract The electrochemical oxidation of ET [bis(ethylenedithio)tetrathiafulvalene] in bromobenzene (electrolyte Bu 4 N[HgBr 3 ]) gave the radical-cation salt (ET) 8 [Hg 2 Br 6 ·PhBr] 2 (1), a new organic metal with a temperature range of 300–125 K. At 125 K a metal—dielectric transition is observed. Crystallographic data for (1):a=19.171(6),b=12.668(4),c=17.777(6) Å, α=118.03(3), β=89.45(2), γ=101.21(3)°, P $$\overline 1 $$ ,Z=1,d calc=2.30 g/cm 3 . The crystal structure of (1) is laminar. In the conducting organic layer the ET radical cations are linked into bands by shortened intermolecular S···S contacts of the “side-to-side” type. The anionic layer consists of centrosymmetric complexes [Hg 2 Br 6 ·C 6 H 5 Br] 2 4− . The Hg 1 and Hg 2 atoms are characterized by a trigonal configuration of the Hg-Br bond which is built up, on account of secondary Hg···Br interactions, into trigonal-bipyramidal for Hg 1 and trigonal-pyramidal (tetrahedral) for Hg 2 . Interaction between the anionic and cationic layers is effected through Br 6 ...S 8 contacts [3.491(7) Å)].
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  • 12
    ISSN: 1573-9171
    Keywords: organic metals ; bis(ethylenedithio)tetrathiafulvalene (ET) ; crystal structure
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract The composition and structure of the radical-ion salt (ET) 2 [Hg(SCN) 2 Cl], a new organic metal withT M-D=50 K, were established in an x-ray structure investigation. Principal crystallographic data:a=36.69(1),b=8.302(8),c=11.732(8) Å, β=90.02(6)°, space groupCc, Z=4,d calc=2.08 g/cm 3 ,R=0.067. The crystal structure of the salt consists of an alternation of organic (cationic) and inorganic (anionic) layers along the axisa. The anionic layer consists of the polymeric chains in which the [Hg(SCN) 2 Cl]− ions are linked together along the axisc through secondary Hg···N bonds with lengths of 2.75(3) and 2.98(8) Å. On account of these interactions the trigonal configuration of the bonds of the Hg atom is built up to trigonal-bipyramidal. In the organic layer with a structure of the κ type the ET cations form dimers with an interplanar distance of 3.53 Å. ET cations belonging to neighboring dimers are linked together through shortened intermolecular S...S contacts with lengths of 3.40–3.50(2) Å.
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  • 13
    ISSN: 1573-1111
    Keywords: Calix[4]arene ; crystal structure ; second-sphere coordination ; nickel(II) ; copper(II) ; pyridine
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract The title compounds crystallize such that bilayers of calixarenes are separated by hydrophilic layers. In each case the transition metal has, in addition to a primary sphere of ligands, a second-sphere coordination by a calixarene. [(H2O)5Ni(NC5H5)]2(Na)[calix[4]arene sulfonate]·3.5 H2O,1, crystallizes in the triclinic space groupP $$\bar 1$$ witha = 12.487(4),b = 14.281(2),c = 15.055(5) Å, α = 85.66(2), β = 80.07(2), γ = 80.48(2)°, andD c = 1.64 g cm−3 forZ = 2. Refinement based on 2441 observed reflections led to a finalR value of 0.066. There are two different environments for the nickel-containing cations: one is positioned within the hydrophilic layer with the pyridine ligand intercalated into the hydrophobic calixarene bilayer and the other is also positioned within the hydrophilic layer, but the pyridine ligand is inserted into the hydrophobic cavity of the calix[4]arene. [(H2O)4Cu(NC5HS)2](H3O)3[calix[4]arene sulfonate]·10 H2O,2, crystallizes in the triclinic space groupP $$\bar 1$$ witha = 15.438(4),b = 15.727(6),c = 12.121(9) Å, α = 112.74(4), β = 102.02(4), γ = 85.34(4)°, andD c = 1.57 g cm−3 forZ = 2. Refinement based on 3925 observed reflections led to a finalR value of 0.107. The structure is similar to that of 1 except that the one copper-containing cation spans the hydrophilic layer and is intercalated into the bilayer of calixarenes on one side and positioned into the calixarene cavity on the other.
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  • 14
    Electronic Resource
    Electronic Resource
    Springer
    Journal of inclusion phenomena and macrocyclic chemistry 14 (1992), S. 55-64 
    ISSN: 1573-1111
    Keywords: Host-guest inclusion compound ; p-,m-,o-xylene ; deoxycholic acid ; symmetry factor ; energy transfer ; photophysical factor ; crystal structure
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract The isomerization processes induced by UV photons in inclusion compounds of the host-guest type are examined, with special attention to the photophysics of the energy transfer process between the host and the guest, as well as to the influence of the host molecular cavity symmetry and the guest molecular symmetry. In particular, the experimental study has been carried out on the isomerization processes ofp-,m-, ando-xylene inside the molecular cavities of deoxycholic acid. The results have been compared with those obtained by irradiating the xylenes in an inert solution of hexane. The main difference is the elimination of by-products when the photochemical process is carried out in the solid state inclusion compound; however, the high purity of the isomerization product corresponds to a decrease in its yield with respect to the reaction in solution, due to the energy transfer process from the host to the guest moiety.
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  • 15
    Electronic Resource
    Electronic Resource
    Springer
    Journal of superconductivity 5 (1992), S. 33-38 
    ISSN: 1572-9605
    Keywords: Yttrium ; copper ; X-ray ; crystal structure
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology , Physics
    Notes: Abstract Single crystals of Y2Cu2O5 were obtained in the flux growth process by controlled heating of a mixture of Y2O3, BaO, and CuO in a molar ratio of 1∶8∶20. These crystals were analyzed by a single-crystal X-ray diffraction analysis. The crystal contains polymeric chains of Cu2O5 interspersed by yttrium ions surrounded by octahedral arrangements of oxygen atoms. Crystal data: space group=Pna21,a=10.799(2) Å,b=3.4990(5) Å,c=12.459(2) Å,Z=4, 380 reflections,R=0.026,R w=0.030.
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  • 16
    ISSN: 0887-3585
    Keywords: amino acid-derived cofactor ; crystal structure ; methylamine dehydrogenase ; molecular replacement ; oxidoreductase ; Paracoccus denitrificans ; pyrroloquinoline quinone ; quinoprotein ; tryptophan tryptophylquinone ; Chemistry ; Biochemistry and Biotechnology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Medicine
    Notes: The three-dimensional structure of the quinoprotein methylamine dehydrogenase from Paracoccus denitrificans (PD-MADH) has been determined at 2.8 Å resolution by the molecular replacement method combined with map averaging procedures, using data collected from an area detector. The structure of methylamine dehydrogenase from Thio-bacillus versutus, which contains an “X-ray” sequence, was used as the starting search model. MADH consists of 2 heavy (H) and 2 light (L) subunits related by a molecular 2-fold axis. The H subunit is folded into seven four-stranded β-segments, forming a disk-shaped structure, arranged with pseudo-7-fold symmetry. A 31-residue elongated tail exists at the N-terminus of the H subunit in MADH from T. versutus but is partially digested in this crystal form of MADH from P. denitrificans, leaving the H subunit about 18 residues shorter. Each L subunit contains 127 residues arranged into 10 β-strands connected by turns. The active site of the enzyme is located in the L subunit and is accessible via a hydrophobic channel between the H and L subunits. The redox cofactor of MADH, tryptophan tryptophylquinone is highly unusual. It is formed from two co-valently linked tryptophan side chains at positions 57 and 107 of the L subunit, one of which contains an orthoquinone. © 1992 Wiley-Liss, Inc.
    Additional Material: 6 Ill.
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  • 17
    ISSN: 1573-904X
    Keywords: pharmaceutical salt selection ; salts of p-aminosalicylic acid ; hydrates ; crystal structure ; thermal stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract The potassium (K), sodium (NA), calcium (CA), and magnesium (MG) salts of p-aminosalicylic acid were obtained, and their thermal behavior was characterized by means of differential scanning calorimetry (DSC) and thermogravimetric analysis (TG). Their crystal and molecular structures were determined by single-crystal X-ray diffraction after powder patterns had shown them to be nonisomorphous. Different degrees of hydration were observed for the solid salts, and an assessment of hydrate stability to dehydration was made from thermogravimetric studies. The onset temperature of dehydration (T t) of each salt varied within the series and exhibited correlation with X-ray determined structure. The observed onset of dehydration of MG and CA was higher than that of NA and is consistent with stronger ion-dipole interactions for the divalent salts. Crystallographic determination of the bond lengths between the metal ion and the water oxygens were 2.4 and 2.9 Å for NA, between 2.0 and 2.1 Å for MG, and 2.4 Å for CA. The open nature and presence of a channel feature in the structure of the sodium salt may have facilitated escape of water molecules from the crystal. Particle presentation (e.g., size, crystallinity) was also shown to affect dehydration behavior.
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  • 18
    Electronic Resource
    Electronic Resource
    Springer
    Pharmaceutical research 9 (1992), S. 365-371 
    ISSN: 1573-904X
    Keywords: celiprolol ; crystal structure ; two-dimensional nuclear magnetic resonance (2D NMR)
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract The crystal structure and nuclear magnetic resonance (NMR) spectra and assignments of celiprolol, N′-[3-acetyl-4[3-[N-t-butylamino-2-hydroxypropoxy]phenyl]-N, N-diethylurea, are reported. Celiprolol crystallizes in the monoclinic space group, P2l/a, with a = 9.081(2), b = 13.800(4), and c = 17.471(5) Å and β = 95.04(2)°. Structure was solved by direct methods; structure refinement to R of 0.058. Intermolecular hydrogen-bonding in the crystal is discussed. The 1H, 13C, and two-dimensional (2D) NMR spectra of the hydrochloride have been obtained and definitive signal assignments made.
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  • 19
    ISSN: 1573-1111
    Keywords: Crown compound ; potassium thiocyanate ; crown cation complex ; crystal structure
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract Single crystal X-ray analysis of the hydrated KSCN complex of benzodinaphthopyridino-21-crown-7 (1) (1 : 1 : 1) is reported. Crystals of the complex are orthorhombic,Pnma, withα = 16.946(4),b = 22.298(4),c = 10.390(8) Å andD c = 1.184 g cm−1,Z = 4. The host macroring (1) has a mirror symmetry and exists in a so-called ‘dentists chair’ conformation. The cation (K−) is coordinated to all the six ether oxygen atoms and also weakly to the pyridine N atom. The SCN− anion group has a statistical type of disorder with opposite orientations of S and N such that nitrogen and sulphur are coordinated to K+. Packing of the host molecules is in columns to form quasi channels with K+, SCN−, and H2O being located inside the stacks.
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  • 20
    ISSN: 1573-1111
    Keywords: Inclusion compound ; hydroxy compound ; crystal structure ; thermal analysis
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract The crystal and molecular structures of the title host compound (I), C35H26O, and its inclusion complexes with water (II), C35H26O·H2O and dimethylsulphoxide (III), C35H26O·C2H6OS are reported. (I) is monoclinicC2/c,a = 9.725(1),b = 20.031(3),c = 26.545(3) Å, β = 90.60(1)0,V = 5170 Å3,Z = 8; (II) is triclinic, $$P\bar 1$$ ,a = 10.206(1),b = 10.324(2),c = 14.425(2) Å, α = 101.68(1), β = 89.92(2), γ = 116.34(1)0,V = 1327 Å3,Z = 2; (III) is monoclinicP21/n,a = 17.832(5),b = 10.109(3),c = 17.901(5) Å, β = 111.93(2)0,V = 2993 Å3,Z =4. The structures were solved by direct methods and refined to final residuals of 0.045, 0.048, and 0.071, respectively. Thermal analysis of the complexes corroborates the crystallographic results.
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  • 21
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    Journal of inclusion phenomena and macrocyclic chemistry 12 (1992), S. 377-387 
    ISSN: 1573-1111
    Keywords: Charles Pedersen ; crown ethers ; phenol-pendant cyclam-zinc(II) complex ; crystal structure
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract The molecular structure of phenol-pendant cyclam-zinc(II) complex,4a, has been determined by X-ray structure analysis. Crystals of4a · ClO4 · CH3OH (C16H27N4OZn · ClO4 · CH3OH) are monoclinic, space groupP21/nn, with four molecules in the unit cell of dimensionsa=31.198(2) Å,b=8.426(1) Å,c=8.214(1) Å, andβ=93.96(1)°. The structure was solved by the heavy atom method and refined anisotropically toR=0.044,R w=0.062 for 1551 independent reflections. The complex assumes a five-coordinate, square pyramidal geometry, where zinc(II) is surrounded by the cyclam moiety in a planar fashion with the pendant phenolate anion occupying an axial position. An extremely short Zn-O(phenolate) bond distance of 1.983(5) Å, in conjunction with the 0.288 Å displacement of Zn(II) above the cyclam N4 plane toward the phenolate, accounts for the extremely low pK a value of 5.8 for the pendant phenol. These facts about4a, in comparison with the previous findings for the Ni(II) (4b) and Cu(II) complexes (4c) with the same ligand, illustrate well the characteristics of zinc(II) ion coordination properties.
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  • 22
    ISSN: 1573-1111
    Keywords: Dioxocyclam ; 5,7-dioxo-1,4,8,11-tetra-azacyclotetradecane ; platinum tetrachloride ; crystal structure ; paramagnetic properties of ionic stacked structure
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract The paramagnetic complex salt of diprotonated dioxocyclam (1,11-dihydro-5,7-dioxo-1,4,8,11tetra-azacyclotetradecane), Pt(II) tetrachloride and water has been synthesized in strongly acidic medium and identified by X-ray structure analysis. The crystals of [(C10H22N4O2)2+(PtCl4)2−]·H2O are monoclinic, space groupP21 c,M r=585.23,a=9.516(1) Å,b=11.926(1) Å,c=16.622(2) Å,β=102.88(2)°,V=1839(1)Å3,Z=4,D x=2.114 g cm−3, λ(MoK α)=0.70930 Å,μ=83.1 cm−1,F(000)=1128,T=292 K,R=0.019 for 2808 observed reflections withI 〉 3δ(I). Alternating moieties of diprotonated dioxocyclam and a PtCl 2− 4 anion form columns running down the c axis. Water molecules are localized in the intercolumnar space and contribute to the extensive hydrogen bond network. The macrocycle conformation is characterized by two sequences of torsional angles, corresponding to two different subunits. The shorter sequence idealized as (-sc, ap, -ac, + ac, ap, +sc) [sc( ±60°), ac( ±120°), ap(180°)], describing the C pseudosymmetric part of the molecule, is centered on a -CH2 group between the two peptide O-C-N-H fragments. The opposite C pseudosymmetric subunit has a nearly (-sc, ac, -SC, ap)2 conformation. Pt is square planar coordinated by four Cl atoms, Pt-Clαve = 2.306(8) Å. The shortest Pt ... Pt distance is 7.200(1) Å.
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  • 23
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    Journal of inclusion phenomena and macrocyclic chemistry 14 (1992), S. 247-256 
    ISSN: 1573-1111
    Keywords: Inclusion compounds ; calixarene ; crystal structure ; hydrogen bonding ; amines
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract The structure of thep-t-butyldihomooxacalix[4]arene triethylamine (1 : 2 complex has been determined by X-ray crystallography. Crystals are monoclinic, space groupCc,a = 22.821(3),b = 15.257(3),c = 16.365(2) Å,β = 97.44(1)°,V = 5650(1) Å3,Z = 4,D calc = 1.03 g cm−3. One triethylamine (Et3N) molecule has one of its ethyl groups pointing inside the cavity of a calixarene molecule; its nitrogen atom is directed exo to this calixarene molecule and is involved in a hydrogen bond with one of the hydroxy groups of a neighbouring calixarene molecule. This scheme leads to columns of alternating host and guest molecules. The other Et3N molecule is in the interhost space. This feature allows us to define the title compound as a complex/clathrate hybrid.
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  • 24
    ISSN: 1573-1111
    Keywords: 1,2-Dialkylated calix[4]arene ; crystal structure ; ethanol inclusion complex ; intramolecular hydrogen bonding patterns
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract The crystal structure of the title compound (1 · C2H5OH) has been determined by single-crystal X-ray analysis and refined to anR-value of 0.074 for 2732 observed reflections [I 〉 2.0σ(I)]. Crystals are triclinic, space group P $$\bar 1$$ , witha = 13.6150(18),b = 13.7195(11),c = 16.5497(16) Å, α = 73.132(7),β = 66.165(9), γ = 65.580(8)° andZ = 2. Calix[4]arene (1) adopts a relatively open distorted cone conformation in the solid state, with two pendantsyn-proximal O-CH2-Py groups. The major conformation determining features in (1 · C2H5OH) are the presence of (a) an intramolecular O-H...O hydrogen bond between adjacent proximal phenolic oxygens, O...O 2.719(7) Å and (b) an intramolecular O-H...N hydrogen bond between a phenolic oxygen and a proximal pyridinyl nitrogen, O...N 2.810(8) Å. The intramolecular hydrogen bonding and the interplanar angles of 65.1(3) and 50.7(3)° between opposite aromatic rings facilitate the inclusion of an ethanol molecule within the calixarene cup.
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  • 25
    ISSN: 1573-1111
    Keywords: Cation binding ; crown ether ; crystal structure ; lariat ether ; synthesis ; triaza-18-crown-6
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract Details of a new synthetic approach to 4,10,16-triaza-18-crown-6 (‘triaza-18-crown-6’) are reported, along with the preparation and binding properties of the following derivatives having the indicated sidearms: CH2C≡CH, CH2CH2OH, CH2CH2OCH3, COCH2OCH3,CH2COOCH2CH3, CH2C6H5, and CH2C6H4−2−NO2. A key intermediate in the synthesis of triaza-18-crown-6 is 4-N-toluenesulfonyl-1,7,13-trioxa-4,10,16-triazacyclooctadecane-9,17-dione. This compound is found by solid state structure analysis to fold to form an intramolecular, doubly-hydrogen bonded complex in which the two N-H protons interact with the two tosyl group oxygens. Details of the structure are reported.
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  • 26
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    New York, NY [u.a.] : Wiley-Blackwell
    Chirality 4 (1992), S. 377-383 
    ISSN: 0899-0042
    Keywords: crystal structure ; molecular mechanics ; MM2-87 ; phenylmorphan ; phenyl-equatorial ; opioid ligand model ; μ-receptors ; K-receptors ; Chemistry ; Organic Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: (+)-2,9α-Dimethyl-5-(m-hydroxyphenyl)morphan is the only phenylmorphan analog whose affinity for opioid K-receptors is greater than its affinity for opioid κ-receptors. Pharmacologically, the compound is a pure opioid antagonist devoid of agonist activity in in vivo assays of antinociception. The absolute configuration of the compound has been determined to be (1R,5S,9R) from an X-ray crystallographic study of the chloride salt. Thus, the absolute configuration corresponds to that of the atypical opioid agonist (-)-phenylmorphan while the weak atypical agonist (-)-2,9α-dimethyl-5-(m-hydroxyphenyl)morphan corresponds to the potent morphine-like (+)-phenylmorphan. The preferred orientations of the phenyl ring for the two stereoisomers were determined using the molecular mechanics program MM2-87 and found to vary from that of the two parent compounds. The atypical properties of the two 9α-methyl analogs is consistent with an opioid ligand model which proposes that morphine-like properties require a particular range of phenyl orientations. There was good agreement between the structure obtained from X-ray crystallography and computed with the MM2-87 program. © 1992 Wiley-Liss, Inc.
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    International Journal for Numerical Methods in Engineering 35 (1992), S. 1941-1966 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In Part I of this paper the kinematic relationships between the absolute, elastic and joint accelerations are developed. In this paper, these kinematic equations are used with the generalized Newton-Euler equations and the relationship between the actual and generalized reaction forces to develop a recursive projection algorithm for the dynamic analysis of open-loop mechanical systems consisting of a set of interconnected rigid and deformable bodies. Optimal matrix permutation, partitioning and projection methods are used to eliminate the elastic accelerations while maintaining the inertia coupling between the rigid body motion and the elastic deformation. Recursive projection methods are then applied in order to project the inertia of the leaf bodies onto their parent bodies. This leads to an optimal symbolic factorization which recursively yields the absolute and joint accelerations, and the joint reaction forces. The method presented in this paper avoids the use of Newton-Raphson algorithms in the numerical solution of the constrained dynamic equations of open-loop kinematic chains since the joint accelerations are readily available from the solution of the resulting reduced system of equations. Furthermore, the method requires only the inversion or decomposition of relatively small matrices and the numerical integration of a minimum number of co-ordinates. Open-loop multibody robotic manipulator systems are used to compare the results and efficiency of the recursive methods with that of the augmented formulations that employ Newton-Raphson algorithms.
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    International Journal for Numerical Methods in Engineering 35 (1992), S. 1991-2002 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In this paper a new method for computing non-linear magnetostatic fields is introduced, which allows the simultaneous coupling of a finite element structure with a magnetic network. Combining the advantages of both methods while avoiding their drawbacks, this coupling yields both an accurate and time-efficient computation.The traditional method of the unknown mesh fluxes is applied for the solution of the magnetic network. The finite element solution, on the other hand, is based on a classical first-order interpolation of the unknown vector potential. The coupling is established by a proper organization of the unknowns on the boundary common to the finite element and network regions. In this way, a single system of non-linear equations is obtained.Moreover, it is shown that the coupled system of equations is equivalent to a single finite element system if generalized base functions are allowed. Consequently, various results from finite element theory may be applied. For instance, the matrix governing the iteratively linearized system of equations can directly be shown symmetrical and positive definite.Finally, the field inside a permanent magnet motor is calculated with the coupled method. Although the number of unknowns is dramatically reduced compared to a full FE calculation, the same level of accuracy is achieved. Hereby, the benefit of the coupled method is clearly proved.
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    International Journal for Numerical Methods in Engineering 35 (1992), S. 2049-2066 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The first-order shear deformation plate theory can be used in the small strain and moderate rotation non-linear elasticity by defining correctly the displacement vector form. In this paper, the problem of the consistency between the displacement vector form and the finite strain tensor approximation is analysed. Then, a new moderate rotation theory is proposed. The variational form of the governing equations is derived for the beam and the plate problems in a consistent way. Then, an iterative numerical procedure based on the finite element method and the secant striffness matrix is developed in order to solve the non-linear differential equation problem. Computations are made for one- and two-dimensional structures, in order to assess the performance of the von Kármán, finite elasticity, classical and the proposed moderate rotation theories.
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    International Journal for Numerical Methods in Engineering 35 (1992), S. 2103-2104 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
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    International Journal for Numerical Methods in Engineering 35 (1992), S. 2067-2078 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Development of techniques to provide rapid and accurate evaluation of the integrations required in boundary element method (BEM) formulations are receiving more attention in the literature. In this work, a series of direct expressions for surface integrals, required for a boundary element solution of the non-homogeneous biharmonic over a general two-dimensional curvilinear surface, are presented. The concept of an isoparametric representation, usually applied to the variation of the field variables and the geometry, is extended to the parametric mapping of the curvilinear geometry. The result renders the typically complicated Jacobian function into a series of polynomial expressions based on the shape function set and several discrete Jacobian values. An application of the isoparametric approximation of the Jacobian for a quadratic element representation is developed. Implementation of this approximation significantly improves the accuracy of the boundary integral solution by eliminating error associated with numerical quadrature. Overall computational efficiency is improved by reducing the time necessary to calculate individual surface integrals and evaluate field variables at internal points. A numerical solution of the boundary integral equations of phenomena governed by the biharmonic equation is presented and compared with an exact analysis.
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    International Journal for Numerical Methods in Engineering 35 (1992), S. 2079-2100 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An infinite boundary element (IBE) is presented for the analysis of three-dimensional potential problems in an unbounded medium. The IBE formulations are done to allow their coupling with the finite element (FE) matrices for finite domains and to obtain the overall matrices without destroying the banded structure of the FE matrices. The infinite body is divided into a number of zones whose contributions are expressed in terms of the nodal quantities at FE nodes by employing suitable decay functions and performing mainly analytical integrations of the boundary element kernels. The continuity and compatibility conditions for the potential and the flux at the FE-IBE interface are developed. The relationships for the contributions of the IBE flux vectors to the FE load vectors are given. The final equations for the IBE are obtained in the usual FE stiffness-load vector form and are easily assembled with the FE matrices for the finite object. A series of numerical examples in heat transfer and electromagnetics were solved and compared with alternative solutions to demonstrate the validity of the present formulations.
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    International Journal for Numerical Methods in Engineering 35 (1992), S. 1427-1442 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper presents a fast numerical algorithm for the implementation of material models for creep into finite element codes. First, an overview of existing algorithms for transient and steady-state creep is given. Next, a new formulation is presented which reduces the constitutive integration to the solution of a scalar non-linear algebraic equation. A solution is shown to exist without the need for subincrementation. Details of the numerical algorithm are then discussed. The paper closes with several numerical examples which illustrate the speed, robustness and accuracy of the proposed procedure as implemented in the Lawrence Livermore National Laboratory finite element codes NIKE2D and NIKE3D.
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    International Journal for Numerical Methods in Engineering 35 (1992), S. 1351-1395 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Structures presenting kinematical inderterminacy are usually called mechanisms. This paper is entirely concerned with assemblies which reveal themselves to be mechanisms at a null value of the load. Among them a first distinction is made between infinitesimal and finite ones, the former being characterized by one or several directions of lower (but not zero) stiffness, whereas the latter show at least one finite admissible displacement for which none of the bars undergoes any elongation. Moreover, there exists the possibility to make a further distinction among the infinitesimal mechanisms, according to which is the order of the stiffness along the direction considered above. The way of evaluating this order is to perform a local analysis of the strain energy of the assembly, once the displacement field is parametrized in terms of a suitable parameter. By means of a finite element technique, this analysis can be easily performed through the numerical approach presented in this report.
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    International Journal for Numerical Methods in Engineering 35 (1992), S. 1487-1502 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A solution strategy to find the shape and topology of structures that maximize a natural frequency is presented. The methodology is based on a homogenization method and the representation of the shape of the structure as a material property. The problem is formulated as a reinforcement problem in which a given structure is reinforced using a prescribed amount of material. Two dimensional, plane elasticity problems are considered. Examples are presented for illustration.
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    International Journal for Numerical Methods in Engineering 35 (1992), S. 1541-1542 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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  • 37
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    International Journal for Numerical Methods in Engineering 35 (1992) 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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  • 38
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    International Journal for Numerical Methods in Engineering 33 (1992) 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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  • 39
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    International Journal for Numerical Methods in Engineering 33 (1992), S. 143-148 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An integral equation whose kernel presents logarithmic singularity is numerically solved by the method of arbitrary collocation points (ACP). As a first step a Gaussian quadrature of order n (hence of polynomial accuracy 2n- 1) is employed for the numerical approximation of the integral. Until now the collocation, which follows, was performed on special points x̄k, determined as roots of appropriate transcedental functions, in order to retain the 2n - 1 degree of polynomial accuracy of the Gaussian quadrature. In this paper an appropriate interpolatory technique is proposed, so that xk may be arbitrary and yet the high (2n - 1) accuracy of the Gaussian quadrature is retained.
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    International Journal for Numerical Methods in Engineering 33 (1992), S. 149-162 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A rank-sufficient flat triangular shell element with drilling degrees-of-freedom is described. A variational basis for this element has been provided by a three-field variational principle with relaxed interelement compatibility and traction continuity conditions. A generalized spurious mode control procedure has been developed in order to stabilize zero energy kinematical modes. Excellent performance has been found in an obstacle course and buckling problems.
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    International Journal for Numerical Methods in Engineering 33 (1992), S. 213-215 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
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  • 42
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: The theory of optimal control and the theory of a substructural chain in static structural analysis are mutually simulated issues. From the minimum potential energy variational principle of the substructural chain, the generalized variational principle with two kinds of variables is derived first. By comparing that generalized variational principle with the variational principle in LQ control theory, the simulation relation is established. Based on that relation, the potential energy and mixed energy formulation of the algebraic Riccati equations are derived, then iterative algorithms are proposed which give the upper and lower bounds to the solution matrix. By using the solutions of the positive and negative co-ordinate algebraic Riccati equations, the canonical transformation matrices for the eigenproblems of the substructural chain and LQ control are constructed respectively, which reduce the eigenproblem to half-size. The properties of the solutions are analysed, which establishes the basis for expansion solutions.
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    International Journal for Numerical Methods in Engineering 33 (1992), S. 217-219 
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    Keywords: Engineering ; Engineering General
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    International Journal for Numerical Methods in Engineering 33 (1992), S. 220-220 
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    Keywords: Engineering ; Engineering General
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    International Journal for Numerical Methods in Engineering 33 (1992), S. 221-222 
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    Keywords: Engineering ; Engineering General
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    International Journal for Numerical Methods in Engineering 33 (1992) 
    ISSN: 0029-5981
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    International Journal for Numerical Methods in Engineering 33 (1992), S. 235-268 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: A theory is presented for the determination of the free vibration characteristics of anisotropic thin cylindrical shells, partially or completely filled with liquid, for two circumferential wave numbers, n = 0, axisymmetric and n = 1, beam-like. The method used was a combination of finite element analysis and classical shell theory. The shell was subdivided into cylindrical finite elements and the displacement functions were obtained using the shell equations. Expressions for the mass and stiffness matrices for a finite element and for the whole structure were obtained. A finite element was developed for the liquid in cases of potential flow. The natural frequencies of the shell, both empty and partially filled, were obtained and compared with existing experiments and other theories.
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    International Journal for Numerical Methods in Engineering 33 (1992), S. 469-502 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A simple, two-noded, finite element model for the three-dimensional buckling analysis of beam assemblages is developed. The underlying generalized-beam theory employed accounts for all coupled significant modes of deformations, including stretching, bending, shear and torsion, as well as warping. Its mixed formulation is of the two-field type, utilizing linear and constant interpolants for displacements and strain fields. Due considerations are given to the effect off inite rotations in space on the non-linear kinematic descriptions as well as the configuration-dependent behaviour of externally applied moment vectors of the conservative and non-conservative types. The performance of the model, and particularly the accuracy of its geometric and load-correction stiffnesses, is assessed in a fairly complete set of numerical simulations.
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    International Journal for Numerical Methods in Engineering 33 (1992), S. 907-927 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The energy release rate G for 2-D rubbery material problems with non-conservative crack surface tractions is calculated by a modified version of virtual crack extension method with finite element solutions. The formulation is demonstrated to be ‘patch-independent’ and therefore a complicated finite element model around the crack tip is not required.
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    International Journal for Numerical Methods in Engineering 33 (1992), S. 929-942 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The purpose of the present paper is the development of a numerical method for the evaluation of the Stress Intensity Factor in mode II at the tips of closed cracks subjected to compressive normal stresses and monotonically increasing shear stresses. A hybrid Boundary Element Technique, originally developed for the analysis of open cracks, has been suitably modified. The Stress Intensity Factor is evaluated directly on the basis of the displacement discontinuities computed at the crack tip element, by taking into account the development of frictional resistance on the crack surfaces. A limited number (10-15) of displacement discontinuity elements is found to be sufficient for an accurate evaluation of the Stress Intensity Factor. Some basic aspects of the mechanical behaviour of closed cracks are also investigated on the basis of the proposed method.
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    International Journal for Numerical Methods in Engineering 33 (1992), S. 963-973 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A simple and efficient triangular finite element is introduced for plate bending applications. The element is a three-node triangular one with three basic degrees of freedom per node and two internal rotation degrees of freedom, using selective reduced integration. Numerical examples indicate that, despite its simplicity, the element is not only competitively accurate, but also useful as a thick-thin triangular plate bending element. It is also pointed out that this element using selective reduced integration is in fact a mixed element.
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    International Journal for Numerical Methods in Engineering 33 (1992), S. 943-961 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: We investigate the Generalized Midpoint Rule for the time integration of elastoplastic constitutive equations for pressure-independent yield criteria. The incremental equations are divided into one scalar hydrostatic pressure/dilation rate equation, and a stress deviator/strain rate deviator tensorial equation, the solution of which reduces to one single scalar equation in the plastic multiplier. The existence and uniqueness of an incremental solution is discussed. The pressure/deviator decomposition is the basis for reduced integration of the pressure term in the Principle of Virtual Work, in order to avoid locking and spurious pressure oscillations. It is also shown that an optimal choice of the parameter of the Midpoint Rule can be computed by reference to the analytical solution of the equations assuming no work hardening. A benchmark test shows that this choice allows increased time steps. This formulation is applied to two classical problems: bulging of a tube under internal pressure and tension test on a notched specimen, and a comparison with the analytical solution is performed. Finally, the hypothesis which sustains these formulations of elastoplasticity (constant strain rate during an increment) is discussed with reference to elastic unloading and residual stress computation.
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    International Journal for Numerical Methods in Engineering 33 (1992), S. 975-995 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper presents a method for creating a Delaunay triangulation connected to a set of specified points. The theoretical aspect is recalled for an arbitrary dimension and the method is discussed in order to derive a practical approach, valid for dimensions 2 and 3, which is simple, robust and well adapted to computation. Convex polyhedral and arbitrary polyhedral situations are introduced.
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    International Journal for Numerical Methods in Engineering 33 (1992), S. 1119-1138 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A geometrically non-linear thin shell element made from classical laminated materials is developed from three dimensional continuum concepts that admits arbitrarily large displacements and rotations. The development shows how explicit integration through the thickness of the element can be accomplished without sacrificing significant accuracy of the element.Computations obtained via the present formulation are compared with four test problems for which numerical data are available. All computations were carried out using the Crisfield-Riks arc length continuation algorithm with a full Newton-Raphson iterative scheme. Excellent agreement is observed for each test problem.
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    International Journal for Numerical Methods in Engineering 33 (1992), S. 1165-1180 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A new explicit variable time-integration methodology and architecture which possesses self-starting attributes, eliminates the need to involve acceleration computations, and which has improved accuracy characteristics in comparison to the traditional central-difference-type formulations customarily advocated is described for applicability to computational structural dynamics. To sharpen the focus of the present study, an explicit variable time-integration architecture which is relatively simple, yet effective, is described. Unlike variable explicit time-integration formulations adopted in the past, the present self-starting variable time-integration architecture and implementation aspects facilitate a simplified representation and a straightforward and effective approach for combining finite element meshes requiring different time steps in a single analysis. Numerical test cases are provided which demonstrate the applicability of the proposed formulations.
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    International Journal for Numerical Methods in Engineering 33 (1992), S. 1139-1163 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Dynamic substructuring or modal synthesis is established as a powerful means by which the computational effort required to perform dynamic analyses of large structures comprising many degrees of freedom can be reduced. For the case where the substructures are rigidly connected a method of synthesis is proposed which gives very substantial improvements in efficiency over existing methods both in terms of the number of floating-point operations which must take place and the on-board computer memory required. The proposed method makes use of a stable co-ordinate transformation which reduces the mass matrix for the constrained composite-system to the identity matrix and makes the stiffness matrix banded. The bandwidth is exactly equal to twice the total number of constraints plus 1. This is usually very small in comparison with the total number of degrees of freedom in the constrained composite-system. The proposed method is ideal for combining a number of substructures into a single new substructure in an efficient way without necessarily disposing of any degrees of freedom. Approximate formulae are presented which give the ratios of the number of operations required for established methods compared with the number needed for the proposed method. These formulae determine when it is appropriate to use the method proposed here.
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    International Journal for Numerical Methods in Engineering 33 (1992), S. 1181-1195 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In this paper we derive the non-singular boundary integral representation of the field gradients for two-dimensional problems of classical potential field theory. Numerical implementation of this representation is developed too. The proposed method eliminates the most inaccurate influence coefficients which arise when singular integral representations are used and the internal point approaches the boundary. Since the integrands in this new method are finite at any internal point, accurate numerical results are achieved even in that portion of a solid which is very close to a discretized boundary. Two test problems are analysed in which the numerical results computed by strongly singular, weakly singular and non-singular integral representations are compared mutually and with exact solutions.
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    International Journal for Numerical Methods in Engineering 33 (1992), S. 1197-1216 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Optimal plastic designs for structural frames can be obtained via static or kinematic considerations, each leading to a mathematical model requiring solution by linear programming. In both cases a mechanism can be found which satisfies the Foulkes optimality condition. However, this mechanism generally has many degrees of freedom and is most unlikely to be the actual collapse mode of the frame. A simple algorithm based on the method of redundant forces is presented for the automatic generation of the alternative optimal collapse mechanisms, any of which may be the actual collapse mode.
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    International Journal for Numerical Methods in Engineering 33 (1992), S. 1217-1236 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In this paper, a ring rolling process is analysed by the Arbitrary Lagrangian Eulerian (ALE) finite element method. Phenomena associated with the process, such as large deformations, elastoplastic material behaviour and the friction on the interface, are included in the analysis. Special modelling on driven, idle and guide rolls is given. Results which include the overall shape of the formed ring, the time histories of roll separating force and driving torque, the distribution of the normal pressure on the ring-roll interface as well as the distribution of effective stresses in the formed ring, are also presented.
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    International Journal for Numerical Methods in Engineering 33 (1992), S. 1237-1249 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: The issue of developing effective and robust schemes to implement a class of the Ogden-type hypereiastic constitutive models, for large-strain analysis of rubber-like materials, is addressed. To this end, explicit forms for the corresponding material tangent-stiffness tensors are developed, and these are valid for the entire deformation range; i.e. with both distinct as well as repeated principal-stretch values. Throughout the analysis the various implications of the underlying property of separability of the strain-energy functions are exploited, thus leading to compact final forms of the tensor expressions. In particular, this facilitated the treatment of the complex cases of uncoupled volumetric/deviatoric formulations for incompressible materials, which are becoming increasingly popular in recent years. The forms derived are also amenable for use with symbolic-manipulation packages for systematic code generation.
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    International Journal for Numerical Methods in Engineering 33 (1992), S. 1251-1267 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Several old and new tetrahedral elements are tested and compared to some classical hexahedral elements for the solution of three-dimensional incompressible fluid flow problems. The proposed elements are created by adding velocity degrees of freedom to the basic trilinear velocity, constant pressure tetrahedron so as to satisfy the Brezzi condition. Numerical tests carried out for an artificial divergence-free flow problem and the lid-driven cubic cavity up to a Reynolds number of 400 are used to compare the proposed elements and assess their accuracy.
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    International Journal for Numerical Methods in Engineering 33 (1992), S. 1269-1287 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: The present paper is concerned with the effective numerical implementation of the two-dimensional dual boundary element method, for linear elastic crack problems. The dual equations of the method are the displacement and the traction boundary integral equations. When the displacement equation is applied on one of the crack surfaces and the traction equation on the other, general mixed-mode crack problems can be solved with a single-region formulation. Both crack surfaces are discretized with discontinuous quadratic boundary elements; this strategy not only automatically satisfies the necessary conditions for the existence of the finite-part integrals, which occur naturally, but also circumvents the problem of collocation at crack tips, crack kinks and crack-edge corners. Examples of geometries with edge, and embedded crack are analysed with the present method. Highly accurate results are obtained, when the stress intensity factor is evaluated with the J-integral technique. The accuracy and efficiency of the implementation described herein make this formulation ideal for the study of crack growth problems under mixed-mode conditions.
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    International Journal for Numerical Methods in Engineering 33 (1992), S. 1305-1320 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: Finite elements based on Mindlin-Reissner theory and three-dimensional theory are used to study the distribution of shear forces and twisting moments in plates with various simple support conditions. Differences between the results obtained using these two theories are highlighted. A crude adaptive mesh refinement procedure is applied to improve the accuracy of the finite-element analysis.
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    International Journal for Numerical Methods in Engineering 33 (1992), S. 1321-1323 
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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 33 (1992), S. 1325-1325 
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    International Journal for Numerical Methods in Engineering 33 (1992), S. 1329-1329 
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    Keywords: Engineering ; Engineering General
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    International Journal for Numerical Methods in Engineering 33 (1992), S. 1327-1328 
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    Keywords: Engineering ; Engineering General
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    International Journal for Numerical Methods in Engineering 33 (1992), S. 1611-1623 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The paper first presents the details of the development of a new six-noded plane triangular finite dynamic element. A block Lanczos algorithm is developed next for the accurate and efficient solution of the quadratic matrix eigenvalue problem associated with the finite dynamic element formulation. The resulting computer program fully exploits matrix sparsity inherent in such a discretization and proves to be most efficient for the extraction of the usually required first few roots and vectors, including repeated ones. Most importantly, the present eigenproblem solution effort is shown to be comparable to that of the corresponding finite element analysis, thereby rendering the associated dynamic element method rather attractive owing to superior convergence characteristics of such elements, presented herein.
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    International Journal for Numerical Methods in Engineering 33 (1992), S. 1721-1736 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: Based on the incremental non-linear theory of solid bodies and the Hellinger-Reissncr principle, a mixed updated Lagrangian formulation of the large displacement motion of solid bodies is derived, and an associated mixed finite element model is developed. The model contains the displacements and stresses as the nodal degrees of freedom. The model is used for the large deformation elasto-plastic analysis of plane problems. In solving non-linear problems, the Newton-Raphson method with arc-length control is adopted to trace the post-buckling response. The computational steps to calculate the elasto-plastic stress increments at Gauss points in the elasto-plastic analysis by the present mixed model are described in detail. Numerical results are presented and compared with those of the displacement model and existing solutions to show the accuracy of the present mixed model in the large deformation elasto-plastic analysis of plane problems.
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    International Journal for Numerical Methods in Engineering 33 (1992), S. 1737-1754 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: An accurate and efficient time domain BEM for 2-D scalar wave problems is presented. Emphasis is on developing analytical boundary elements (explicit solutions of the element matrices). The solutions are obtained under the condition of straight line elements and by bringing the problem to a simple and genral form of double convolution equation which is then solved by the Cagniard-De Hoop method. Six kinds of elements for any combination of the spatial interpolation functions of order 0, 1, 2 with the temporal interpolation functions of order 0, 1 are given in a compact form. It is pointed out that if the order of temporal interpolation function is higher than 1, or if the continuity of velocity or acceleration is required, the time-stepping technique will face difficulty. A method to solve this problem is also presented.Advantages of using the analytical elements instead of a numerical integral procedure are apparent. Problems with such things as singular integrals, accuracy and stability are solved. Methodology and solutions are demonstrated by a comparative study of two example problems. Numerical solutions reveal that the computation is efficient, accurate and stable.
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    International Journal for Numerical Methods in Engineering 33 (1992), S. 1771-1773 
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    Keywords: Engineering ; Engineering General
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    International Journal for Numerical Methods in Engineering 33 (1992) 
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    International Journal for Numerical Methods in Engineering 33 (1992), S. 1755-1769 
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    Notes: An a posteriori error estimation method for finite element solutions for three-dimensional elastic problems is presented based on the theory developed by the authors for two-dimensional problems.1 The error is estimated for the finite element solutions obtained using three-dimensional 8-node elements with a linear interpolation function in an arbitrary hexahedron. The method is successfully applied to three-dimensional elastic problems. In order to decrease computing time and memory use, the error is estimated element by element. The major difficulty in the element-wise error estimation technique is satisfying the self-equilibrium condition of applied forces, especially in three-dimensional problems. These forces are mainly due to traction discontinuity on the element boundaries. The difficulty is circumvented by employing an element-wise optimal procedure. It is also shown that a very accurate stress solution can be obtained by adding estimated error to the original finite element solutions.
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    International Journal for Numerical Methods in Engineering 33 (1992), S. 1813-1822 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper is concerned with the problem of modelling the motion of a bubble close to a rigid structure in an infinite fluid. It is well known that the boundary integral method is a powerful technique for modelling the motion of a single bubble in a fluid. In this paper we shall present a modified boundary integral method for modelling the motion of a bubble close to a fixed finite rigid structure, and discuss a numerical scheme for solving the resulting integral equation for three-dimensional problems. Finally, we illustrate our method with some typical numerical results.
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    International Journal for Numerical Methods in Engineering 33 (1992), S. 1861-1874 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: In recent years progress has been made in applying moving and deforming mesh systems to phase change problems. This allows the numerical attention where it is needed, near the migrating phase change zone. In spatially unbounded problems one hopes that numerically finite outer boundaries either escape significant activity or are automatically pushed further away as activity nears. Not infrequently this approach fails. Temperature activity often spreads more rapidly than phase change, thereby reaching far boundaries; stretching of the mesh by movement of far boundaries can challenge mesh control and cause ill-conditioning. In this paper the advantages of time dependent mesh adaption are enhanced by the joining of a new formulation for infinite elements to far boundaries. This is accomplished through a co-ordinate transformation within the framework of conventional 2-D quadratic, biquadratic, and linear-quadratic elements. Standard 2 by 2 Gauss-Legendre quadrature suffices throughout and normal Galerkin finite element features are undisturbed, including strict conservation of energy. The formulation is independent of global co-ordinates, entails no restrictions on the unknown function and should be applicable to other problem types. All test cases on quadrilateral and triangular grids show very significant improvements with infinite elements relative to comparable solution systems using strictly finite grids.
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    International Journal for Numerical Methods in Engineering 33 (1992), S. 1843-1859 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: A general, well-structured and efficient method is advanced for the solution of-a large class of dynamic interaction problems including a non-linear dynamic system running at a prescribed time-dependent speed on a linear track or guideway. The method uses an extended state-space vector approach in conjunction with a complex modal superposition. It allows for the analysis of structures containing both physical and modal components. The physical components studied here are vehicles modelled as linear or non-linear discrete mass-spring-damper systems. The modal component studied is a linear continuous model of a track structure containing beam elements which can be generally damped and which can be embedded in a three-parameter damped Winkler-type foundation. The complex modal parameters of the track structure are solved for. Algebraic equations are established which impose constraints on the transverse forces and accelerations at the interfaces between the moving dynamic systems and the track. An irregularity function modelling a given non-straight profile of the non-loaded track or a non-circular periphery of the wheels is also accounted for. Loss of contact and recovered contact between a vehicle and the track can be treated. The system of coupled first-order differential equations governing the motion of the vehicles and the track and the set of algebraic constraint equations are together compactly expressed in one unified matrix format. A time-variant initial-value problem is thereby formulated such that its solution can be found in a straightforward way by use of standard time-stepping methods implemented in existing subroutine libraries. Examples for verification and application of the proposed method are given. The present study should be of particular value in railway engineering.
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    International Journal for Numerical Methods in Engineering 33 (1992), S. 1891-1925 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: The primary aim of this research is to implement the arbitrary Lagrangian-Eulerian finite element description to model large deformation of interacting bodies. A pure Lagrangian description is often incapable of representing their contact with sufficient precision. In this work, the arbitrary Lagrangian-Eulerian (ALE) description has been extended to the surface nodes of interacting bodies to overcome these limitations. A penalty formulation has been implemented to account for the impenetrability constraint. The materials have been characterized as elastic-viscoplastic. Implicit integration schemes have been used at the global and constitutive levels for'improved stability.
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    International Journal for Numerical Methods in Engineering 33 (1992), S. 1875-1890 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: In order to obtain the curvature changes of the exterior surface of a shell subjected to an internal pressure, it is necessary to evaluate the displacement derivatives up to the second order. To this end, a hexahedronal element is developed with three-dimensional elastic properties utilized. At a nodal point on the surface of the shell, the first-order derivatives of the three displacement components are used as degrees of freedom (d.o.f.) in addition to the components themselves. However, at a nodal point not on the surface, only the three displacement components are used. Therefore, an element with aii exterior surface has a total of 48 d.o.f. and other elements have 24 d.o.f.The stiffness matrix of the 8-node subparametric hexahedronal high-order element is derived from the strain energy consideration. The cubic shape functions in the surface co-ordinates and linear shape functions through the shell thickness are used. The second derivatives of displacement components are continuous at any point on the exterior surface of the element, although they may not be continuous across the nodal line of two adjacent elements.
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    International Journal for Numerical Methods in Engineering 33 (1992), S. 1927-1940 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: An efficient method is developed to compute the sensitivities of eigenvalues, eigenvectors and frequency responses in a reduced approximate rnodel. The reanalyses of a modified structure for those dynamic responses are also derived in the approximate model. An optimization process utilizing the efficiently calculated sensitivities and reanalyses of the modified structure is formed. The difficulties of finding eigenvector sensitivities for repeated modes have also been addressed and averted in the approximate model. Two numerical examples show satisfactory outcomes by using this proposed approach.
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    International Journal for Numerical Methods in Engineering 33 (1992), S. 2109-2127 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A finite element formulation for geometric non-linear analysis of elastic straight thin-walled beams is presented. The updated Lagrangian procedure is used for a stiffness matrix derivation-to analyse large displacements or buckling behaviour of space frames. The stiffness matrix is developed for a generic cross-section and is equally efficient for symmetric, monosymmetric or asymmetric open sections. Some non-linear strain terms usually neglected in the literature have been considered, resulting in a formulation which also includes the initial bimoment and torsion effect for all cross-sections analysed. The proposed method has been implemented and the results of sample problems are presented.
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  • 81
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    International Journal for Numerical Methods in Engineering 33 (1992), S. 2129-2143 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Linear and non-linear boundary eigenvalue problems are discretized by a new finite element like method. The reason for the new construction principle is the non-linear dependence of the dynamic stiffness element matrix on an eigenparameter. The dynamic stiffness element matrix is evaluated for a fixed number of parameters and is then elementwise replaced by a polynomial in the eigenparameter by solving least squares problems. A fast solver is introduced for the resulting non-linear matrix eigenvalue problem. It consists of a combination of bisection method and inverse iteration. The superiority of the newconstructionprinciple in comparison with the finite or dynamic element method is demonstrated finally for some numerical examples.
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  • 82
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    International Journal for Numerical Methods in Engineering 33 (1992), S. 2201-2203 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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  • 83
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    International Journal for Numerical Methods in Engineering 33 (1992), S. 2199-2199 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
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  • 84
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    International Journal for Numerical Methods in Engineering 33 (1992), S. 2181-2197 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Assumed field-consistent strain formulations of the displacement finite element procedure can lead to poor convergence and spurious stress oscillations if the assumed strain fields are not variationally correct, i.e. they do not satisfy an important orthogonality condition emerging from the equivalence sought between assumed strain displacement procedures and mixed procedures based on the Hellinger-Reissner theorem. Failure to ensure variational correctness introduces errors which can be equated to the presence of spurious loading mechanisms that cause stress oscillations. In this paper, we use the Timoshenko beam element to demonstrate that field-consistency and variational' consistency are two complementary but mutually exclusive principles - one does not imply the other and that both are necessary to successfully implement a displacement type finite element for constrained media.
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  • 85
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    International Journal for Numerical Methods in Engineering 34 (1992) 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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  • 86
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    International Journal for Numerical Methods in Engineering 34 (1992), S. 1-1 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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  • 87
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    International Journal for Numerical Methods in Engineering 33 (1992), S. 2145-2179 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The continuity and differentiability of object functions is a basic prerequisite for the application of gradient methods in optimization. However, for parameters defining the shape of an electromagnetic device, the finite element discretization in the field analysis introduces discontinuities into the object function which slow down the convergence rate. Additionally, depending on the geometric parametrizaiion employed, the optimization frequently yields shape contours that are impracticable for manufacturing purposes. This paper investigates the problems inherent in geometric parametrization and shows that the discontinuities in the object function are caused by changes in mesh topology as the geometric parameters vary; these changes inevitably follow from the use of free meshing algorithms. As a solution to these shortcomings a structural mapping technique is outlined that maps surface displacements onto the parameters of the finite element mesh and obtains the parameter dependent geometric variations without a change in mesh topology. This resulting geometric parametrization yields continuous object functions without artificial local minima and results in smooth surface contours of the optimized device. Using this new parametrization technique, design sensitivity analysis, is shown to be a reliable and essential part in the efficient application of gradient methods for shape optimization.
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  • 88
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    International Journal for Numerical Methods in Engineering 34 (1992), S. 3-3 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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  • 89
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    International Journal for Numerical Methods in Engineering 34 (1992), S. 61-71 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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  • 90
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    International Journal for Numerical Methods in Engineering 34 (1992), S. 39-59 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The first part of this study addresses the controversy ‘degenerated solid approach’ versus ‘shell theory’. It is shown that both formulations differ only in the kind of discretization if they are based on the same mechanical assumptions. In particular for degenerated shell elements different versions of explicit integration across the thickness are discussed. Among these are the approximation ‘Jacobian across the thickness is constant’, proven to be too restrictive, and the series expansion of the inverse Jacobian which turns out to be unnecessary although it leads to equations of the same order as those of a ‘best first approximation’ of a shell theory.The second part deals with the description of large rotations. It is demonstrated for problems formulated in three components of a rotation vector that a straightforward derivation results in a symmetric tangent stiffness matrix. However, a modified version is also added leading to an unsymmetric matrix already discussed in the literature. For shell problems with only two rotational variables both formulations coincide.
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  • 91
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    International Journal for Numerical Methods in Engineering 34 (1992), S. 73-115 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A non-linear shell theory, including transverse shear strains, with exact description of the kinematical fields is developed. The strain measures are derived via the polar decomposition theorem allowing for an explicit use of a three parametric rotation tensor. Thus in-plane rotations, also called drilling degrees of freedom, are included in a natural way. Various alternatives of the theory are derived. For a special version of the theory, with altogether six kinematical fields, different mixed variational principles are given. A hybrid finite element formulation, which does not exhibit locking phenomena, is developed. Numerical examples of shell deformation at finite rotations, with excellent element performance, are presented. Comparison with results reported in the literature demonstrates the features of the theory as well as the proposed finite element formulation.
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  • 92
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    International Journal for Numerical Methods in Engineering 34 (1992), S. 9-33 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Computational Mechanics or Computational Applied Science is today the base on which most of the achievements of engineering and physics are built. Its concern is the solution of complex mathematical theories in numerical terms, without which the translation of these into practical artifacts would be impossible. Indeed, by providing such quantitative measures it enhances the understanding of the physical phenomena and stimulates further development of theory and physical experiment.Most of the theory underlying physical phenomena is cast in terms of, often involved, differential equations for which closed forms of solution are seldom possible. Numerical approximation or discretization processes are necessary for quantitative solution. Here the first steps were taken at the start of this century by the pioneering work of Richardson introducing finite difference approximations. The invention of relaxation methods by Southwell during the Second World War allowed many practical solutions to be achieved. However, it was the advent of the electronic digital computer that marked the turning point in Computational Mechanics. The dramatic escalation of the power of these machines, which still continues today, allowed the development of the field of Computational Mechanics as we know it.It is through this computer power that such methods of approximations as finite elements, finite differences, boundary solutions and spectral processes became a practical reality, though each was anticipated in the pre computer area. It is not surprising therefore, that the mathematical foundations and the full development of such methods have been accomplished only relatively recently.Today we see the field of activity subdivided between those specializing in the development of the various computational approximation processes and those seeking optimal numerical solutions for their particular field of application. It is the objective of this Congress and indeed of the International Association of Computational Mechanics to provide a forum at which an interdisciplinary exchange of information can take place between the various sections and disciplines of the whole field. Indeed, this is the way progress can best be achieved. Recent history indicates that substantial advances are as frequently made due to a method seeking a new application as through a problem requiring a solution.In recent history we have seen on occasion a liaison of a particular computational approximation method to a field of application occurring through historical accident. Here the intimate association of the finite method and the field of SOLID MECHANICS (CSM or Computational Solid Mechanics) and that of the finite differences with FLUID DYNAMICS (CDF or Computational Fluid Dynamics) can be observed as classical examples. Today the advent of new application fields and a better understanding of the approximation theory are helping to break down the barriers and ensure a more rational matching of objectives and methods. We shall illustrate the lecture with examples of such recent progress and state some possibilities as yet unexplored. Indeed, we are sure that the Congress will achieve in much more detail the same aims.This presentation stresses the essential unity of the subject and discusses some areas where progress and research are currently active. Two of such, adaptive error controlled analysis and treatment of hyperbolic (fluid) problems, are singled out due to their wide applications.
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    International Journal for Numerical Methods in Engineering 34 (1992), S. 165-169 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: For the analysis of shell structures with finite displacements and rotations displacement-based and mixed finite-rotation shell elements are developed starting from consistent tensorial shell theories. The constraints for the description of the deformed normal vector have been considered at the element level as subsidiary conditions so that finite rotations in arbitrary strongly nonlinear situations can be considered without any difficulty. The efficiency of the finite-rotation elements is demonstrated by numerical examples.
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    International Journal for Numerical Methods in Engineering 34 (1992), S. 117-164 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In Parts I to V of the present work, the formulation and finite element implementation of a non-linear stress resultant shell model are considered in detail. This paper is concerned with the extension of these results to incorporate completely general non-linear dynamic response. Of special interest here is the dynamics of very flexible shells undergoing large overall motion which conserves the total linear and angular momentum and, for the Hamiltonian case, the total energy. A main goal of this paper is the design of non-linear time-stepping algorithms, and the construction of finite element interpolations, which preserve exactly these fundamental constants of motion. It is shown that only a very special class of algorithms, namely a formulation of the mid-point rule in conservation form, exactly preserves the total linear and angular momentum. For the Hamiltonian case, a somewhat surprising result is proved: regardless of the degree of non-linearity in the stored-energy function, a generalized mid-point rule algorithm always exists which exactly conserves energy The conservation properties of a time-stepping algorithm need not, and in general will not, be preserved by the spatial discretization. Precise conditions which ensure preservation of these conservation properties are derived. A number of numerical simulations are presented which illustrate the exact conservation properties of the proposed methodology.
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  • 95
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    International Journal for Numerical Methods in Engineering 34 (1992), S. 171-177 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A universal method which can be used to generalize thin plate elements to thick ones without adding any extra degree of freedom (DOF) is presented in this paper. To illustrate this method, a rectangular moderately thick plate element with 12 DOF is constructed on the basis of the well known thin plate ACM element. The element can be used in the analysis of both thin and thick plates. Shear locking is avoided.
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  • 96
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    International Journal for Numerical Methods in Engineering 34 (1992), S. 179-195 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper presents a method for a quick evaluation of stresses and displacements in a plate structure for elastostatic problems. First, an approximation is built from the mathematical structure of the solutions for starshaped domains, which is representative of long wavelength effects. Second, a variational formulation consistent with this approximation is proposed. Finally, two alternative procedures for coupling adjacent domains are demonstrated.
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  • 97
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    International Journal for Numerical Methods in Engineering 34 (1992), S. 223-231 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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  • 98
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    International Journal for Numerical Methods in Engineering 34 (1992), S. 197-208 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The present paper is concerned with the improvement of a finite element for the analysis of plate bending structures. The element formulation is based upon the Mindlin plate concept. The displacement field of this element is formed by adding non-conforming modes to two rotational displacement components of an 8-node plate element. The element has the requisite numbers of zero eigenvalues associated with rigid body modes to avoid the spurious zero energy mode. It is shown that the results obtained by the element converged to the exact solutions very rapidly as the mesh is refined and exhibited reliable solutions through numerical studies for standard benchmark problems. This element is shown to overcome the shear locking problem completely in a very thin plate situation, even for irregular meshes.
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    International Journal for Numerical Methods in Engineering 34 (1992), S. 209-220 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In structural elements that allow shear deformation, uniformly reduced integration is used to avoid shear and membrane locking. The spurious modes of an underintegrated stiffness matrix can be filtered using perturbation methods. Although finite elements with perturbed stiffness show very good results, the displacements still conceal a component of spurious modes, albeit with very small magnitude depending on the perturbation factor. To desensitize the numerical results completely from the perturbation factor, a projection of the applied force is proposed to complement the perturbation of the stiffness such that spurious modes are not excited, thus providing robustness to the filtering of spurious modes. The proposed methodology is general in nature, but is applied in this paper to a 9-node shell element with uniformly reduced integration as an illustration. The perturbation of the stiffness matrix and the projection of the force vector are performed at the element level, avoiding expensive local-global transformations. As a consequence of the force projection, the perturbation factor for the stiffness can be arbitrarily small, and the element yields accurate results for a wide range of shell thickness.
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    International Journal for Numerical Methods in Engineering 34 (1992), S. 233-247 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A new computational model for the analysis of friction phenomena is presented in this work. The model is a regularized form of the Coulomb friction law, which stems from the analogy of friction and plasticity phenomena. The basic difference from the classical plasticity is the non-linear form of both the normal and the tangential elastic compliance. The numerical implementation of the model is also discussed. The methodology presented herein is used for the analysis of both dynamic and quasi-static problems. The dynamic substructuring and the static condensation are used to enhance the computational efficiency.
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