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  • 1990-1994  (6,038)
  • Engineering  (3,320)
  • Engineering General  (3,144)
  • Atomic, Molecular and Optical Physics  (1,617)
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  • 101
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 49 (1994), S. 539-548 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A set of exact conditions is compiled for the purpose of developing and testing approximations for the exchange-correlation energy as a functional of the electron density. Special emphasis is placed upon recently developed density-scaling relationships. Commonly used generalized gradient approximations are compared against several of these conditions. A direct tabular comparison of these functionals (not of calculated properties) with one another is also made. © 1994 John Wiley & Sons, Inc.
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  • 102
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 49 (1994), S. 527-537 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: We have demonstrated molecular dynamics simulations using a combination of the classical molecular dynamics with density functional theory for argon clusters. Three different molecular dynamics schemes, which differ in their treatment of the potential energy and forces, have been carried out. The first uses a Lennard-Jones potential. In the second, the potential is computed using the Harris functional, and in the third, a combination of Lennard-Jones and Harris functional potentials is used. In addition to direct examination of the trajectories, the velocity autocorrelation function and its power spectrum have been computed to demonstrate the agreement between these three methods. The present studies show that a scheme that used a combination of model potentials and density functional theory provides a very useful tool for the dynamics simulation of systems that contain some fragments in which the analytical model potentials are not available. © 1994 John Wiley & Sons, Inc.
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  • 103
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 49 (1994), S. 511-526 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Local spin density (LSD) methods were used to study the concerted 1,3-dipolar cycloadditions for fulminic acid plus acetylene, fulminic acid plus ethylene, and nitrone plus ethylene. Cartesian Gaussian double-zeta split-valence basis sets augmented with one set of polarization functions (DZVP) were used for the LSD calculations. The LSD calculations were performed with the LSD exchange functional (Dirac) and with the Vosko, Wilk, and Nusair correlation energy functional (VWN). Nonlocal spin-density corrections (NLSD) were estimated with the exchange functional of Becke and the correlation energy functional of Perdew (VWN + BP) and Becke, and the correlation energy functional of Lee, Yang, and Parr (B-LYP). Vibrational frequencies were computed at the VWN and B-LYP levels by numerical differentiation of the analytical first derivatives of the energy. Each of these reactions was examined using Hartree-Fock and Møller-Plesset perturbation theory for comparison. Geometry optimizations were carried out at the Hartree-Fock level with the 6-311G(d,p) basis set, and correlation energies were computed up to the MP4SDTQ/6-311G(d,p) level of theory. For the reactions of fulminic acid plus acetylene, fulminic acid plus ethylene, and nitrone plus ethylene, our best estimated density functional barrier heights are 7.8 ± 1.5, 8.9 ± 0.3, and 11.05 ± 1.9 kcal/mol, respectively. These results are in reasonable agreement with the correlated wave-function calculations and experimental estimates. © 1994 John Wiley & Sons, Inc.
    Additional Material: 4 Ill.
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  • 104
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 49 (1994), S. 549-557 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: In this work, a way to approximate the correlation energy functional starting from a model correlation factor is shown. The problem is addressed by using formally exact properties of the second-order density matrix and actual values of correlation energies for atoms. An Ansatz for the correlation factor is proposed that allows one to derive some known and some new correlation energy density functionals. Results for atomic systems show the reliability of the approach. © 1994 John Wiley & Sons, Inc.
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  • 105
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 49 (1994) 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Type of Medium: Electronic Resource
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  • 106
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 49 (1994), S. 575-579 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: An analysis is presented of the results of earlier ab initio computational studies of cyclobutadiene, cyclooctatetraene, and 1,4-dihydropyrazine. The first and third of these are normally categorized as antiaromatic. All three molecules are polyenes, even when the last two are forced into planar conformations. There is no driving force for extensive π delocalization, even when it would appear to have been facilitated. Calculated isodesmic energies show a net destabilization only in the case of cyclobutadiene, which we attribute to strain and repulsion between the π electrons of the C=C double bonds. The other two molecules have negative isodesmic energies, indicative of net stabilizing effects. We conclude that the concept of antiaromaticity is useful for identifying molecules that resist the apparent opportunity for extensive © delocalization, but that it does not intrinsically imply net destabilization. © 1994 John Wiley & Sons, Inc.
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  • 107
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 49 (1994), S. 559-573 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Use of orthogonalized Hartree product (OHP) orbitals as the reference orbitals in coupled-cluster (cc) calculations is presented. Since such orbitals are determined without exchange, they provide as “classical” a description as possible. The OHP orbitals were generated by implementing Harris's formulation of the original Hartree method. Some computational considerations of the formulation are discussed. A critical evaluation of the OHP method as an orbital localization scheme is presented. The OHP orbitals were used as the reference in CCD and CCSD calculations and compared with corresponding Hartree-Fock (HF) reference CC results. The average variation of localized Hartree product (LHP) reference CCSD energy from that of the HF reference is 0.83 kcal/mol, whereas for CCD, the average variation is 234 kcal/mol, indicating the importance of single-excitation effects in CC calculations with non-HF references. © 1994 John Wiley & Sons, Inc.
    Additional Material: 2 Ill.
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  • 108
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 52 (1994), S. 195-203 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A series of complete coupled-cluster singles, doubles, and triples (CCSDT) calculations have been performed with Hartree-Fock (HF) and Brueckner (B) orbitals. Calculations have been performed with a double-zeta plus polarization basis set on the H2O, SiH2, NH2, BeO, C2, CN+, and BN molecules. Calculations on H2O and SiH2 at equilibrium and stretched geometries show negligible difference between HF-and B-CCSDT energies. This is also true for NH2, except when the bonds have been stretched to twice their equilibrium values, at which point there is about a 2.5 milli-Hartree (mEh) difference. Calculations on the isoelectronic systems BeO, C2, CN+, and BN were performed at equilibrium geometries. Even though these systems have large T1 amplitudes, the difference between HF- and B-CCSDT energies is only about 1 mEh. For the CCSD method and the CCSD(T) method, which includes triple excitations in an approximate, noniterative manner, however, somewhat larger differences are observed between and HF-and B-CC results. Finally, some properties of BN were computed using HF- and B-CC methods. There are quite small differences between the HF- and B-CCSDT results, but significantly larger ones for the more approximate CCSD and CCSD(T) methods. For this difficult system, where the CCSD(T) approximation seems to be inadequate for HF orbitals, the use of Brueckner orbitals improves the agreement of CCSD(T) with CCSD(T) substantially for re and we, although the difference for μ is unaffected. © 1994 John Wiley & Sons, Inc.
    Additional Material: 6 Tab.
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  • 109
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    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 52 (1994), S. 181-194 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A computational study, using relativistic effective core potentials, is presented of transition metalmain group multiply bonded complexes, of interest in the context of catalysis and chemical vapor deposition of TM/MG materials. Model d0 transition metal complexes chosen are of the general form ClnME where M = Zr (n = 2), Ta (n = 3), and W (n = 4). Main group elements of interest are the tetrels (E = C, Si, Ge, Sn), pnictogens (E = N, P, As, Sb), and chalcogens (E = O, S, Se, Te). A comparison between calculated metric data and available experimental data for a wide range of TM = MG complexes will help in further assessing efficient computational approaches to TM complexes, particularly of the heavier MG elements, as a function of metal, ligand and level of theory. In the present work restricted Hartree Fock (RHF) and Møller-Plesset second order perturbation theory (MP2) wavefunctions were employed. In most cases there are small differences between RHF and MP2 calculated geometries, with both methods showing good agreement with experimental data, suggesting these approaches will be suitable for the study of larger, more experimentally relevant models. Changes in ZrE bond lengths for E = chalcogen (upon going from RHF to MP2) suggest a fundamentally different description between the Zr-oxo bond and heavier chalcogens, a result supported by recent experimental data for a series of Zr-chalcogenidos. To date no examples have been reported of arsinidene and stibinidene complexes. Computational results show similar behavior among the heavier pnictogen complexes, i.e., LnM = EH (E = P, As, Sb), suggesting that strategies used to synthesize phosphinidenes may be suitable in the search for the first LnM = AsR and LnM = SbR complexes. Additionally, calculations suggest that design of ligand sets which yield linearly coordinated phosphinidenes (and presumably As and Sb analogues) will lead to phosphinidenes with stronger metal-pnictogen bonds and increased thermodynamic stability versus nonlinearly coordinated examples. © 1994 John Wiley & Sons, Inc.
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  • 110
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    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 52 (1994), S. 205-214 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Relativistic pair correlation energies of Xe were computed by employing a recently developed relativistic coupled cluster theory based on the no-pair Dirac-Coulomb-Breit Hamiltonian. The matrix Dirac-Fock-Breit SCF and relativistic coupled cluster calculations were performed by means of expansion in basis sets of well-tempered Gaussian spinors. A detailed study of the pair correlation energies in Xe is performed, in order to investigate the effects of the low-frequency Breit interaction on the correlation energies of Xe. Nonadditivity of correlation and relativistic (particularly Breit) effects is discussed. © 1994 John Wiley & Sons, Inc.
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  • 111
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    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 52 (1994), S. 215-226 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Topological properties of the charge density \documentclass{article}\pagestyle{empty}\begin{document}$ \rho (\vec r) $\end{document} of a series of diatomic molecules, as well as ethane, ethene, and acetylene are calculated at the Hartree-Fock level employing various basis sets, and by the AM1 method. The effect of the core orbitals on the bonding regions in these molecules is examined. The results help to evaluate the utility of AM1 wavefunctions for analyzing the topological properties of the charge density. © 1994 John Wiley & Sons, Inc.
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  • 112
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    International Journal of Quantum Chemistry 51 (1994), S. 343-344 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
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  • 113
    Electronic Resource
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    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 51 (1994), S. 397-405 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Slater-type orbitals (STOs) with a single-exponent by shell or by subshell have been constructed to reduce the number of integrals evaluated in the electronic calculations. The expansion of orbitals in these new basis sets has been carried out in detail for the ground state of the Ne atom. We have carried out a study of STO basis sets with a different size for this atom that could help to propose empirical rules for the selection of these basis sets for other atoms. The usefulness of STOs with single-exponent by shell and subshell and the splitting of s and p functions are discussed. © 1994 John Wiley & Sons, Inc.
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  • 114
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    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 51 (1994), S. 407-415 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: An application of symplectic implicit Runge-Kutta (RK) integration schemes, the s-stage Gauss-Legendre Runge-Kutta (GLRK) methods of order 2s, for the numerical solution of molecular dynamics (MD) equation is described. The two-stage fourth-order GLRK method, the implicit midpoint rule, and the three-stage diagonally implicit RK method of order four are studied. The fixed-point iteraction was used for solving the resulting nonlinear system of equations. The algorithms were applied to a complex system of N particles interacting through a Lennard-Jones potential. The proposed symplectic methods for MD integration permit a wide range of time steps, are highly accurate and stable, and are thus suitable for the MD integration. © 1994 John Wiley & Sons, Inc.
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  • 115
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    International Journal of Quantum Chemistry 51 (1994), S. 425-437 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The rapidly developing field of statistical theory of spectra of many-electron systems is briefly reviewed. In particular, new formal developments, their implementations in studying general properties of the model spaces, and links to the reduction problem are addressed. Applications in molecular and atomic spectroscopy are also discussed. © 1994 John Wiley & Sons, Inc.
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  • 116
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    International Journal of Quantum Chemistry 51 (1994), S. 447-463 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The convergence properties of the expansions of (a) the function 1/r and (b) the function exp(-αr) in an even-tempered basis of Gaussians are studied analytically. The starting points are the Gaussian integral representations of 1/r and exp(-αr). One arrives at an expansion in a finite number of Gaussians in three steps: (1) a restriction of the integration domain, (2) a variable transformation, and (3) discretization of the integral. The cutoff error goes in both cases essentially as exp(-ah), and the discretization error, as exp(-b/h). The minimum overall error is reached for the β-parameter of an even-tempered basis β ∽ exp(c/√n), where n is the dimension of the basis, and the error itself decreases as ∊ ∽ exp(-d√n). Different optimum basis parameters are obtained depending on which quantity one wants to minimize, e.g., the error of the energy expectation value, the distance in Hilbert space, the variance of the energy, or the density at the nucleus. © 1994 John Wiley & Sons, Inc.
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  • 117
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    International Journal of Quantum Chemistry 51 (1994), S. 473-485 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Quantum Chemistry can today boast the fact that ordinary chemists - by means of personal computers and programs available - can study many theoretical properties of molecules by solving the Schrödinger equation and get an advance idea of how to properly arrange their experiments to find new features. For small molecules, they can use ab initio programs of the Hartree-Fock type, and for large molecules, they can use semiempirical programs available. To achieve higher accuracy and to include electron correlation properly, however, one has in the ab initio approach to use configurational interaction methods and giant computers, whereas in the semiempirical methods, the effect of correlating is often taken into account in the adjustable parameters forming the basis for this approach. In connection with the ab initio methods, it is further emphasized that the resolvent methods combined with the partitioning technique provide an excellent conceptual and mathematical framework for getting solutions of any accuracy desired, but that most of the programming of this approach remains to be done. Ordinary wave mechanics is valid at absolute zero of temperature, and - in order to include such important chemical concepts as temperature, entropy, free energy, etc. - one has to go over to general quantum theory and the Liouvillian formalism. One can stil start from the Coulombic Hamiltonian, but it becomes of importance to include the nuclear motion properly and preferably on the same level as that of the electronic motion. It is further emphasized that the irreversibility problem is not yet fully solved, that the theory of the interaction between matter and electromagnetic fields still needs some improvements, and that the question of the proper introduction of relativistic corrections in the quantum theoretical treatment of molecular systems involving heavier atoms still has a great deal to desire. © 1994 John Wiley & Sons, Inc.
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  • 118
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A microscopic formulation of solution chemical reactions, taking reactants and medium structures into consideration, is presented on the basis of microscopic understandings obtained by recent quantum chemical methods (i.e., ab initio molecular orbital theory, etc.). Assuming thermal equilibrium of the medium bath, an effective internal Hamiltonian is derived, and, further, its derivative with respect to internal normal coordinates is proved explicitly to give the same force field as is provided by the free-energy surface or potential of mean force. The free-energy surface can be expressed in the composite normal coordinate system (CNCS) consisting of some normal coordinate systems of isolated reactants and surrounding solvent molecules (i.e., medium solvent molecules). In CNCS, in use of diagonal elements obtained in the Hessian matrix of the free-energy surface, effective normal-mode frequencies, which reflect the equilibrium solvent effect, are estimated. Furthermore, on the generalized Langevin equation (GLE) treatment, a closed expression of the time-dependent frictional coefficient is derived on a microscopic basis, reflecting the reactant and solvent structures. The nonequilibrium effect is estimated by an analytical expression similar to that in the Grote-Hynes theory. The rate constant is evaluated for a typical model system and it is shown that the equilibrium rate constants should be reduced by a factor 0.997. Finally, it is concluded that the present microscopic theory is reasonably applicable to the estimation of chemical reaction rate constants in solution. © 1994 John Wiley & Sons, Inc.
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  • 119
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A number of physical processes, such as autoionization, predissociation, ac- or dc-field-induced ionization, multiphoton dissociation, or chemical transformations, can be formulated as problems involving a nonstationary state satisfying a time-independent complex eigenvalue Schrödinger equation (CESE). The CESE gives rise to all the conceptual and practical difficulties associated with the polyelectronic structures of excited states, as well as novel ones due to the presence of external fields and to the physical significance of the continuous spectrum. In a series of articles from this institute, it has been shown how advanced electronic structure theory and methods suitable for excited states can be integrated in a practical way into selected elements of the rigorous theory of discrete states interacting with the continous spectrum in order to solve the CESE nonperturbatively and efficiently and compute properties such as positions and widths of inner hole or multiply excited states, multiphoton ionization rates, multichannel predissociation lifetimes, nonlinear static and frequency-dependent polarizabilities, and tunneling rates. The present article constitutes a review of the basic features of this theory and its computational methods. © 1994 John Wiley & Sons, Inc.
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  • 120
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    International Journal of Quantum Chemistry 52 (1994) 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
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  • 121
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    International Journal of Quantum Chemistry 51 (1994), S. 569-575 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A method for finding the chemical potential for an electronic system with density ρ = Σρi represented within the Kohn-Sham approximation is proposed. To find the chemical potential of the system under consideration, we propose to refer to the definition μ = δE/δρ and to apply the mathematical properties of functional derivatives. Particularly, in the case examined, the result μ = μ(r) ≠ const has been obtained, which may be explained in the framework of the calculus of variation. Taking the limit limr→∞ μ(r) as the best approximation to the proper equilibrium chemical potential of a free atom, one obtains μ = -I, where I denotes first ionization energy. A possibility of further applications of the proposed method in relation to crystalline systems is also discussed. © 1994 John Wiley & Sons, Inc.
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  • 122
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    International Journal of Quantum Chemistry 52 (1994), S. 339-348 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The hydration energies of the proton, hydroxyl ion, and several inorganic ions were calculated using the multicavity self-consistent reaction field (MCa SCRF) method developed for the quantum-mechanical modeling of rotationally or flexible systems in dielectric media. The ionic complexes H3O+(H2O)4, OH-(H2O)4, NH4+(H2O)4, and Hal-(H2O)4, where Hal = F, Cl, or Br, have been studied. Each complex was divided between five spheres, corresponding to the central ion and four water molecules in their first coordination sphere, respectively. Each cavity was surrounded by a polarizable medium with the dielectric permittivity of water at room temperature (80). The ionic hydration energies of ions were divided into specific and nonspecific parts. After accounting for the cavity-formation energy using scaled particle theory, good agreement between the total calculated and experimental hydration energies was obtained for all ions studied. © 1994 John Wiley & Sons, Inc.
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  • 123
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    International Journal of Quantum Chemistry 52 (1994), S. 89-96 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: We presnet a theoretical study of the effect of the conjugation length on the electronic properties and second-order molecular polarizabilities β in p-amino-p′-nitrodiphenylacetylene molecules where the number of triple bonds in the conjugated segment varies from 1 to 4. The β values are calculated via an intermediate neglect of differential overlap/single configuration interaction (INDO/SCI) sum-over-states (SOS) approach. We test the convergence of the SOS method and the validity of the two-state model to describe the β response. The results indicate that increasing the conjugation length results in a decrease of the charge transfer within the molecule. The two-state model is shown to break down as the conjugated segment extends to four triple bonds; this is due to the appearance of several low-lying nearly isoenergetic excited states that significantly contribute to the β response. The theoretical results are in excellent agreement with recent experimental data. © 1994 John Wiley & Sons, Inc.
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  • 124
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Based on the generalized relationship for calculating the nuclear spin-spin coupling constants and the correlation of the bond stretching frequencies with the coupling constants, a novel generalized reationship, which includes the contributions of not only the hybrid orbitals, but also the net atomic charges, is introduced for calculation of the bond stretching frequencies and employed to elucidate the C—H stretching frequencies in hydrocarbons and heterosubstituted hydrocarbons on the basis of the MBOHO calculation employing the CNDO/2 approximation. By use of the obtained concrete realtionships, one can get different νCH value for the C—H bonds existing in different chemical environments, which is coincident with chemical intuition. The calculated numerical results show that for hydrocarbons the contribution of the net atomic charges can be neglected, but it is necessary for heterosubstituted hydrocarbons to include the contribution of the net atomic charges to the C—H stretching frequencies. The calculated C—H stretching frequencies are in good ageement with the experimental data, which shows its reasonableness. © 1994 John Wiley & Sons, Inc.
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  • 125
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    International Journal of Quantum Chemistry 52 (1994), S. 135-146 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The so-called shake-up satellites accompanying C1s photoionization in C60 have been studied theoretically by means of INDO/CI. It is found that the lowest shake-up satellites in C60 correspond to global charge-transfer excitions that move charge from the opposite side of the fullerence cage to the core-hole region, whereas higher-energy satellites tend to move charge from regions nearer to the core hole. Analogies are drawn, with, on the one hand, smaller model molecules such as napthalene and acenaphtylene and, on the other hand, infinite systems such as graphite. © 1994 John Wiley & Sons, Inc.
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  • 126
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    International Journal of Quantum Chemistry 52 (1994), S. 165-175 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A Hamiltonian model to describe molecular vibrations of triatomic molecules is proposed. The Hamiltonian is based on the use of the Kratzer potential variable for the stretching motions and a perturbed Poschl Teller potential for the bending one. The perturbation and variational treatments to compute the vibrational energies of this Hamiltonian can be developed using a zero-order system that includes part of the couplings between the stretching and bending motions. All the matrix elements involved in these calclations can be then evaluated in closed form. A numerical application to the HCN molecule is made. © 1994 John Wiley & Sons, Inc.
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  • 127
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    International Journal of Quantum Chemistry 52 (1994), S. 247-265 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Electron density theory is first employed to express the potential energy curve of the H2+ molecular ion in terms of bond midpoint properties. For heavy homonuclear diatomics, low-ordr density gradient theory is used, but now for the chemical potential, with a similar conclusion to that for H2+. Homonuclear clusters of alkali atoms are then treated in some detail. Finally the dissociation of doubly charged clusters is considered, by a study of supermolecular treated in some detail. Finally the dissociation of doubly charged clusters is considered, by a study of supermolecular ions (Na20+)2 and (K20+)2, again using a density gradient expansion in low order. The deviation between the barrier for fission and the Coulomb barrier is linear in the bond midpoint density over a substantial range of fragment separation. © 1994 John Wiley & Sons, Inc.
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  • 128
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    International Journal of Quantum Chemistry 52 (1994), S. 211-225 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Coupled-cluster (CC) methods at the level of CCSD, CCSD+T(CCSD), CCSD(T), CCSDT-1, and CCSDT-3 are applied to calculations of the dipole moment and polarizability of the CN molecule, ionization potentials and electron affinities of the oxygen and iron atoms and CN molecule, and the energy splitting of the 5D and 5F states of the iron atom. Both UHF and ROHF references are applied. Extended basis sets are used in some comparison of CC data to experiment. All calculated atomic and molecular properties are known as challenging problems, suitable for a careful analysis of the performance of sophisticated versions of the CC approach. Attention is paid to energy terms distinguishing CCSD(T) from CCSD+T(CCSD). We exploit results from various iterative and noniterative high-level CC methods in the assessment of error bars in calculations of atomic and molecular properties. © 1994 John Wiley & Sons, Inc.
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  • 129
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    International Journal of Quantum Chemistry 52 (1994), S. 481-500 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: We report some of our recent results from theoretical modeling of the interaction between metals and π-conjugated molecules. We apply the semiempirical Austin Model 1 method for the investigation of two fundamentally different systems: sodium interacting with diphenylpolyenes and aluminum interacting with poly (p-phenylenevinylene) and derivatives. In the former case, electronic-structure calculations are also performed using the nonempirical pseudopotential Valence Effective Hamiltonian (VEH) technique. For sodium interacting with diphenylpolyenes, we investigate the geometric and electronic structure modifications that are induced upon charge transfer in a series of diphenylpolyenes with an even number of carbons (from stilbene to α,ω-diphenyltetradecaheptaene, i.e., one to seven double bonds in the polyene part of the molecule). Densities of valence states generated from the VEH calculations are directly compared to experimental ultraviolet photoelectron spectroscopy valence band spectra; these are recorded during successive sodium exposure of the molecular solids. The charge-storage states in the series are discussed in terms of soliton-antisoliton-pairs and polaron-like states induced upon doping (reduction). Introducing aluminum atoms onto poly (p-phenylenevinylene) systems allows us to study the initial stages of interface formation. We find that aluminum atoms preferentially react with the vinylene linkages in both poly (p-phenylenevinylene) and poly (2,5-dimethoxy-p-phenylenevinylene). When carbonyl groups appear on the side of the chains, as in poly (2,5-dialdehyde-p-phenylenevinylene), new reactive sites are induced, leading to structures with stabilities comparable to those in the most stable configurations involving a single vinylene group. In all three systems investigated, the interaction with aluminum induces major modifications of the polymer chains with interruptions of the π-system caused by formation of sp3-like defects. © 1994 John Wiley & Sons, Inc.
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  • 130
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    International Journal of Quantum Chemistry 52 (1994), S. 553-563 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The energy surfaces of Mn+/SCN- and Mn+/OCN- (M = Li+ and Mg2+) ion pairs have been calculated at the Hartree-Fock and MP2 levels of theory. The electrostatic potential and the actual binding energies are compared. Besides linear ion pairs, nonlinear ones are also found and are in some cases the most stable ones. The electrostatic potential and the actual binding to cations are compared. © 1994 John Wiley & Sons, Inc.
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  • 131
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    International Journal of Quantum Chemistry 52 (1994), S. 541-551 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The minimum-energy structures and bonding properties of the hydrogenated lithium clusters, Li4H2 and Li7H, have been investigated by means of an ab initio Monte Carlo simulated annealing method. The minimum-energy structures of Li4H2 and Li7H are found to resemble those of the triangular planar (D3h) isomer of Li6 and Td isomer of Li8 clusters, respectively. © 1994 John Wiley & Sons, Inc.
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  • 132
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    International Journal of Quantum Chemistry 52 (1994), S. 329-337 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The full-optimized-APSG approach based on the MC SCF technique is developed and applied to study ground-state properties of one-dimensional correlated systems. The effects of electron-electron interactions and bond relaxation are considered for the conjugated diatomic polymer; charge distribution and bond relaxation are calculated for the N = 50 chain within a wide range of site energy and e-e integral modulation involving the case of alternancy symmetry for diatomic systems. With relation to the results obtained, the problem of the neutral-ionic transition in mixed-stack crystals is discussed. © 1994 John Wiley & Sons, Inc.
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  • 133
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    Topics: Chemistry and Pharmacology
    Notes: The basic concepts of fractal geometry are reviewed and applied to quasi-two-dimensional zinc electrodeposits. Among the different structures developed during zinc electrodeposition, we have identified the open texture (obtained at large zinc sulfate concentration and small applied potential values) as a typical fractal self-similar structure. © 1994 John Wiley & Sons, Inc.
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  • 134
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    International Journal of Quantum Chemistry 52 (1994), S. 465-478 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Results of density functional calculations will be reported on a variety of hydrogen-bonded complexes, ranging from weak to strong hydrogen bonds. The charged bimolecular NH3—NH4+ complex and the dimers of water and methanol were investigated using a local approximation of the exchange-correlation potential and two different nonlocal potentials with gradient corrections. In the case of the water dimers, the dependence of the results on the extension of the atomic basis set has also been investigated. The equilibrium structures of all complexes have been determined. Dipole moments, hydrogen-bond lengths, and hydrogen-bonding energies, calculated with corrections for the basis-set superposition error using the counterpoise method, have been found to agree well with the corresponding experimental results. © 1994 John Wiley & Sons, Inc.
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  • 135
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    International Journal of Quantum Chemistry 52 (1994), S. 457-463 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Although several authors proposed the existence of long-range correlations in DNA sequences [W. Li and K. Kaneko, Europhys. Lett. 17, 655 (1992); R.F. Voss, Phys. Rev. Lett. 68, 3805 (1992); C.-K. Peng et al., Nature 356, 168 (1992)], we claim that the real character of the correlations remains uncertain. To corroborate long-range correlations, one should prove that the correlation functions decay as an inverse power of the distance between the nucleotides in the DNA sequence. Instead of a direct calculation of the correlation functions, one can calculate either the Fourier transforms of the sequences or the characteristics of “DNA walk.” In our previous work we pointed out that the character of the results depends upon the way the DNA sequences are chosen. When looking for the correlations separately in introns and separately in exons, we found that the resulting correlations are short range. In this work, we discuss the numerical aspects of two computational approaches: the calculation of correlation function and the evaluation of “DNA walk” characteristics. We present the analytic results for the case of exponential correlations. © 1994 John Wiley & Sons, Inc.
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  • 136
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    International Journal of Quantum Chemistry 52 (1994), S. 491-506 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Quantum chemical calculations for two different kinds of native proteins (pig insulin and hen egg white lysozyme) were done by the extended negative factor counting method in which the matrix elements have been calculated at the ab initio level with the help of a minimal basis and the simulation of the aqueous solution environment. The hopping conductivities were worked out by the formulas of the random walk theory of Lax and co-workers. The electronic density of states of these native proteins confirmed the conclusions obtained previously from aperiodic model peptides chains. The results show that the ac conductivity vs. frequency curve of these native proteins lies in the range of some typical good inorganic amorphous conductors and thus confirm that proteins, if doped, are amorphous conductors. The behavior of the ac conductivities of the proteins in different ranges of frequencies are discussed. © 1994 John Wiley & Sons, Inc.
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    International Journal of Quantum Chemistry 52 (1994), S. 625-632 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: We test an exchange-correlation functional with explicit dependence on kinetic-energy density as well as the density, its gradient, and its Laplacian, on the Gaussian-2 thermochemical data base. With a small degree of exact-exchange mixing, we find average errors with respect to experiment of order 2 kcal/mol, 0.15 eV, and 2 kcal/mol, respectively, for atomization energies, ionization potentials, and proton affinities. © 1994 John Wiley & Sons, Inc.
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  • 138
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    International Journal of Quantum Chemistry 52 (1994), S. 633-644 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The Density-Functional method, with Linear Combination of Atomic Orbitals, has been applied to eight crystals: the lattice equilibrium parameters, and the lattice formation energies have been calculated at the Hartree-Fock level (HF), at the hybrid Hartree-Fock Density-Functional level (DFT/HF), and at the Kohn-Sham Density-Functional level (DFT). The band structures and the electronic charge distributions calculated at the DFT and HF levels are compared. © 1994 John Wiley & Sons, Inc.
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  • 139
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    International Journal of Quantum Chemistry 52 (1994), S. 767-797 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: We obtain an analytic expression for the total energy of a metallic cluster formed by N atoms of valence v and with net charge Q, by solving variationally the extended Thomas-Fermi version of density functional theory within the spherical jellium model. The energy is expressed as an expansion (mass formula) in decreasing powers of the cluster radius RI = rsZ1/3, with Z = vN, and rs, the one electron radius of the bulk, \documentclass{article}\pagestyle{empty}\begin{document}$$ E\left( {r_s ,Z,Q} \right) = \sum\limits_{n = - 2}^3 {a_n \left( {r_s } \right)Z^{n/3} + Q\sum\limits_{n = 0}^2 {W_n \left( {r_s } \right)Z^{ - n/3} + \frac{1}{2}\frac{{Q2}}{{R_I + d\left( {r_s } \right)}},} } $$\end{document} and the coefficients of this mass formula are functions of rs. Contributions of volume (RI3), surface (RI2), curvature (RI), constant (RI0), (1/RI), and (1/RI2) are clearly separated in the formula. The Chemical potential, work function, electron affinity, and ionization potential are easily obtained for neutral and charged clusters of any electronic density in the metallic range. A general estimation of the critical size for stability against electron detachment of negatively charged clusters is also obtained. The stability of highly charged clusters against fragmentation is also studied. © John Wiley & Sons, Inc.
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  • 140
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    International Journal of Quantum Chemistry 52 (1994), S. 957-961 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The applicability of the local density approximation (LDA) and of corresponding gradient corrections (for the exchange and correlation energy) for the treatment of the hydrogen bond is investigated. As test systems, we consider the water dimer and the H2O…HX complexes (X = F, Cl, Br): Using an LCAO scheme, their equilibrium geometries and interaction energies are ćalculated and compared with experimental data and with other calculations. We obtain that the LDA gives the geometries in qualitative agreement with other data, whereas the energies are overestimated. The use of the gradient corrections (GC) according to Becke and Perdew leads to a significant improvement of the geometry, and especially of the interaction energies. The calculations indicate further that LDA + GC should also be able to describe weaker intermolecular interactions than the usual hydrogen bond. Finally, a short discussion of the charge distribution and the dipole moments of the H2O…HX complexes is performed. © 1994 John Wiley & Sons, Inc.
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  • 141
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    International Journal for Numerical Methods in Engineering 37 (1994), S. 1481-1497 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A procedure for the optimization of stretched triangular grids is described. The method is based on the construction and minimization of a function that represents a generalized version for stretched grids of a non-linear spring system. The function is minimized using a gradient method based on the steepest descent. Examples are provided to show the applicability of the method to computational fluid dynamics problems.
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  • 142
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    International Journal for Numerical Methods in Engineering 37 (1994), S. 1465-1480 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Multigrid method is used to accelerate the convergence of the numerical solution of the set of partial differential equations for generating the Body-Fitted Co-ordinate system (BFC) for both simply and doubly connected domain problems. The multigrid method is based on the full approximation scheme with bilinear interpolation as prolongation operator. The other components of the multigrid method such as the relaxation method, restriction operator, number of relaxation sweeps per cycle and direction of relaxation sweeps are varied with a view to obtaining the general principle in implementing an efficient multigrid algorithm for the generation of the BFCs.
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  • 143
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    International Journal for Numerical Methods in Engineering 37 (1994), S. 1531-1555 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In Part I of this work, Paulino et al.1 have presented an algorithm for profile and wavefront reduction of large sparse matrices of symmetric configuration. This algorithm is based on spectral properties of a Finite Element Graph (FEG), An FEG has been defined as a nodal graph G, a dual graph G* or a communication graph G· associated with a generic finite element mesh. The novel algorithm has been called Spectral FEG Resequencing (SFR). This algorithm has specific features that distinguish it from previous algorithms. These features include (1) use of global information in the graph, (2) no need of a pseudoperipheral vertex or the endpoints of a pseudodiameter, and (3) no need of any type of level structure of the FEG. To validate this algorithm in a numerical sense, extensive computational testing on a variety of problems is presented here. This includes algorithmic performance evaluation using a library of benchmark test problems which contains both connected and non-connected graphs, study of the algebraic connectivity (λ2) of an FEG, eigensolver convergence verification, running time performance evaluation and assessment of the algorithm on a set of practical finite element examples. It is shown that the SFR algorithm is effective in reordering nodes and/or elements of generic finite element meshes. Moreover, it computes orderings which compare favourably with the ones obtained by some previous algorithms that have been published in the technical literature.
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  • 144
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    International Journal for Numerical Methods in Engineering 37 (1994), S. 1557-1572 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: To exploit the benefits of parallel computer architectures for multibody system simulation, an interdisciplinary approach has been pursued, combining knowledge of the three disciplines of dynamics, numerical mathematics and computer science. An analysis of the options available for the formulation and numerical solution of the dynamical system equations yielded a surprising result. A method initially proposed to solve the inverse problem of dynamics is the best choice to generate the system equations required for solving the simulation problem, when relying on implicit integration routines. Such routines have the particular advantage of handling stiff systems, too. The new O(N)-residual formalism, generating the system equations in a form required for implicit numerical integration, has a high potential to benefit from parallel computer architectures. Two strategies of medium and coarse grain parallelization have been implemented on a Transputer network to obtain a package for parallel multibody simulation. An analysis of the performance of this package demonstrates for typical multibody simulation problems that the new code is five times faster than existing codes when implemented on a serial computer. An additional speed-up by the same order of magnitude is obtained when the code is implemented on a Transputer network.
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    International Journal for Numerical Methods in Engineering 37 (1994), S. 181-201 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A general Finite Volume Method (FVM) for the analysis of structural problems is presented. It is shown that the FVM can be considered to be a particular case of finite elements with a non-Galerkin weighting. For structural analysis this can readily be interpreted as equivalent to the unit displacement method which involves mainly surface integrals. Both displacement and mixed FV formulations are presented for static and dynamic problems.
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  • 146
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    International Journal for Numerical Methods in Engineering 37 (1994), S. 229-256 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An element-free Galerkin method which is applicable to arbitrary shapes but requires only nodal data is applied to elasticity and heat conduction problems. In this method, moving least-squares interpolants are used to construct the trial and test functions for the variational principle (weak form); the dependent variable and its gradient are continuous in the entire domain. In contrast to an earlier formulation by Nayroles and coworkers, certain key differences are introduced in the implementation to increase its accuracy. The numerical examples in this paper show that with these modifications, the method does not exhibit any volumetric locking, the rate of convergence can exceed that of finite elements significantly and a high resolution of localized steep gradients can be achieved. The moving least-squares interpolants and the choices of the weight function are also discussed in this paper.
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  • 147
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    International Journal for Numerical Methods in Engineering 37 (1994), S. 37-48 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A pseudo-transient (static) linear, geometric, material and combined geometric and material non-linear analyses of composite laminates are presented. A nine-noded isoparametric quadrilateral finite element belonging to the Lagrangiar family is used in space discretization. An explicit time marching scheme is employed for time integration of the resulting discrete ordinary differential equations with the special forms of diagonal fictitious mass and/or damping matrices. Elasto-plastic material behaviour is incorporated using the flow theory of plasticity. In particular, a modified version of Hill's initial yield criterion is used in which anisotropy parameters of plasticity are introduced. The shear deformation is accounted for by assuming a constant transverse shear strain across the thickness of the laminate and the geometric non-linearity is considered in the sense of von Karman strains. The layered element approach is adopted for the treatment of plastic behaviour through the thickness. A wide range of numerical examples is presented to demonstrate the validity and efficiency of the present approach. The results for combined non-linearity are also presented. The variety of results presented here, which are based on realistic material properties of often-used advanced laminated composite plates, and especially those for combined non-linear analysis, should serve as a reference for future investigations.
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    International Journal for Numerical Methods in Engineering 37 (1994), S. 91-105 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A variationally coupled finite element-boundary element method is developed for transient problems. A single variational statement is obtained for the entire domain and the unknown tractions, which may be discontinuous on the interface and are often a source of difficulties, are eliminated. Moreover, no interface conditions need be taken into consideration at the level of the discretized equation. The discrete equations for the coupled system can be obtained directly without any intermediate steps. The method generalizes a coupling method previously developed by the authors for statics. Numerical examples show that the solutions obtained by the present method agree very well with those obtained by analytical solutions.
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    International Journal for Numerical Methods in Engineering 37 (1994), S. 431-455 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A six-node triangle plate/shell element is developed for the analysis of laminated composite structures. This model is formulated using Hamilton's principle along with a first-order (Reissner/Mindlin) shear deformation theory. The element is based upon an isoparametric representation along with an interdependent interpolation strategy; bicubic polynomials for the transverse displacement and biquadratic polynomials for the element geometry, in-plane displacements and rotations. The resulting element, which is evaluated using exact numerical integration, has correct rank and is free of shear ‘locking’. Numerical results are presented that validate the new element and prove its outstanding convergence capabilities in comparison to existing triangular elements using standardized test problems (elastic eigenvalue analysis, patch test, static simply supported square-plate solutions) and experimentally measured vibration data of cantilevered isotropic and composite plates.
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    International Journal for Numerical Methods in Engineering 37 (1994), S. 475-496 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The collapse of ordinary finite elements to generate the desired strain singularity at the crack tip for fracture mechanics applications can lead to unwanted additional singularities in that area. Although neither the quarter-point nor the half-point 8-node two-dimensional (2-D) and 20-node three-dimensional (3-D) elements exhibit this behaviour, the present article proves that arbitrarily small deviations from the quarter-point element can be constructed which do have additional singularities. Since the general behaviour of the half-point element is not affected by small modifications, this element is better suited to match complex body geometries.
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    International Journal for Numerical Methods in Engineering 37 (1994), S. 537-538 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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  • 152
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    International Journal for Numerical Methods in Engineering 37 (1994), S. 517-536 
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    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: The superconvergent patch derivative recovery method of Zienkiewicz and Zhu is enhanced by adding the squares of the residuals of the equilibrium equation and natural boundary conditions. In addition, a new conjoint polynomial for interpolating the local patch stresses over the element which significantly improves the local projection scheme is presented. Results show that in the 4-node quadrilateral, the equilibrium and boundary condition residuals usually improve accuracy but not the rate of convergence, whereas in the 9-node quadrilateral, results are mixed. The conjoint polynomial always improves the accuracy of the derivative field within the element as compared to the standard nodal interpolation, particularly in 4-node quadrilaterals.
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    International Journal for Numerical Methods in Engineering 37 (1994), S. 279-296 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: An hybrid stress element formulation based on internal, incompatible displacements is used to develop efficient Mindlin plate elements. The 4-node quadrilateral Mindlin plate element is derived from a modified energy functional. Both displacements and stresses are defined in the natural co-ordinate interpolation system. The assumed stress field is obtained by tensor transformation and so chosen as to ensure that the element is co-ordinate invariant and stable. Shear locking is avoided through an appropriate identification of the internal, incompatible displacement field. The role played by incompatible displacements in the formulation of hybrid stress elements for thin and moderately thick plates is discussed. Numerical applications are presented to illustrate the accuracy and reliability of the suggested Mindlin plate element.
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  • 154
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    International Journal for Numerical Methods in Engineering 37 (1994), S. 605-621 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: In the present paper, we analyse the computational performance of the Lanczos method and a recent optimization technique for the calculation of the p (p ≤ 40) leftmost eigenpairs of generalized symmetric eigenproblems arising from the finite element integration of elliptic PDEs. The accelerated conjugate gradient method is used to minimize successive Rayleigh quotients defined in deflated subspaces of decreasing size. The pointwise Lanczos scheme is employed in combination with both the Cholesky factorization of the stiffness matrix and the preconditioned conjugate gradient method for evaluating the recursive Lanczos vectors. The three algorithms are applied to five sample problems of varying size up to almost 5000. The numerical results show that the Lanczos approach with Cholesky triangularization is generally faster (up to a factor of 5) for small to moderately large matrices, while the optimization method is superior for large problems in terms of both storage requirement and CPU time. In the large case, the Lanczos-Cholesky scheme may be very expensive to run even on modern quite powerful computers.
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  • 155
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    International Journal for Numerical Methods in Engineering 37 (1994), S. 387-411 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: A new eight-node quadrilateral shear-bending Reissner-Mindlin plate finite element for the very thin and thick plates without locking and spurious zero-energy modes is presented. The element has very good convergence characteristics both for thin and thick plates, is hardly insensitive to mesh distortions, and passes the patch tests. The formulation of the element is derived from a displacement variational principle and some general criteria to compute inconsistent transverse shear strains. These criteria have been applied with success to four- and eight-node quadrilateral plate finite elements and could be applied to construct triangular elements. The eight-node quadrilateral shear-bending plate finite element proposed has been found to be very efficient.
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  • 156
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    International Journal for Numerical Methods in Engineering 37 (1994), S. 457-474 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: A theory is proposed in this paper to explain, in a unified manner, the three rational approaches using the incompatible displacements uλ in the hybrid element formulation. Limited to the plane stress case, the theory suggests that the introduction of uλ is to constrain the total value of the invariant I2(= σxσy - τxy2) of the assumed stresses over the element to zero. In the plane stress case, this is the well-known condition for the stress distributions to be independent of the elastic constants of the material. The theory proposed is also used to explain the closeness of the performances of the four 4-node hybrid stress membrane elements, 5β-I, 5β-II, 5β-A and 5β-C, that have been developed previously. The differences among them are shown to be of the second degree in the distortion measures of the element shape, when they are compared on the basis of the non-vanishing total value of I2 of their respectively adopted assumed stress field. Several numerical examples are used to verify and to illustrate the proposed theory.
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  • 157
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    International Journal for Numerical Methods in Engineering 37 (1994) 
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  • 158
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    International Journal for Numerical Methods in Engineering 37 (1994), S. 1825-1840 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: This paper presents a boundary element formulation for the permanent Navier-Stokes equations in which the well-known closed-form fundamental solution for the steady Stokes equations is employed. In this way, from the integral representation formulae for the Stokes' equations, an integral equation is found in which the original non-linear convective terms of the Navier-Stokes equations appear as a domain integral. Additionally, the method of dual reciprocity is used to transform the domain integral to boundary integrals (this method is closely related to the method of particular integrals also used in the literature to transform domain integrals to boundary integrals). Numerical results are presented for the three-dimensional internal flow in a cylindrical container with a rotating cover, in which the accuracy of the method is shown.
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  • 159
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    International Journal for Numerical Methods in Engineering 37 (1994), S. 2291-2309 
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    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: The helicoidal beam model developed in the first part of this work is applied here to the development of a mixed finite element for space-curved and twisted beams undergoing large displacements and finite rotations. Starting from the governing weak form expressed by the principle of virtual work, a consistent linearization is obtained in the following and a novel updated Lagrangian finite element implementation is thoroughly discussed.The unique features and the distinguishing properties previously claimed for the helicoidal model are shown here to imply remarkable numerical consequences. For this purpose, meaningful example problems regarding the non-linear static response of beams are addressed in the following and the results are compared with those available from the literature.Furthermore, a finite element in time for the rigid body dynamic problem is developed within the framework of the helicoidal geometry. The underlying philosophy of this novel finite element for dynamics is the realization of the helicoidal decomposition of the rigid body motion within a time step.
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    International Journal for Numerical Methods in Engineering 37 (1994) 
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    International Journal for Numerical Methods in Engineering 37 (1994), S. 2311-2335 
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    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: A finite element approach for shape optimization in two-dimensional (2-D) frictionless contact problems is presented in this work. The goal is to find the shape that gives a constant distribution of stresses along the contact boundary.The whole formulation, including mathematical model for the unilateral problem, sensitivity analysis and geometry definition is treated in a continuous form, independently of the discretization in finite elements. Shape optimization is performed by direct modification of geometry through B-spline curves and an automatic mesh generator is used at each new configuration to provide the finite element input data for numerical analysis and sensitivity computations. Using augmented-Lagrangian techniques (to solve the contact problem) and an interior-point mathematical-programming algorithm (for shape optimization), we obtain several results reported at the end of the article.
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    International Journal for Numerical Methods in Engineering 37 (1994), S. 2337-2338 
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    International Journal for Numerical Methods in Engineering 37 (1994), S. 1881-1896 
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    Notes: This paper presents the first endeavour to exploit a generalized differential quadrature method as an accurate, efficient and simple numerical technique for structural analysis. Firstly, drawbacks existing in the method of differential quadrature (DQ) are evaluated and discussed. Then, an improved and simpler generalized differential quadrature method (GDQ) is introduced to overcome the existing drawback and to simplify the procedure for determining the weighting coefficients. Subsequently, the generalized differential quadrature is systematically employed to solve problems in structural analysis. Numerical examples have shown the superb accuracy, efficiency, convenience and the great potential of this method.
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    International Journal for Numerical Methods in Engineering 37 (1994), S. 3015-3018 
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    International Journal for Numerical Methods in Engineering 37 (1994), S. 3019-3021 
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    International Journal for Numerical Methods in Engineering 37 (1994) 
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    International Journal for Numerical Methods in Engineering 37 (1994), S. 3005-3014 
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    Notes: Since Soize introduced the concept of fuzzy structures in structural acoustics there has been little activity clarifying the basic elements which underlie his theory. Soize's papers are not easy reading due to the high level of mathematical formalism. In addition Soize simultaneously bases this fuzzy structure theory on two components: (1) a model for one Degree Of Freedom (DOF) fuzzy oscillators, and (2) a medium frequency solution method developed previously. It is unclear as to the role of the two components, although others have already undertaken a study of the medium frequency method by itself.In the present paper a fundamental analysis of the first component, the one-DOF fuzzy oscillators, is undertaken. The symbolic manipulation program Mathematica is utilized to gain insight into this component of Soize's fuzzy theory. The resulting Mathematica simulations are easy to use and interpret, and they provide valuable insight into the parameters composing Soize's fuzzy oscillators. It is determined that in many cases of structural acoustics, where there is small damping and a medium to high modal density, the fuzzy mass primarily determines what effect a discrete fuzzy oscillator will have as an attachment.
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    International Journal for Numerical Methods in Engineering 37 (1994), S. 3023-3036 
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    Notes: A new numerical approach has been devised for performing accurate absorbing-emitting non-scattering radiation calculations for Cartesian co-ordinate based problems with one ordinate symmetry using only the solution plane formed by the other two ordinates. To accomplish this, the method makes use of ‘effective intensity rays’ which only exist and have meaning in the solution plane of the problem but which are made, through a special procedure, to contain the information of the third dimension. This novel procedure thus eliminates the problem of solid angles and greatly reduces both the complexity and computational expense involved in the solution of such problems. Yet it can do this without producing loss in accuracy. The approach is ultimately intended for use in combustion problems involving high temperatures and optically thin media. For verification purposes the method is applied to the problem of heat exchange in infinitely long rectangular enclosures and is found to give excellent results over a optical thickness range that includes the optically very thin case.
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    International Journal for Numerical Methods in Engineering 37 (1994), S. 1978-1979 
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    International Journal for Numerical Methods in Engineering 37 (1994), S. 2525-2525 
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    International Journal for Numerical Methods in Engineering 37 (1994), S. 2005-2039 
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    Notes: A method is described which constructs three-dimensional unstructured tetrahedral meshes using the Delaunay triangulation criterion. Several automatic point creation techniques will be highlighted and an algorithm will be presented which can ensure that, given an initial surface triangulation which bounds a domain, a valid boundary conforming assembly of tetrahedra will be produced. Statistics of measures of grid quality are presented for several grids. The efficiency of the proposed procedure reduces the computer time for the generation of realistic unstructured tetrahedral grids to the order of minutes on workstations of modest computational capabilities.
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    International Journal for Numerical Methods in Engineering 37 (1994), S. 2109-2123 
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    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: A coupled transient thermoelastic behaviour of an axial-cracked hollow circular cylinder subjected to a sudden heating is investigated in this study. It is shown that surface heating may induce the compressive thermal stress near the inner surface of the cylinder which in turn may force the cracked surfaces to close together. Assuming that the existence of the crack does not alter the temperature distribution, we can divide this problem into two parts and solve it by the principle of superposition. First, the temperature and transient thermal stress distributions along the axisymmetric surface of the imaginary cylinder without crack are obtained by finite element implicit time integration method Secondly, the opposite sense of the stress distributions along the cracked surfaces, which is obtained previously, is treated as the traction boundary conditions; the contact length and contact pressure of the real cracked cylinder are obtained by modified elimination finite element scheme. Finally, we also obtained the normalized stress intensity factor for the crack tip of the cylinder. It is concluded that the effect due to thermoelastic coupling term on stress intensity factor becomes more important for higher coupling coefficient, and this coupling term also results in a small time lag in temperature, thermal stress and stress intensity factor.
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    International Journal for Numerical Methods in Engineering 37 (1994), S. 2149-2150 
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    International Journal for Numerical Methods in Engineering 37 (1994), S. 2699-2700 
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    International Journal for Numerical Methods in Engineering 37 (1994), S. 2583-2608 
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    Notes: In continuum mechanics within specific classes of problems, one- or two-dimensional theories are often simpler to apply than the more complete three-dimensional one. This is, for example, the case of thin bodies, such as plates or shells, which may be studied using appropriate two-dimensionai theories.Within this approach, the reduction of the dimension is traded for a loss of information relative to the motion in the transverse direction. For example, in the case of non-linear material behaviour, classical plasticity plate theories are usually not able to model the effects related to the spreading of plasticity through the cross-section.In the present paper we discuss a generalized plasticity plate model, which can be used to reproduce some of the three-dimensional effects in a two-dimensional setting. We present the continuous and the discrete time model, including both isotropic and kinematic hardening mechanisms; moreover, the form of the tangent matrix consistent with the discrete model is addressed.Finally, some examples (cantilever beam, clamped circular plate and clamped square plate under monotonic and cyclic loading) are studied numerically using a three-dimensional classical plasticity theory, a classical plasticity plate theory and the proposed plate theory. The generalized plasticity plate model matches the three-dimensional response with greater accuracy, than the classical plasticity plate model.
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    International Journal for Numerical Methods in Engineering 37 (1994), S. 2679-2697 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: The dynamic behaviour of liquid-filled shells of revolution is investigated considering the soil-structure interaction and the fluid-structure interaction, respectively. In the circumferential direction the loads and variables are approximated by Fourier series. The shell is modelled through shell ring elements including non-linear behaviour, coupled with isoparametric continuum ring elements and special infinite elements for the soil and isoparametric pressure ring elements for the fluid. Transient loadings like earthquake excitation and the non-linearities of the shell and the soil require an analysis in the time domain. To reduce the size of the problem, linear parts of the system are condensed by the substructure technique. The soil region is divided into two parts, a near field permitting non-linearities like plastification or uplifting of the shell, and a far field for the treatment of radiation of energy.The boundary conditions for the shell footing have a strong influence on the distribution of the axial membrane forces and, hence, on the stability limit, which is mostly governed by plastic collapse and caused by the dynamically activated pressure acting on the tank wall. It is shown how the soil properties influence the dynamic stability of the shell under harmonic excitation and under realistic earthquake motion.
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    International Journal for Numerical Methods in Engineering 37 (1994), S. 2701-2702 
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    International Journal for Numerical Methods in Engineering 37 (1994), S. 2717-2733 
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    Notes: This paper presents a Wave Equation Model (WEM) to solve advection dominant Advection-Diffusion (A-D) equation. It is known that the operator-splitting approach is one of the effective methods to solve A-D equation. In the advection step the numerical solution of the advection equation is often troubled by numerical dispersion or numerical diffusion. Instead of directly solving the first-order advection equation, the present wave equation model solves a second-order equivalent wave equation whose solution is identical to that of the first-order advection equation. Numerical examples of 1-D and 2-D with constant flow velocities and varying flow velocities are presented. The truncation error and stability condition of 1-D wave equation model is given. The Fourier analysis of WEM is carried out. The numerical solutions are in good agreement with the exact solutions. The wave equation model introduces very little numerical oscillation. The numerical diffusion introduced by WEM is cancelled by inverse numerical diffusion introduced by WEM as well. It is found that the numerical solutions of WEM are not sensitive to Courant number under stability constraint. The computational cost is economical for practical applications.
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    International Journal for Numerical Methods in Engineering 37 (1994), S. 3825-3842 
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    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: A flat shell element based on the free-formulation finite element concept is developed for analysing geometrically non-linear thin composite shells. A corotational form of the updated Lagrangian formulation is utilized. Numerical results for typical validation problems are presented in order to demonstrate the accuracy and validity of this element. These results are obtained by solving the incremental equilibrium equations through the cylindrical arc-length method.
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    International Journal for Numerical Methods in Engineering 37 (1994), S. 3809-3823 
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    Notes: In this paper we investigate the additional storage overhead needed for a parallel implementation of finite element applications. In particular, we compare the storage requirements for the factorization of the sparse matrices that would occur on a parallel processor vs. a uniprocessor. This variation in storage results from the factorization fill-in. We address the question of whether the storage overhead is so large for parallel implementations that it imposes severe limitations on the problem size in contrast to the problems executed sequentially on a uniprocessor. The storage requirements for the parallel implementation are based upon a new ordering scheme, the combination mesh-based scheme. This scheme uses a domain decomposition method which attempts to balance the processors' loads and decreases the interprocessor communication. The storage requirements for the sequential implementation is based upon the minimum degree algorithm. The difference between the two storage requirements corresponds to the storage overhead attributed to the parallel scheme.Experiments were conducted on regular and irregular, 2-D and 3-D problems. The meshes were decomposed into 2-256 subdomains which can be executed on 2-256 processors, respectively. The total storage requirements or fill-in for most of the 2-D problems were less than a factor of two increase over the sequential execution. In contrast, large 3-D problems had zero increase in storage or fill-in over the sequential execution; the fill-in was less for the parallel execution than the sequential execution. Thus, we conclude that the storage overhead attributed to the use of parallel processors will not impose severe constraints on the problem size. Further, for large 3-D applications, the combination mesh-based algorithm does better than minimum degree for reducing the fill-in.
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    International Journal for Numerical Methods in Engineering 37 (1994), S. 3843-3868 
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    Notes: Incrementally objective integration schemes are proposed for the accurate and efficient determination of design sensitivity coefficients (DSCs) for solid mechanics problems with both material and geometrical non-linearities. The derivation of these schemes are based on the direct differentiation of objective schemes that are used in stress analysis for problems of this class. Two widely used objective stress rates, the Jaumann rate and the Green-Naghdi rate, are considered here within the same setting with only minor changes of the integration scheme. Numerical results are presented for a simple shear problem with different material constitutive laws, including a hypoelastic model and a unified isotropic viscoplastic model, for these two objective rates. The numerical results are compared with analytical solutions or direct integration solutions. The close agreement among these solutions demonstrates the accuracy and efficiency of the proposed scheme.
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    International Journal for Numerical Methods in Engineering 37 (1994), S. 3869-3903 
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    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Development of a finite deformation elasto-plasticity model based on the multiplicative decomposition of the deformation gradient is presented and discussed in detail. The formulation presented in this paper includes the derivation of the full set of equations for the Drucker-Prager yield criterion. The equations, which are not available elsewhere, are developed within a framework using a spectral decomposition approach. Further, expressions for the consistent (algorithmic) tangent moduli in the finite strain regime are developed. Since the finite deformation framework employed to obtain the expressions presented here collapses to the classical infinitesimal plasticity framework when the finite strain assumption is no longer necessary, the finite deformation consistent tangent moduli are compared to the consistent tangent moduli valid for use with infinitesimal plasticity. Validation of the implemented finite deformation elasto-plastic Drucker-Prager model is performed through the solution of the concrete slump test. Comparisons between an existing approximate analytical solution and experimental data are presented, and results are discussed in detail.
    Additional Material: 11 Ill.
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  • 185
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    International Journal for Numerical Methods in Engineering 37 (1994), S. 3905-3919 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper presents a parallel implementation of the boundary element method for MIMD computer architectures to determine the effective properties of two heterogeneous physical systems. The first physical system is comprised of spheres sedimenting in a viscous fluid at low Reynolds numbers. The effective property is characterized by the hindered settling function which is a measure of the average sedimentation velocity. The second physical system is a short-fibre reinforced composite. The effective property for this system is the composite modulus. The determination of effective properties of heterogeneous media requires performing statistical analyses of several realizations of physical systems based on defining characteristics of the media. The boundary element method is particularly well suited for studying such systems because of the simplification in the discretization associated with the method. However, as the number of heterogeneities to be modeled is increased so are the computational demands. Parallel computation offers the opportunity to model systems of greater complexity. We discuss a parallel boundary element formulation based on the torus-wrap mapping. In this approach, blocks of the coefficient matrix associated with the discretized boundary element equations are assigned to processors as opposed to more traditional parallel boundary element implementations where rows or columns are assigned to processors. The torus-wrap mapping can be shown to minimize communication volume between processors during the LU factorization. Therefore, the present formulation scales well with increases in the number of processors.
    Additional Material: 5 Ill.
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  • 186
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    International Journal for Numerical Methods in Engineering 37 (1994), S. 4263-4284 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The use of inconsistent displacement fields for Mindlin plate elements causes unmatched coefficients to appear in shear strain interpolations. The role of the numerical integration order in relation to these unmatched coefficients, and the existence of optimal stress points are explained through the use of the reduced minimization concept. This concept makes it possible to test whether assumed displacement fields or shear strain fields result in inconsistent strain fields which contain spurious constraints. We have included applications of reduced minimization to the conventional C0-continuous elements, which employ reduced integration, and to quadrilateral Mindlin plate elements of Hinton and Huang to demonstrate how these elements alleviate shear locking.
    Additional Material: 4 Ill.
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  • 187
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    International Journal for Numerical Methods in Engineering 37 (1994), S. 715-716 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
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  • 188
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    International Journal for Numerical Methods in Engineering 37 (1994) 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
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  • 189
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    International Journal for Numerical Methods in Engineering 37 (1994), S. 693-713 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A method using techniques of computational geometry for generating tetrahedral finite element meshes in three-dimensional polyhedral regions is presented. The input to the method consists of the boundary faces of the polyhedral region and possibly internal and hole interfaces, plus the desired number of tetrahedra and other scalar parameters. The region is decomposed into convex polyhedra in two stages so that tetrahedra of one length scale can be generated in each subregion. A mesh distribution function, which is either automatically constructed from the first-stage convex polyhedron decomposition or supplied by the user, is used to determine the tetrahedron sizes in the subregions. Then a boundary-constrained triangulation is constructed in each convex polyhedron, with local transformations being used to improve the quality of the tetrahedra. Experimental results from triangulations of three regions are provided.
    Additional Material: 19 Ill.
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  • 190
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    International Journal for Numerical Methods in Engineering 37 (1994), S. 763-775 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The aim of the present study is to show that the developed particle dynamics method is able to describe important characteristics of powder assemblies. In the method, the interaction forces that are introduced between the particles are electrostatic attractive forces and elastic repulsive forces. Energy dissipation by friction at contact surfaces and damping during cohesive collision were also considered. Several numerical experiments on the angle of repose, packing and compaction are carried out. The initial position and the size of the particles are randomly distributed based on the Monte-Carlo method. The simulation results show that the method can be used to evaluate the effect of particle characteristics on flowability of powder assemblies.
    Additional Material: 7 Ill.
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  • 191
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    International Journal for Numerical Methods in Engineering 37 (1994), S. 737-762 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An iterative and incremental algorithm is presented for the Design Sensitivity Analysis (DSA) of elastoplastic structures. Geometrical non-linearity is included in the formulation, and the structure may be subjected to a cyclic loading. The key concept is discussed using an elastoplastic truss. It is shown that the Design Sensitivity Coefficients (DSCs) are path-dependent and discontinuous at the time at which yielding takes place in a member (yield time). In the proposed algorithm, the yield time is considered to be a function of the design variables. In this way, the discontinuity in the DSCs at the material transition points can be overcome in a simple and routine way. Incremental response analysis and DSA are carried out simultaneously using the Newton-Raphson type iterative procedure. Since the proposed algorithm is completely consistent with the analysis procedure, it can be implemented into an existing code for structural analysis. Application to distributed parameter structures with kinematic and/or isotropic hardening is discussed using the von Mises yield condition and the elastic-predictor radial-return method. DSA is carried out for a ten-bar truss with a piecewise linear constitutive relation. It is shown that the DSCs found using the proposed method agree quite well with those calculated by the central difference method. Finally, an alternate method without any iteration for DSA is proposed and the results from the two methods are compared.
    Additional Material: 8 Ill.
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  • 192
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    International Journal for Numerical Methods in Engineering 37 (1994), S. 717-735 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Sheet metal forming is simulated by finite element methods using a stress resultant constitutive law in this paper. A Lagrangian description of axisymmetric and plane-strain shell deformation is first reviewed. Then a stress resultant constitutive law in rate form is presented, where the effect of thickness reduction due to large plastic deformation is considered. A finite element formulation in terms of stress resultants and their work-conjugate generalized strain rates is derived based on the virtual work principle. A hemispherical punch stretching operation and a plane-strain draw operation are simulated by a finite element program based on the finite element formulation. The results of these finite element simulations are in good-agreement with those using the through-the-thickness integration method. The results of the hemispherical punch stretching simulation suggest that the coupling term of moments and membrane forces of the modified Ilyushin yield function should be eliminated to avoid numerical instability under stretching-dominated conditions for this rate-independent plasticity formulation. Further, the results suggest that the hardening rule in a power-law form based on the small-strain approach must be modified to take account for finite deformation effects of combined stretching and bending. Under the plane-strain draw operation, the sheet experiences a large amount of bending before the final stretching. The simulation based on the stress resultant constitutive law can produce this essential aspect of deformation pattern as that of the through-the-thickness integration method, whereas a simulation based on a membrane theory cannot. In conclusion, the results of these simulations indicate that a finite element program based on the stress resultant constitutive law can simulate sheet-forming processes with much shorter computational time than that based on the through-the-thickness integration method.
    Additional Material: 11 Ill.
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  • 193
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    International Journal for Numerical Methods in Engineering 37 (1994), S. 813-826 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A return mapping algorithm is presented for the numerical time integration of the constitutive equations for elastoplasticity with isotropic yield surfaces, constructed from all three invariants of the stress tensor. Based on the first-order backward Euler difference formula (BDF), the governing equations for the stresses are solved in the space of the invariants and the discretized persistence parameter. The stresses are recovered afterwards. The solution concept is applied to a pressure-independent yield function, expressed in terms of the second and third invariant of the stress tensor. The numerical performance of the method is demonstrated with two examples.
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  • 194
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    International Journal for Numerical Methods in Engineering 37 (1994), S. 793-812 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A technique for refining three-dimensional tetrahedral meshes is proposed in this paper. The proposed technique is capable of treating arbitrary unstructured tetrahedral meshes, convex or non-convex with multiple regions resulting in high quality constrained Delaunay triangulations. The tetrahedra generated are of high quality (nearly equilateral). Sliver tetrahedra, which present a real problem to many algorithms are not produced with the new method. The key to the generation of high quality tetrahedra is the iterative application of a set of topological transformations based on the Voronoi-Delaunay theory and a reposition of nodes technique. The computational requirements of the proposed technique are in linear relationship with the number of nodes and tetrahedra, making it ideal for direct employment in a fully automatic finite element analysis system for 3-D adaptive mesh refinement. Application to some test problems is presented to show the effectiveness and applicability of the new method.
    Additional Material: 15 Ill.
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  • 195
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    International Journal for Numerical Methods in Engineering 37 (1994), S. 1027-1038 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The stiffness matrix of a plane four-node quadrilateral finite element is given in closed form. When expressed as a FORTRAN subroutine and compared with the classical method of forming the stiffness matrix using Gaussian integration, the approach gives a CPU time speed-up of the order of 2-3 on a vector machine and of the order of 4-5 on a scalar machine. The technique used to generate the terms of the stiffness matrix made use of a computer algebra system which could clearly be extended to generate the matrices for other elements types.
    Additional Material: 2 Ill.
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  • 196
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    Numerical Linear Algebra with Applications 1 (1994), S. 75-101 
    ISSN: 1070-5325
    Keywords: Variable-step preconditioners ; Nonlinear preconditioning ; Generalized conjugate gradient method ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: When solving large size systems of equations by preconditioned iterative solution methods, one normally uses a fixed preconditioner which may be defined by some eigenvalue information, such as in a Chebyshev iteration method. In many problems, however, it may be more effective to use variable preconditioners, in particular when the eigenvalue information is not available.In the present paper, a recursive way of constructing variable-step of, in general, nonlinear multilevel preconditioners for selfadjoint and coercive second-order elliptic problems, discretized by the finite element method is proposed. The preconditioner is constructed recursively from the coarsest to finer and finer levels. Each preconditioning step requires only block-diagonal solvers at all levels except at every k0, k0 ≥ 1 level where we perform a sufficient number ν, ν ≥ 1 of GCG-type variable-step iterations that involve the use again of a variable-step preconditioning for that level.It turns out that for any sufficiently large value of k0 and, asymptotically, for ν sufficiently large, but not too large, the method has both an optimal rate of convergence and an optimal order of computational complexity, both for two and three space dimensional problem domains.The method requires no parameter estimates and the convergence results do not depend on the regularity of the elliptic problem.
    Additional Material: 8 Tab.
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  • 197
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    Numerical Linear Algebra with Applications 1 (1994), S. 65-74 
    ISSN: 1070-5325
    Keywords: Elasticity ; Finite elements ; preconditioning ; Multilevel ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The basic theory of the strengthened Cauchy-Buniakowskii-Schwarz (C.B.S.) inequality is the main tool in the convergence analysis of the recently proposed algebraic multilevel iterative methods. An upper bound of the constant γ in the strengthened C.B.S. inequality for the case of the finite element solution of 2D elasticity problems is obtained. It is assumed that linear triangle finite elements are used, the initial mesh consisting of right isosceles triangles and the mesh refinement procedure being uniform. For the resulting linear algebraic systems we have proved that γ2〈0.75 uniformly on the mesh parameter and on Poisson's ratio ν ∊ (0, 1/2). Furthermore, the presented numerical tests show that the same relation holds for arbitrary initial right triangulations, even in the case of degeneracy of triangles.The theoretical results obtained are practically important for successful implementation of the finite element method to large-scale modeling of complicated structures. They allow us to construct optimal order algebraic multilevel iterative solvers for a wide class of real-life elasticity problems.
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  • 198
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    Numerical Linear Algebra with Applications 1 (1994), S. 247-263 
    ISSN: 1070-5325
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: This paper presents a row relaxation method for solving the regularized ℓp least norm problem \documentclass{article}\pagestyle{empty}\begin{document}$$ {\rm minimize}P({\rm x}) = \frac{1}{2}\varepsilon \parallel {\rm x}\parallel _{\rm 2}^{\rm 2} + \parallel A{\rm x} - {\rm b}\parallel _p^p /p $$\end{document} where e and p are positive constants, 1〈p〈∞ The interest that we have in this problem lies in the observation that for small values of E the minimizer of P (X ) is a good substitute for a minimizer of the unregularized problem \documentclass{article}\pagestyle{empty}\begin{document}$$ {\rm minimize }U({\rm x}) = \parallel A{\rm x} - {\rm b}\parallel _p^p /p $$\end{document} It is shown that the dual of the regularized problem has the form \documentclass{article}\pagestyle{empty}\begin{document}$$ {\rm minimize }D({\rm y}) = {\rm b}^T {\rm y} - \frac{1}{2}\varepsilon \parallel A^T {\rm y/}\varepsilon \parallel _2^2 - \parallel {\rm y}\parallel _q^q /q $$\end{document} where q = p /(p - 1). Moreover, if y solves the dual problem then X = ATy/∊ solves the primal problem and P(ATy/∊) = D(y). Maximizing the dual objective function by changing one variable at a time results in a row relaxation method that resembles Kaczmarz's method. This feature makes the new method suitable for solving large sparse C, problems that arise in computerized tomography, geophysics, and groundwater hydrology. Numerical experiments illustrate the feasibility of our ideas.
    Additional Material: 5 Tab.
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    Numerical Linear Algebra with Applications 1 (1994), S. 331-333 
    ISSN: 1070-5325
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
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  • 200
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    Numerical Linear Algebra with Applications 1 (1994), S. 313-329 
    ISSN: 1070-5325
    Keywords: Discretization method ; Nonlinear ABS class ; Newton-type method ; Quadratic convergence ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In this paper we give a class of algorithms for solving nonlinear algebraic equations using difference approximations of derivatives. The class is a modification of the original ABS class with the advantage of requiring less function evaluations. Special cases include the methods of Brown and Brent and the discretized Newton method, which is formulated in a way requiring fewer function evaluations per iteration.
    Additional Material: 1 Tab.
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