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  • 1
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 10 (1976), S. 145-170 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper describes a new finite element scheme for the analysis of instability phenomena of arbitrary thin shells. A computationally efficient procedure is proposed for calculating the non-linear stiffness and tangential stiffness matrices for a doubly-curved quadrilateral element defined by co-ordinate lines. The essential feature is the explicit addition of the non-linear terms into the rigid-body motion of the element. Thus the non-linear and tangential element stiffness matrices can easily be generated by transforming the generalized element stiffness matrix for linear analysis, and the non-linear terms of these matrices are separated into a number of component terms multiplied by the rigid-body rotations. These component terms can be stored permanently and used to calculate efficiently the non-linear and tangential stiffness matrices at each iteration. Illustrative examples are presented which confirm the validity of the present approach in the analysis of instability phenomena of thin plates and shells.
    Additional Material: 9 Ill.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 18 (1982), S. 1045-1054 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A finite element analysis of a class of non-stationary random diffusion problems is considered. By using the one-dimensional heat equation with random initial condition and random external excitation, the statistical numerical formulation is presented. Two typical numerical examples are given for somewhat simplified problems by which the validity of the finite element scheme is discussed. The results obtained by the finite difference scheme are also shown.
    Additional Material: 2 Ill.
    Type of Medium: Electronic Resource
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  • 3
    ISSN: 0006-3525
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The sugar-phosphate-sugar complex C10H18O8P, a unit of the polynucleotide chains, was analyzed, making use of 100 conformational energies computed in the Hartree-Fock approximation with a small basis set of Gaussian type orbitals. The geometry of the conformations [which corresponds to the C(2′)-endo deoxy system], the basis set, and the computed total energies are reported in this work. In addition, a number of attempts are presented where we searched for a computationally very simple analytical expression apt to fit, with reasonable accuracy, the computed energies. Lennard-Jones type potential seems to offer an appropriate form capable of reproducing the positions of the maxima and the minima resulting from ab initio computations, but neither the 6-12 nor other similar forms seem to be able to correctly reproduce the intensity of the barriers. Form a details analysis of the barriers to rotation about the bonds O(5′) - C(5′) and C(5′) - C(4′) in terms of nonboned interactions, we found that a substantial improvement in the fit of analytical to ab initio energies may be obtained by distinguishing between atoms characterized by the same atomic number but having different chemical characteristics, like the oxygen atoms of the phosphate group, on one hand, and the oxygen atoms of the sugar rings and the hydroxyl groups, on the other.
    Additional Material: 3 Ill.
    Type of Medium: Electronic Resource
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  • 4
    Electronic Resource
    Electronic Resource
    New York : Wiley-Blackwell
    Biopolymers 17 (1978), S. 2045-2045 
    ISSN: 0006-3525
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Type of Medium: Electronic Resource
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  • 5
    ISSN: 0006-3525
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: In the first paper of this series we showed that the total electronic energy, computed ab initio in the Hartree-Fock approximation for both independent and coupled rotations of the five torsional angles in the sugar-phosphate-sugar complex C10H18O8P, can be reproduced with reasonable accuracy by a Lennard-Jones 6-12 potential, with different attractive and repulsive parameters assigned to the four oxygens of the phosphate group, on one hand, and the four oxygens of the sugar rings and the hydroxyl groups, on the other. The conclusion was reached on the basis of some attempts at the derivation of analytical expressions capable of correctly describing the energies obtained with the quantum mechanical computations. An analysis of the barriers to internal rotation for the angles ϕ and ψ indicated the possibility of improving the description through addition of further terms, in particular of an intrinsic torsional potential. In order to obtain a fit based on all internal rotations of the sugar-phosphate-sugar molecules, and coupling numerical accuracy with physical significance, we made a study of the possible contributions to the conformational energy: intrinsic torsional energy, electrostatic interactions, London attractions, van der Waals repulsions. The results of this study show that the best description of ab initio energies is offered by a potential containing a Lennard-Jones 6-12 term and an intrinsic torsional term.
    Additional Material: 3 Ill.
    Type of Medium: Electronic Resource
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  • 6
    Electronic Resource
    Electronic Resource
    New York : Wiley-Blackwell
    Biopolymers 17 (1978), S. 67-84 
    ISSN: 0006-3525
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Conformational energy maps for the four combinations of two consecutive torsional angles of the backbone structure of polydeoxyribonucleotides are presented. Both the C(2′)-endo and the C(3′)-endo conformation of sugar rings were considered. The energies were evaluated with an analytical expression representing the best fit to ab initio energies computed in the Hartree-Fock approximation, and consisting of a contribution from nonbonded interactions of the Lennard-Jones 6-12 type and an intrinsic torsional potential. It is shown that the minima of these maps are in excellent agreement with the most stable conformations as obtained from x-ray crystallographic analysis of nucleic acids and polynucleotides.
    Additional Material: 8 Ill.
    Type of Medium: Electronic Resource
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