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  • Articles: DFG German National Licenses  (707)
  • 1985-1989  (707)
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  • 1988  (707)
  • Engineering General  (570)
  • Physical Chemistry  (137)
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  • Articles: DFG German National Licenses  (707)
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  • 1985-1989  (707)
  • 1890-1899
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  • 101
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 26 (1988), S. 95-108 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In field systems containing a divergenceless vector, the problem may be posed in terms of a vector potential for convenience. For the solution of the magnetic vector potential in three dimensional problems with current sources, there exist three standard variational formulations in the literature. While all these are known to give verifiable physical solutions, there is some question as to which is to be preferred. Indeed, one of them is invalid for infinite dimensional fields in that, without the finite element trial functions, it will not give unique solutions since it does not explicitly impose the divergence of the vector potential.In this paper, we look at the formulations in the light of the restrictions imposed by the finite element trial functions for tetrahedral elements and arrive at the curious result that that formulation which is totally invalid when the vector potential is unrestricted by trial functions, is in fact valid in finite element analysis and, at the same time, is the best. We further show that this formulation yields naturally non-divergent vector potential solutions, strictly as a result of the trial functions.
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  • 102
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 26 (1988), S. 167-181 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A new efficient method of eigenvalue reanalysis has been developed based on the perturbation method such that first the differential equations which describe the change of the eigenvalues and eigenvectors of a system being modified are derived from the perturbation method and then the solutions of these equations are obtained by following them up with the solutions of more simple equations. The special features of this method are that it can give a clear correspondence between the eigenpairs before and after system modification, and that the computer run time spent by this method is far shorter than that of revised analysis by FEM when only a few selected modes are used in the form of an approximate computation. In addition, this approximate computation can give more accurate results than the perturbation method. The efficiency of the proposed method has been verified by applying it to a simple spring-mass model as well as a 600 degrees-of-freedom model which receive structural modification.
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  • 103
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 25 (1988), S. 545-559 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The application of potential theory to the solution of theory of elasticity problems harks back to an old tradition, witness the Boussinesq treatment of the half-space point loading.In a preceding study by the authour,1 it has been shown how plane thermoelastic problems can be solved by using only numerical methods suited to treat the Laplace operator Δ2ϕ, hence by introducing only one d.o.f. or every node of the discretization.In the present paper it is proposed to show how similar techniques can be used in a three-dimensional case. The reduction achieved in the number of nodal unknowns is from three d.o.f. to one; thus it is hoped that - notwithstanding the greater complexity of the present treatment - a computational advantage can be gained over the direct approach, at least for discretization meshes of a few thousands of nodes (which is not unusual for 3-D domains).The basic formulation draws from fairly classical works2-6 and differs from more recent ones (e.g. Goodier as quoted in Reference 7) insofar as the particular solutions of the thermoelastic problems do not ntail, in the present approach, any integration, but rather are expressed directly in terms of the thermal field.
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  • 104
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 25 (1988), S. 593-609 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: To solve the transient heat-conduction equation, the Pade-approximation is introduced into the Finite Difference Method. But, if the time step is chosen too large relatively to the element size the Euler method (Pade (0,1) approximation) and the Crank-Nicolson solution (Pade (1,1)-approximation) lead to significant oscillations. In contrast, the Full Implicit scheme (Pade (1,0)-approximation) does not show this oscillatory behaviour, but is more inaccurate. Compared to these time stepping algorithms the presented Weighted Time Step method is seen to offer definite advantages.
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  • 105
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 25 (1988), S. 625-633 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper reviews the work done to date on the numerical simulation of forest fires. A general model to predict forest fire spread under different conditions is presented and studied. The model is based on nth order reaction theory, and is sufficiently simple and flexible to conveniently deal with variations in wind velocity, forest properties, fire breaks and other phenomena of interest to the fire controller. The effects of changing various parameters in the equations are illustratd. Results for zero and constant wind velocity are given, together with the effect of abrupt wind changes and fire breaks.
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  • 106
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 26 (1988), S. 19-38 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The present paper discusses the numerical solution of steady-state non-linear heat conduction problems in composite bodies by using the boundary element method. Two kinds of non-linearities are considered: the temperature dependence of the thermal conductivity and boundary conditions of the radiative type. By introducing the integral of conductivity as a new variable the governing equation of the problem becomes linear in the transform space. Transformed boundary conditions of the Dirichlet and Neumann types are also linear but convective boundary conditions become non-linear. Also, discontinuities arise in the value of the integral of conductivity across the interface between materials with different properties since continuity of temperature is imposed. The problem is numerically solved by discretizing the external and interface boundaries of the region under consideration with constant boundary elements and applying an iterative scheme of the Newton-Raphson type.
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  • 107
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    International Journal for Numerical Methods in Engineering 26 (1988), S. 81-93 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A class of least-squares finite element methods has been developed for first-order systems and here we study this approach for hyperbolic problems. The formulation of the least-squares method is developed in detail and compared with the Petrov-Galerkin and Taylor-Galerkin procedures. A stability analysis is carried out and the extension to the non-linear problem described. Numerical comparison studies demonstrate the performance of the method and suggest that it is a promising alternative to existing schemes. Applications considered include the convection equation, inviscid Burger's equation and shallow-water equations.
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  • 108
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 26 (1988), S. 1-18 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An automatic remeshing scheme has been developed to enable finite element simulation of even complicated forming processes. It has been demonstrated that for many practical applications the incorporation of this technique in the existing computer codes is indispensable not only for more accurate solutions but sometimes just for striving to obtain solutions. In order to avoid the tedious procedures of, e.g. interrupting the analysis, performing rediscretization, mapping of current state variables and preparing the new set of boundary conditions, methods for automating the remeshing procedures and the related accuracy problems have been presented. Several examples, such as a heading process, an extrusion process through a square die, and a one-blow impression-die forging process with flash have been successfully tested out with this automatic remeshing scheme.
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  • 109
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    International Journal for Numerical Methods in Engineering 26 (1988), S. 153-165 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A creep analysis capability, using a generalized viscoelastic model, is introduced to process the creep behaviour coupled with elastoplastic deformation. The formulation is based on the step-by-step time integration of the Kelvin-Maxwell rheological model with non-constant parameters.The concept of a rheological model is extended to the multiaxial stresses by the Prandtl-Reuss stress-strain relationship, from which the tangential stiffness matrix is formed for Newton's iteration. If the plastic deformation is coupled with creep, the algorithm will seek a solution in two distinct steps. Various choices of empirical creep laws are available and small variations in temperature are allowed as implemented in the general purpose finite element analysis program.
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  • 110
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    International Journal for Numerical Methods in Engineering 26 (1988), S. 217-230 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: During mechanical system kinematic and dynamic analysis, linear and non-linear algebraic equations must be solved. Algebraic equations are often ill-conditioned, due either to physical singularities or large numerical errors, in which case solutions may have large errors or analysis methods may fail. Causes of ill-conditioned problems are studied and illustrated with examples. Ill-conditioned matrices and matrix condition numbers are discussed and an efficient and reliable indicator of ill-conditioned matrices is suggested. In constrained kinematic and dynamic analysis, equations are solved repetitively, so symbolic factorization is used. The ill-conditioning problem due to symbolic factorization is discussed and methods of detecting ill-conditioning are suggested. Three examples are studied to demonstrate the effectiveness and use of condition numbers and ill-conditioned system detection methods.
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  • 111
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    International Journal for Numerical Methods in Engineering 26 (1988), S. 289-289 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
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  • 112
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    International Journal for Numerical Methods in Engineering 26 (1988) 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
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  • 113
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    International Journal for Numerical Methods in Engineering 26 (1988), S. 313-327 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Cubic basis functions in one dimension for the solution of two-point boundary value problems are constructed based on the zeros of Chebyshev polynomials of the first kind. A general formula is derived for the construction of polynomial basis functions of degree r, where 1 ≤r 〈 ∞. A Galerkin finite element method using the constructed basis functions for the cases r = 1, 2 and 3 is successfully applied to three different types of problem including a singular perturbation problem.
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  • 114
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    International Journal for Numerical Methods in Engineering 26 (1988), S. 349-359 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An algorithm is presented which integrates different groups of nodes of a finite element mesh with different time steps and different integrators. Since the nodal groups are updated independently no unsymmetric systems need be solved. Stability is demonstrated by showing that an energy norm of the solution decreases after every update if the time step is less than a given critical value. The element eigenvalue inequality theorem is used to give the critical time step in terms of element eigenvalues.
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  • 115
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    International Journal for Numerical Methods in Engineering 26 (1988), S. 379-391 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The accuracy of a new class of concurrent, procedures for transient finite element analysis is examined. A phase error analysis is carried out which shows that wave retardation leading to unacceptable loss of accuracy may occur if a Courant condition based on the dimensions of the subdomains is violated. Numerical tests suggest that this Courant condition is conservative for typical structural applications and may lead to a marked increase in accuracy as the number of subdomains is increased. Theoretical speed-up ratios are derived which suggest that the algorithms under consideration can be expected to exhibit a performance superior to that of globally implicit methods when implemented on parallel machines.
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  • 116
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    International Journal for Numerical Methods in Engineering 26 (1988), S. 393-411 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The boundary element method (BEM) has been known for some time to be extremely useful for the solution of elastic stress analysis problems involving high stress/strain gradients. In particular, the method has been extensively used for the study of both two and three-dimensional fracture mechanics problems. Recent analytical and numerical developments coupled with the general availability of greatly increased computing capacity have made both elastic and inelastic three-dimensional stress analysis feasible for complex geometries such as those found in gas turbine engine components.This paper summarizes the features of an advanced stress analysis method based on BEM for elastic and inelastic analyses of multizone or substructured three-dimensional solids. The elastic analyses involve isotropic or cross anisotropic media with thermal and centrifugal loading. The inelastic analyses include isotropic plasticity with variable hardening and kinematic plasticity with multiple yield surfaces.
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  • 117
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    International Journal for Numerical Methods in Engineering 26 (1988), S. 489-509 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A complementary energy based variational principle, using first order stress functions, is developed for plane linear elastic couple-stress problems. The principle is analogous to that used in a total potential energy based Mindlin/Reissner thick plate bending analysis and as such is a generalization of the classical analogy between plate stretching and plate bending. Traction boundary conditions are enforced using a Lagrange multiplier technique. The resulting C0 finite element ‘equilibrium stress model’ is validated by investigating the reduction of the stress concentration factor associated with a small hole in a field of uniform tension.
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  • 118
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    International Journal for Numerical Methods in Engineering 26 (1988), S. 511-524 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A mixed explicit-implicit numerical integration algorithm for creep stress analysis is presented in this paper. This method allows simultaneously use of, and thus benefit from, both these integration schemes. The continuum damage constitutive model is also implemented in this algorithm. The present method is suitable for the prediction of creep crack growth in solids using the continuum damage approach.Numerical examples using different constitutive equations have been included to demonstrate the high efficiency of the proposed algorithm.
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  • 119
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    International Journal for Numerical Methods in Engineering 26 (1988), S. 525-526 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
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  • 120
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    International Journal for Numerical Methods in Engineering 26 (1988), S. 571-587 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The non-linear field-boundary-element technique is applied to the analysis of snap-through phenomena in thin shallow shells. The equilibrium path is traced by using the arc-length method and the solution strategy is discussed in detail. The results show that, as compared to the approaches based on the popular symmetric-variational Galerkin finite element formulation, the current approach based on an unsymmetric variational Petrov-Galerkin field-boundary-element formulation gives a faster convergence while using fewer degrees of freedom. The illustrative numerical examples deal with post-buckling responses of several shallow shells with different geometries.
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  • 121
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    International Journal for Numerical Methods in Engineering 26 (1988), S. 617-630 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This article presents a numerical procedure for the analysis of a planar, continuous, flexible member. Large displacements and rotations, non-linear material behaviour and general cross sections are admitted. A shooting method is utilized along with Newton-type iteration for improved estimates. The resulting computer program is used to compare with numerical and analytical solutions of problems solved by others, and to present the solution to a problem which brings out very clearly the effects of both geometric and material non-linearities.
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  • 122
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    International Journal for Numerical Methods in Engineering 26 (1988), S. 647-662 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The essential character of the primary elliptic-hyperbolic operator encountered in the modelling of viscoelastic flows is encaptured in a non-linear fifth-order two-point boundary value problem in one dimension. Expansions in terms of beam functions and Chebyshev polynomials are used to compute solutions to the primary two-point boundary value problem within a spectral Galerkin formulation. An investigation of the performance of the methods with respect to the level of non-linearity is carried out. Accurate results are obtained with Chebyshev polynomials for high levels of non-linearity, whereas the behaviour of beam function expansions proves far more sensitive to the level of non-linearity.
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  • 123
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    International Journal for Numerical Methods in Engineering 26 (1988), S. 705-715 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A polynomial displacement basis for the three-node plate bending element (Zienkiewicz-triangle) is developed from a relaxed C1-continuity requirement called the interpolation test. The test provides a general convergence criterion for non-conforming shape functions and a practical guideline to select a proper displacement basis. The resulting simple displacement type element passes the patch test. Several reduced numerical integration schemes are discussed and numerical testing provides a comparison with the standard element formulated by Zienkiewicz.
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  • 124
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    International Journal for Numerical Methods in Engineering 26 (1988), S. 677-693 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Based on a new functional in which displacements, strains and stresses are taken as independent variables, a set of three 8-node hexahedral hybrid elements QS11-1, QS11-2 and QS11-3 is developed. The adoption of separated stress and displacement variables proves to be effective in improving the accuracy of the elements.The new elements are all capable of yielding converging results, and they all possess the properties of having no zero energy deformation modes and of being co-ordinate invariant. From the numerical example of a beam under bending it is concluded that exact solutions can be obtained for right prism elements, while good results are still attainable for severely distorted elements.The relationship between the new hybrid elements and the conventional displacement elements is also explored in this paper.
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  • 125
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    International Journal for Numerical Methods in Engineering 26 (1988), S. 743-762 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The causes of shear locking and other discretization errors are analysed using a physically interpretable notation. This analysis provides insights that allow the errors due to shear locking to be removed either directly or indirectly. St. Venant's principle is incorporated into the stiffness matrix to directly eliminate shear locking from bending elements. Rules-of-thumb are suggested by the same analysis that will insure the absence of errors due to shear locking at the cost of additional degrees of freedom. It is also shown that aspect ratio stiffening in membrane elements is partially due to the same modelling error that produces shear locking. The source of parasitic shear is also identified and a direct procedure for eliminating it is given. A two node Timoshenko beam element and a four node membrane element are fully developed in symbolic form. The procedure is directly applicable to plate bending elements.
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  • 126
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    International Journal for Numerical Methods in Engineering 26 (1988), S. 769-784 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In the present paper an incremental procedure is formulated for first-order elastoplastic analysis of plane frame structures discretized into a finite number of beam elements and described by piecewise linear elastic-perfectly plastic constitutive laws, under the assumption of both reversible and irreversible behaviour of material and using piecewise linear yield conditions at any desired degree of discretization in the space of the active stress resultants (axial force, shear force and bending moment).The proposed method, by using the independent elastic-plastic kinematical compatibility equations, restrains the problem sizes within not more than twice the number of the redundant unknowns in the complete elastic frame, regardless of the degree of discretization of the piecewise linear yield conditions, still maintaining the advantage exhibited by the Mathematical Programming methods of requiring only one factorization of the matrix governing the problem when no local unloading occurs. Furthermore, the outlined algorithm allows the additional computational effort to be restrained in the case of local unloading, inasmuch as it requires a new factorization to be performed of a part of the matrix governing the problem, whose size is small with respect to the total size of the matrix.
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  • 127
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    International Journal for Numerical Methods in Engineering 26 (1988), S. 823-841 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Comparison of different quadratures for evaluation of the improper wavenumber integrals which arise in evaluation of the Green functions for a viscoelastic half space and harmonic line loadings is investigated. The model is assumed to be of the plane strain type. Extensive testing of the numerical accuracy for various quadratures is performed. A measure of numerical efficiency of the quadratures is proposed and compared for different integration formulae. It was determined that among the procedures tested the Clenshaw-Curtis quadrature offers the most efficient way of evaluating the wavenumber integrals numerically.
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  • 128
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    International Journal for Numerical Methods in Engineering 26 (1988), S. 815-821 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The paper describes the basic ideas of Monte Carlo annealing algorithms for structural optimization with discrete design parameters. The algorithm generates randomly a set of design parameters, with probability depending on the objective function and given by the Boltzmann-Gibbs distribution. In this model the search for the global minimum is simulated by a relaxation process of the statistical mechanical system with the Hamiltonian proportional to the objective function. The rate of the convergence of the method and its dependence upon the annealing probability are discussed. Numerical implementation of the method for the weight optimization of the ten-bar planar cantilever truss is presented. The results of numerical simulation are compared with those obtained by the dual methods. The principal conjecture is that the method is fairly efficient and has great potential for applicaton in engineering design.
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  • 129
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    International Journal for Numerical Methods in Engineering 26 (1988), S. 875-890 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The backward mapping approach for computation of global domains of attraction of asymptotically stable non-critical equilibrium points of dynamical systems is presented. A basis for the proposed approach is an extension of Lyapunov's direct method due to LaSalle and Lefschetz. An iterative process that converges to the global domain of attraction of an asymptotically stable equilibrium point is formulated. The method applies to both continuous time and discrete time multidimensional systems. It is shown that the backward mapping approach proposed by C. S. Hsu for spiral equilibrium points of second order discrete time systems is a particular case of the algorithm presented here. The proposed method can be used for autonomous systems as well as for systems with periodic coefficients. When applied to discrete time formulation of dynamical systems, the method can be used to determine the regions of stability of periodic solutions. The paper concludes with a number of illustrative examples that demonstrate the usefulness of the proposed approach.
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  • 130
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    International Journal for Numerical Methods in Engineering 26 (1988), S. 913-933 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An analysis of thin plates by C0 elements is presented. The fundamental part of it is the formulation of a set of constraints that relate the rotational degrees of freedom to the translational degrees of freedom and which are weaker than the usual Kirchhoff constraints. A penalty term associated with these constraints is then introduced instead of the usual expression for the shear strain energy. It is shown that the approach is effective for both quadrilateral and triangular elements.
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  • 131
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    International Journal for Numerical Methods in Engineering 26 (1988), S. 935-952 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A new collocation method based on quadratic splines is presented for second order two-point boundary value problems. First, O(h4) approximations to the first and second derivative of a function are derived using a quadratic-spline interpolant of u. Then these approximations are used to define an O(h4) perturbation of the given boundary value problem. Second, the perturbed problem is used to define a collocation approximation at interval midpoints for which an optimal O(h3-J) global estimate for the jth derivative of the error is derived. Further, O(h4-J) error bounds for the jth derivative are obtained for certain superconvergence points. It should be observed that standard collocation at midpoints gives O(h2-J) bounds. Results from numerical experiments are reported that verify the theoretical behaviour of the method.
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  • 132
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    International Journal for Numerical Methods in Engineering 26 (1988), S. 953-971 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A compact scheme is applied to three dimensional elasticity problems for composite materials, involving simple geometries. The mathematical aspects of this approach are discussed, in particular its solution by iteration methods. A vector processor code implementing the compact scheme is presented, and several numerical experiments are summarized.
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  • 133
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    International Journal for Numerical Methods in Engineering 26 (1988), S. 1001-1002 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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  • 134
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    International Journal for Numerical Methods in Engineering 26 (1988), S. 1005-1027 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A new ‘direct’ elastoplastic boundary element formulation for axisymmetric bodies is developed. The procedure exploits certain features of the constitutive relationship to express the unknwon non-linear initial stress rate tensor as a scalar quantity which can then be eliminated from the boundary equation system though a back substitution of the (modified) stress rate equations.This formulation is implemented in a multi-region system that utilizes quadratic isoparametric shape functions to model the geometry and field variables of the boundary and domain of a body. The kernel functions are presented in Appendix I and the singularities associated with these kernels are discussed. New techniques are described to calculate the coefficients associated with the singular nodes.
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  • 135
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    International Journal for Numerical Methods in Engineering 26 (1988) 
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    Keywords: Engineering ; Engineering General
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  • 136
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    International Journal for Numerical Methods in Engineering 26 (1988), S. 1029-1037 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper is concerned with the development of an efficient eigenproblem solution algorithm and an associated computer program for the economical solution of the free vibration problem of complex practical spinning structural systems. Thus, a detailed description of a newly developed block Lanczos procedure is presented in this paper that employs only real numbers in all relevant computations and also fully exploits sparsity of associated matrices. The procedure is capable of computing multiple roots and proves to be most efficient compared to other existing similar techniques.
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  • 137
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    International Journal for Numerical Methods in Engineering 26 (1988), S. 1039-1055 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper presents a simple procedure for modifying the dynamic coupled soil-pore fluid equations in a manner which allows a stable and efficient staggered solution procedure to be used. The solution method is simpler than an alternative suggested by Park15 and has a direct physical interpretation. This stabilized procedure is efficient in numerical time domain analysis of soil-pore fluid occurring in earthquake and consolidation problems. Numerical examples of one and two dimensional saturated poroelastic media demonstrate the procedure.
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  • 138
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    International Journal for Numerical Methods in Engineering 26 (1988), S. 1101-1128 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A simple and effective linear C0-triangular element for plates and shells is developed on the basis of the Hellinger-Reissner mixed variational principle with independently assumed stress and displacement fields. Two main features are emphasized in this development concerning the assumed transverse shear stress field. Firstly, this assumption results in edge-type penalty constraints in the thin plate/shell regimes. Secondly, the element is used in the form of a four-triangle, cross-diagonal macroelement mesh. As a result, the element is shown to be free from shear locking in thin plate/shell applications, and it satisfied all the appropriate patch tests required for Kirchhoff plate models. In addition, the element exhibits good overall convergence properties in a variety of test problems for plates and shells. Finally, from the computational standpoint, the element is very efficient since all stiffness component matrices are derived in explicit forms.
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  • 139
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    International Journal for Numerical Methods in Engineering 26 (1988), S. 1963-1987 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The constitutive relationship between fields in electromagnetic media is cast in error form. For well-posed static problems, the error splits systematically into complementary functionals. Error minimization provides a universal variational principle that generates complementary and dual solution formulations. The error, which is wholly attributed to the numerical constraints in approximate solutions, is always defined and computable locally and globally.
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  • 140
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    International Journal for Numerical Methods in Engineering 26 (1988), S. 2331-2343 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A new approach for choosing the stress terms for a hybrid stress element is based on the condition of vanishing of the virtual work along the element boundary due to the stress terms higher than constant and the additional incompatible displacement. Examples using 4-node plane stress elements have shown that when the incompatible displacements also satisfy the constant strain patch test the resulting elements will provide the most accurate solutions. Advantages of this approach for the formulation of an axisymmetric solid are also indicated.
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  • 141
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    International Journal for Numerical Methods in Engineering 26 (1988), S. 2319-2330 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The use of the boundary-element method (BEM) for three-dimensional potential flow problems is described herein. The specific application for which the program is designed is the flow in fractured porous media. There are several enhancements to the usual boundary-element calculations. The method uses linear elements to approximate better the boundary conditions and the solution on the surfaces as compared to constant elements; accurate integration over high-aspect-ratio triangles is achieved by computing all the integrals in closed form, as opposed to numerical cubature or mixed exact-numerical integration schemes; and the zoning for inhomogeneous regions uses an efficient method which reduces the size of the problem and avoids difficulties with singularities.
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  • 142
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    International Journal for Numerical Methods in Engineering 26 (1988), S. 2347-2349 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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  • 143
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    International Journal for Numerical Methods in Engineering 26 (1988), S. 2403-2438 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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  • 144
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    International Journal for Numerical Methods in Engineering 26 (1988), S. 2517-2529 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Boundary integral equation (boundary element) methods have the advantage over other commonly used numerical methods that they do not require values of the unknowns at points within the solution domain to be computed. Further benefits would be obtained if attention could be confined to information at one small part of the boundary, the particular region of interest in a given problem. A local boundary integral equation method based on a Taylor series expansion of the unknown function is developed to do this for two-dimensional potential problems governed by Laplace's equation. Very accurate local values of the function and its derivatives can be obtained. The method should find particular application in the efficient refinement of approximate solutions obtained by other numerical techniques.
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  • 145
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    Journal of Physical Organic Chemistry 1 (1988) 
    ISSN: 0894-3230
    Keywords: Organic Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
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  • 146
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    Journal of Physical Organic Chemistry 1 (1988), S. 123-131 
    ISSN: 0894-3230
    Keywords: Organic Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: Photolysis of N-alkyl-N-(3-aryl-3-butenyl) ureas (1) in acetonitrile gave cyclization products, 3-aryl-3-methyl-pyrrolidines, in good yields, whereas irradiation of 1 in methanol afforded methanol adducts as well as the cyclization products. Both the reactions are singlet reactions, and the cyclization is presumed to proceed via 1,6-hydrogen transfer from exciplexes with charge transfer character.
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  • 147
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    Journal of Physical Organic Chemistry 1 (1988), S. 143-151 
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    Keywords: Organic Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: The dependence of the catalytic efficiencies of sodium carboxymethylamylose (NaCMA) for the hydrolysis of N-lauryl-3-acetoxypyridinium iodide (1) and p-nitrophenyl dodecanoate (3) on its degree of substitution (D. S. = 0·00, 0·12, 0·18, 0·24, 0·29 and 0·35) and on the pH values of the solutions (pH = 7·32, 7·80, 8·10 and 9·30) have been studied. At fixed D. S. values, the observed hydrolysis rates of 1 and 3 increase with increasing concentrations of NaCMA and follow saturation kinetics. At fixed concentration of NaCMA, the rates increase with decreasing D. S. values until they reach maxima at D. S. = 0·00. Furthermore, at any D. S. value the catalytic efficiency increases with increasing pH values of the solutions. All these results indicate that the hydroxyl groups are actually the principal catalyzing groups.
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  • 148
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    Journal of Physical Organic Chemistry 1 (1988) 
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    Keywords: Organic Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
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  • 149
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    Journal of Physical Organic Chemistry 1 (1988), S. 191-195 
    ISSN: 0894-3230
    Keywords: Organic Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: The photochemical reaction of MAQO with various aromatic amines were studied by ESR. The results show that nitroxide radicals are stable productrs of the photooxidation of both diphenylamines and phenylamines. The photolyzed phenothiazine does not yield nitroxide as the final product, instead it gives the neutral radical as the stable final product.
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  • 150
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    Journal of Physical Organic Chemistry 1 (1988), S. 209-223 
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    Keywords: Organic Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: The equilibrium acidities of phenylacetonitrile, and 20 of its m- and p-substituted derivatives have been measured in Me2SO solution. Their pKa′s plot linearly with those of the corresponding anilines. Combination of the pKa′s of these acids with their oxidation potentials, Eox(HA), and those of their conjugate bases, Eox(A-), provide an estimate of the acidities of the corresponding radical cations. The pKHA+ values for ArCH2CN+., where Ar is Ph, 1- and 2-naphthyl, and 9-anthryl, are -32, -18·5, -17·5, and -11, respectively, compared to 21·9, 20·85, 20·65, and 19·8 for the corresponding ArCH2CN acids. Acidities of PhCH(Me)CN+., Ph2CHCN+., 9-CN-FlH+., and 9-CN-XnH+. are -33, -35, -25, and -27, respectively, compared to 23·0, 17·5, 8·3, and 13·6 for the corresponding acids from which they were derived. The homolytic bond dissociation energies (BDEs) for the benzylic C—H bonds in these arylacetonitriles, estimated by combining pKHA with Eox(A-), fall in the range of 69 kcal/mol for 9-CN-XnH to 82 kcal/mol for PhCH2CN. For GC6H4CH2CN+. radical cations the acidities are decreased, relative to G=H, when G is an electron donor substituent and increased when G is an acceptor. The BDEs of the benzylic C—H bonds in GC6H4CH2CN are weakened by up to 4 kcal/mol by para donors and strengthened by up to 1·2 kcal/mol by m- or p-acceptors. The significance of these changes in BDEs with regard to the use of σ. scales and the ΔAOP method for estimating substituent effects on radical stabilities is discussed.
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  • 151
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    Journal of Physical Organic Chemistry 1 (1988), S. 281-285 
    ISSN: 0894-3230
    Keywords: Organic Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: The thermal and photochemical decompositions of 5 have been studied. Both reactions lead to CBr2 transfer in good to high yields. With the 2-pentenes as substrates, CBr2 transfer is stereospecific in the classical singlet carbene manner.
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  • 152
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    Journal of Physical Organic Chemistry 1 (1988), S. 305-308 
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    Keywords: Organic Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: Decomposition of the tosylhydrazone salts formed from cubyl carboxaldehyde and homocubanone, potential precursors of cubylcarbene (5) and homocubanylidene (6), leads in each case to products derived from 6. It is suggested that homocub-1(9)-ene (7) is the active ingredient in the formation of 6 from both precursors. The hydrazones formed from N-aziridylamines are useful photochemical sources of 6, and presumably other carbenes. Flash vacuum pyrolysis of the tosyl hydrazone salts and hydrazones at 600°C leads to indene.
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  • 153
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    Journal of Physical Organic Chemistry 1 (1988), S. 317-332 
    ISSN: 0894-3230
    Keywords: Organic Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: Light- and heat-induced decompositions and reactions with nucleophiles of 6,6,8,8-tetramethyl-2-selena-3,4-diaza-7-oxabicyclo[3.3.0]octa- 1(5),3-diene have been studied. In contrast with the conversion to the cyclopentyne derivative (9), selenium containing intermediates (6a, 6b, and 7) were efficiently trapped using several reagents to give various kinds of organoselenium compounds. Of particular note is the isolation of a stable selenirane derivative (16) obtained by the cycloaddition of the photochemically generated selenirene intermediate (7) with furan. The character and reactivity of the intermediates are also discussed.
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  • 154
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    Journal of Physical Organic Chemistry 1 (1988), S. 359-362 
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    Keywords: Organic Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: Reaction rates for solvolysis of a mustard analogue are accurately correlated by the solvatochromic equation without inclusion of a nucleophilicity term, and thus the equation is shown to reveal mechanistically significant information.
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  • 155
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    Journal of Physical Organic Chemistry 1 (1988), S. 119-121 
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    Keywords: Organic Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: Reduction of aromatic aldehydes by benzeneselenol is found to be promoted by molecular oxygen to give corresponding alcohols in good yields. No reduction took place without oxygen.A free radical process involving SH2 reaction at the selenium atom is proposed where the phenylseleno radical attacks the selenium atom of selenohemiacetal, the adduct of benzeneselenol to aldehyde, to give the ketyl radical which then abstracts hydrogen from benzeneselenol. The intermediacy of selenohemiacetal is supported by a quantitative reduction of α-methoxybenzyl phenyl selenide, which is used as a model compound of the intermediate.
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  • 156
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    Keywords: Organic Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: The dependency of the wrapping-up capability of sodium carboxymethylamylose (NaCMA) on its degree of substitution (D. S. = 0·00, 0·12, 0·18, 0·24, 0·29, 0·35 and 0·41) have been studied, using two guest species, iodine and cetyl-trimethylammonium bromide (CTAB). The λmax values of NaCMA-iodine helical inclusion complexes decrease with increasing D. S. values and the amounts of encapsulated iodine by NaCMA as measured by amperometric titrations also decrease with increasing D. S. values. With CTAB as the substrate, the largest number of binding sites, n, and the dissociation constants Kd have been determined by the method of surface tension versus the CTAB concentration plots. The results show that n decreases while Kd increases with increasing D. S. values. All these observations point to the fact that the wrapping-up capability of NaCMA decreases with increasing degrees of substitution. The results are discussed in terms of host-guest and host-solvent hydrophobic-lipophilic interactions as well as intramolecular hydrogen-bonding.
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    Journal of Physical Organic Chemistry 1 (1988), S. 161-167 
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    Keywords: Organic Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: The temperature-dependence of the kinetic isotope effects for branched reactions proceeding via a common intermediate has been simulated by calculations. It is shown that, under certain conditions, anomalously small isotope effects on the Arrhenius preexponential factors, as well as unusually large observed isotope effects, may originate from the branching.
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  • 158
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    Journal of Physical Organic Chemistry 1 (1988), S. 153-160 
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    Keywords: Organic Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: The structures of the allyl anion (1) and two fluoro-substituted derivatives, perfluoro (2) and 1,1-difluoro (3) have been calculated by ab inito molecular orbital theory. Geometries were gradient optimized, and force fields and an MP-2 correlation correction were determined at stationary points. The calculations were done with a double zeta basis set augmented by d functions on carbon (DZ + Dc). Final self-consistent field (SCF) and MP-2 energy calculations were done with the DZ + Dc basis set augmented by diffuse functions. The ground state of 1 is the planar allyl anion (C2v). The rotation barrier in 1 is 21·1 kcal/mol at the MP-2 level. The cyclopropyl carbanion is 27·0 kcal/mol higher in energy at the MP-2 level. The perfluoroallyl anion is not planar, and the rotated structure is 25·7 kcal/mol more stable than the C2v structure at the MP-2 level. The lowest energy structure on the potential energy surface for 2 is the perfluorocyclopropyl carbanion which is 27·8 kcal/mol more stable than the C2v structure at the MP-2 level. The 1,1-difluoroallyl anion is also not planar. Here the most stable structure on the potential energy surface is the rotated allyl anion which is 8·3 kcal/mol more stable than the all-planar allyl anion structure.
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  • 159
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    Keywords: Organic Chemistry ; Physical Chemistry
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    Topics: Chemistry and Pharmacology , Physics
    Notes: 2,2′-Diselenocyanato-1,1′-binaphthyl(1), the first selenium-containing binaphthyl derivative, has been synthesized in optically active form the corresponding diamine by diazotization followed by the reaction with potassium selenocyanate. Its molecular structure is determined by X-ray diffraction method. It is revealed that selenium atoms have hypervalent penta-coordination in the crystal.
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    Journal of Physical Organic Chemistry 1 (1988), S. 185-190 
    ISSN: 0894-3230
    Keywords: Organic Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: From the 1H-NMR spectra of the various pyrrole compounds, 1-substituted 2,5-dimethylpyrroles having two substituent groups on the carbon adjacent to the nitrogen atom were found to be very much hindered compounds. 1-[(1-Substituted)-2-phenylethyl]-2,5-dimethylpyrroles showed the restricted rotation, and the phenyl group of the most stable conformer was in close proximity to the pyrrole group due to dipole interaction. These NMR observations were supported by force field conformational analysis.
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  • 161
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    Journal of Physical Organic Chemistry 1 (1988), S. 333-349 
    ISSN: 0894-3230
    Keywords: Organic Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: New series of platinum complexes of cyclopropenylidenes of the types of PtX2(CP)2 and trans-PtX(PBu3)2(CP) have been synthesized, where CP is di-t-butylcyclopropenylidene (BCP) or bis(diisopropylamino)cyclopropenylidene (ACP). The 13C-NMR chemical shifts, and 13C-195Pt coupling constants (1JPtC) for the complexes are discussed in comparison with those values derived from closely related series of compounds, trans-PtCl(PR3)2L; L — —CH3, —C6H5 and —C≡CBu-t. An excellent linear relationship through the origin was obtained between 1JPtC and the formal ‘s’ % character of the carbon directly bonded to Pt for the series trans-PtCl(PR3)2L in which the Pt—C bond is regarded as a pure σ-linkage, whereas 1JPtC deviates largely from this relationship when pπ—dπ bonding interaction possibly exists in the Pt—C bond. The NMR data suggest the strong nmr trans-influence of the cyclopropenylidenes and that in the Pt—CP bond the σ-interaction is appreciable but the π-interaction is negligible.
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  • 162
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    Journal of Physical Organic Chemistry 1 (1988), S. 103-114 
    ISSN: 0894-3230
    Keywords: Organic Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: The effect of solvent additives on the course of TiO2 photocatalyzed oxygenation of α-methylstyrene has been studied. While the addition of small amounts of nonhalogenated alcohols to TiO2 powders suspended in acetonitrile was found to decrease the rate of photooxygenation, added halogenated alcohols increase the rate of reaction. In addition, the solvent additives affect the observed product distribution.
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  • 163
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    Journal of Physical Organic Chemistry 1 (1988), S. 115-117 
    ISSN: 0894-3230
    Keywords: Organic Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: A novel oxygen induced reduction of α,β-unsaturated carbonyl compounds is discovered. The reduction of the carbon-carbon double bond of α,β-unsaturated carbonyl compounds by benzeneselenol was caused by an introduction of molecular oxygen into the reaction system. This reduction is likely to proceed via a radical chain pathway involving an SH2 type reaction between a phenylseleno radical and a 1,2-adduct of benzeneselenol to the carbonyl group of the α,β-unsaturated carbonyl compound to give an allylic radical which absracts a hydrogen atom from benzeneselenol to form the reduction product.
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  • 164
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    Journal of Physical Organic Chemistry 1 (1988), S. 169-178 
    ISSN: 0894-3230
    Keywords: Organic Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: The development of positive charge β to silicon in a saturated five-membered ring has been studied in the cis- and trans-2-(trimethylsilyl)cyclopentyl trifluoroacetates. The cis substrate solvolyzes in 97% trifluoroethanol at 25° C about 5 times faster than the analogous six-membered ring, after correction for differences in ring strain. The trans substrate solvolyzes about 360 times more slowly than the analogous six-membered ring. These changes are in agreement with a hyperconjugative mechanism for interaction between the silyl group and the developing positive charge. The expected cosine-squared dependence of hyperconjugation on the Si—C—C—X dihedral angle suggests that the cis dihedral angle is reduced somewhat from the 60° in the six-membered ring, and the trans dihedral angle is reduced substantially from the 180° in the six-membered ring.
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  • 165
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    Journal of Physical Organic Chemistry 1 (1988) 
    ISSN: 0894-3230
    Keywords: Organic Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
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  • 166
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    Journal of Physical Organic Chemistry 1 (1988), S. 247-257 
    ISSN: 0894-3230
    Keywords: Organic Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: The rate of hydrolysis of the aromatic vinyl ether o-carboxy-α-methoxy-β,β-dimethylstyrene was found to be accelerated 25-fold by ionization of its carboxylic acid group, but the effective molarity which may be calculated if all of this rate acceleration is ascribed to intramolecular general acid catalysis is only EM = 1 · 1 m. This is similar to the small effective molarities found before for intramolecular catalysis by carboxylic acid groups of aliphatic vinyl ethers, which shows that, unlike the situation in other intramolecular reactions, e.g. ketone enolization, the extra rigidity of aromatic over aliphatic systems does not improve the efficiency of intramolecular catalysis in vinyl ether hydrolysis.It is suggested that this behaviour is the result of reduced conjugation between the vinyl ether group and the aromatic ring in the transition state of the vinyl ether hydrolysis reaction, which retards the rate and offsets any improvement effected by increased rigidity of the aromatic system.
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  • 167
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    Journal of Physical Organic Chemistry 1 (1988), S. 287-298 
    ISSN: 0894-3230
    Keywords: Organic Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: Ab initio STO-3G and 6-31G minimized geometries of 5-oxo- (9), 6-oxo-7-oxabicyclo[2.2.1]hept-2-yl cation (12) and 7-oxabicyclo[2.2.1]hept-2-yl cation (15) were obtained. The energy barriers for their Wagner-Meerwein rearrangements to the more stable 5-oxo- (11), 6-oxo-3-oxabicyclo[2.2.1]hept-2-yl (13) and 3-oxabicyclo[2.2.1]hept-2-yl (17) cations, respectively, have been evaluated and compared with those calculated for the rearrangement of the 5-oxo (18) and 6-oxobicyclo[2.2.1]hept-2-yl cations (20). In agreement with experimental data, the ‘true migratory aptitude’ of an acyl group is higher than that of β-oxoalkyl group in competitive Wagner-Meerwein rearrangments that are ‘energetically unbiased’. The ease of the acyl group 1,2-shift toward an electron-deficient center is related to the electron-donating ability of the carbonyl group due to favorable n(CO) ↔ σ σ ↔ p(C+) hyperconjugative interaction.
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  • 168
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    Journal of Physical Organic Chemistry 1 (1988), S. 299-303 
    ISSN: 0894-3230
    Keywords: Organic Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: Iodide ion promotes the free radical reaction of isopropylmercury idide with bromotrichloromethane to yield isopropyl bromide with rate enhancement in the order of 104. The reaction involves electron transfer from i-PrHgI2- to the trichloromethyl radical in a long kinetic chain process. Iodide ion also promotes the free radical chain conjugate addition of tert-butylmercury chloride to α,β-unsaturated ketones, esters, phosphonate esters and sulfones. Competitive reactivity studies indicate that lithium di-tert-butylcuprates or tri-tert-butylzincates react with 2-cycloalkenones by a mechanism involving attack by tert-butyl radicals. No evidence for radical attack is observed for the corresponding n-butyl ate complexes of copper or zinc.
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  • 169
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    Journal of Physical Organic Chemistry 1 (1988), S. 197-207 
    ISSN: 0894-3230
    Keywords: Organic Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: ESR spectra of l-cyano-2-(trimethylsilyl)ethyl and related radicals were recorded. Temperature dependent ESR spectra of these radicals revealed that electron-releasing trimethylsilylmethyl and electron-withdrawing cyano groups synergetically functioned to stabilize the radical centers due to σ-π captodative effects.
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  • 170
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    Keywords: Organic Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: The excellent linearity (R2 = 0·997) of a plot of pKa values for 17 m- and p-substituted benzyl phenyl sulfones, GC6H4CH2SO2Ph, vs. those for the corresponding arylacetonitrile, GC6H4CH2CN, demonstrates that substituent solvation and substituent solvation assisted resonance (SSAR) effects for p-CN, p-COPh, and p-SPh are nearly identical in these two substrates. The PhSO2 group in PhCH2SO2Ph increases the BDE of the α-C—H bond by 2 kcal/mol, relative to toluene. The α-C—H bonds in GC6H4CH2SO2Ph sulfones are stabilized by 1-2 kcal/mol by acceptor G′s (m-CN, p-CN, m-CF3, p-CF3), but weakened by 1 and 5 kcal/mol, respectively, by donors (p-OMe and p-NMe2). The GC6H4CH2SO2Ph+. radical cation with G = H has a pKHA+. = -25. Its acidity is increased when G is an acceptor by as much as 9 to 10 kcal/mol (G = 3-CN, 3-CF3, 4-CF3, 4-NO2), but is decreased when G is a donor by as much as 33 kcal/mol (G = NMe2). When G = 4-SPh the radical cation is stabilized, relative to G = H, by a larger amount (25 kcal/mol) than when G = 4-OMe (18 kcal/mol). Structural changes along the series PhCH2SO2Ph, 2-naphthyl-CH2SO2Ph, 9-anthryl CH2SO2Ph cause negligible changes in the acidities of these acids, but sizable decreases in the acidities of the corresponding radical cations. Introduction of a phenylsulfonyl group into the methyl group of 9-methylanthracene or the 9-position of fluorene or xanthene increase the BDEs by 3, 2, and 7 kcal/mol, respectively. These effects of PhSO2 groups are compared and contrasted with those of CN groups.
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  • 171
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    Journal of Physical Organic Chemistry 1 (1988), S. 267-273 
    ISSN: 0894-3230
    Keywords: Organic Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: The PE spectra of four stable bicyclic triaziridines with trifluoromethyl, methyl, phenyl, spirocyclopentane and spirocyclohexane substituents are measured. From a comparison of these experimental data with MNDO calculations the energies and the interactions of the nitrogen lone-pair orbitals were obtained. The trifluoromethyl group may be reliably simulated by a fluorine atom. The ionization potentials are unexpectedly high and so are the cyclovoltammetric anodic potentials. The MNDO valence electron densities are in agreement with the comparatively small differences in the chemical shifts of the differently substituted nitrogens of the triaziridine rings.
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  • 172
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    Journal of Physical Organic Chemistry 1 (1988), S. 275-280 
    ISSN: 0894-3230
    Keywords: Organic Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: In order to examine the substituent effect of ethylenedithio and trimethylenedithio groups on electron acceptors, the two title compounds were prepared in one step from the corresponding quinones. These species behave as weak π-electron acceptors owing to the electronic and sterical effects of the fused groups. Only the bis(ethylenedithio) derivative formed a charge-transfer complex with tetrathiotetracene, which showed a moderate electric conductivity of 2·0 × 10-2 S cm-1. In addition, both species oxidized copper, sodium, and potassium iodides to give the corresponding deeply colored metal salts, most of which were semiconductive. The naphtho analogs were similarly studied, but hardly served as electron acceptors.
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  • 173
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    Journal of Physical Organic Chemistry 1 (1988), S. 259-265 
    ISSN: 0894-3230
    Keywords: Organic Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: 1-(Phenylazo)-1-(2-pyridyl)ethyl hydroperoxide, 1, 1-(phenylazo)-1-(2-furyl)ethyl hydroperoxide, 2, phenylazo(2-furyl)methyl hydroperoxide, 3, 1-(phenylazo)-1-(4-anisyl)ethyl hydroperoxide, 4, were synthesized in moderate yield by autoxidation of the phenylhydrazones in benzene. The ionic oxidation of benzyl methyl sulfide in benzene by 1-4 yielded the sulfoxide and the metastable α-azo hydroxides in essentially quantitative yield. The reaction was of the first order in α-azo hydroperoxide and sulfide, respectively. The relative reactivity series found was: 1(1.0) 〈4(1.4) 〈 phenylazo(4-anisyl)methyl hydroperoxide 5 (2·9) 〈2 (3·8) 〈 3 (9·6). α-Methyl substitution was found to slow the rate of oxygen-atom trasfer by a factor of 2 to 2.5. The low relative reactivity of 1 was opposite that expected based on electronic effects. Competitive intramolecular hydrogen bonding of the hydroperoxy proton to the pyridyl nitrogen in 1 accounted for the observed result.
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  • 174
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    Journal of Physical Organic Chemistry 1 (1988), S. 241-245 
    ISSN: 0894-3230
    Keywords: Organic Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: The rates of solvolysis of l-aryl-l-phenyl-2,2-dimethylpropyl(1) p-nitrobenzoates and of aryldiphenylmethyl-p-nitrobenzoates (2) were measured in 80% acetone. An inverse order of reactivity, kp-CF3/km- CF3 〉 l was observed for 1 but not for 2. The X-ray crystallogoraphic study of the parent compounds, l,l-diphenyl-2,2-dimethylpropyl-p-nitrobenzoate (1b) and triphenylemethyl benzoate (3b), and of 2-phenyl-2-propyl-p-nitrobenzoate (4) indicated that in the highly congested system 1 both phenyl rings were nonplanar, whereas the phenyl rings in 3 and 4 were essentially planar.
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  • 175
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    International Journal for Numerical Methods in Engineering 26 (1988), S. 1281-1298 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The method of optimal weighting functions for symmetric problems is described in a general form. It is based on a Petrov-Galerkin formulation in which the best approximation property and other mathematical features are achieved for a chosen norm, different from the original ‘energy norm’ of the problem. The nonlocality of the weighting functions is shown to have only a minor effect on the efficiency of the method, although a localization scheme is also suggested. The method is applied to a one- and two-dimensional singular perturbation problems, as well as to a cylindrical shell problem.
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  • 176
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    International Journal for Numerical Methods in Engineering 26 (1988), S. 1299-1309 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A new boundary element formulation has been developed for two- and three-dimensional acoustic eigenfrequency analyses. The formulation is based on the well known method of constructing a solution of a differential equation in terms of a complementary function and particular integral. An advanced isoparametric implementation with automatic error control in the integration is used. A number of realistic examples of application to automotive acoustic cavities are described.
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  • 177
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    International Journal for Numerical Methods in Engineering 26 (1988), S. 1325-1343 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A new finite-volume approach is developed and applied to the two-dimensional continuity and convective-diffusive energy equations. The variation of the field variables is approximated by bi-quadratic interpolation formulae over the space occupied by the finite volume and the region surrounding it. These are used in the integral conservation laws for energy and mass. The convective transport is modelled using a new upstream-weighting approach which uses volume averages for the energy transported across the boundaries of the finite volume. The weighting is dependent on the skewness of the velocity field to the surfaces of the finite volume as well as its strength. It is adaptive to local flow conditions. Two test cases are treated which have exact solutions. The first is not new and involves a rotating shaft. The errors are less than 0.06 per cent for this case. The second case is new and involves convection past a source and sink. In contrast to the first case, the global Peclet number is a strong parameter, and cell Peclet numbers (Peh) range from 0 to 20. The maximum error is 2.3 per cent for Peh = 4, and there is no evidence of numerical diffusion for even the largest value of Peh. For both test cases, the maximum error occurs at moderate values of Peh and diminishes at the extreme low and high values.
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  • 178
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    International Journal for Numerical Methods in Engineering 26 (1988), S. 1403-1431 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Buckling of compression flanges of welded I-beams consisting of more than one lamella is characterized by partial loss of contact between the lamella welded to the web and the neighbouring lamella. The boundaries of the contact regions of the buckling modes of the two lamellae are originally unknown. Thus, the present elasto-plastic plate-stability problem is coupled with a contact problem. It represents a unilateral problem because eigenforms with penetrations of lamellae are physically impossible. This problem is solved first for the elastic material domain. The Rayleigh-Ritz method is used for determining symmetric eigenforms. A finite-strip technique is employed for determining unsymmetric eigenforms. The solution of the unilateral elastic plate-buckling problems serves as the starting point for the iterative solution of the corresponding elasto-plastic plate-stability problem. The buckling pressures obtained are compared with corresponding buckling stresses resulting from a classical design procedure disregarding the interaction of the lamellae at buckling.
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  • 179
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    International Journal for Numerical Methods in Engineering 26 (1988) 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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  • 180
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    International Journal for Numerical Methods in Engineering 26 (1988), S. 1893-1905 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A uniform linear semi-infinite beam in a uniform linear ambient medium is studied. The beam performs stationary harmonic damped non-synchronous space vibration in simultaneous tension, torsion, bending and shear. Hysteretic and viscous dampings of the beam material and ambient medium are considered. Four new generalized complex Kolousek functions are derived. A 6 × 6 complex symmetric stiffness matrix is established for a semi-infinite beam member excited at its end by prescribed harmonic translations and rotations which have the same frequency but may be out of phase. This matrix extends the range of application of the so called ‘exact analysis’ of non-proportionally damped built-up beam structures as described in a previous paper by Lundén and Åkesson.1 Numerical examples are given, including applications of the computer program SFVIBAT-DAMP. Power flows are studied.
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    International Journal for Numerical Methods in Engineering 26 (1988), S. 1907-1908 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    International Journal for Numerical Methods in Engineering 26 (1988), S. 1909-1912 
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    Keywords: Engineering ; Engineering General
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    International Journal for Numerical Methods in Engineering 26 (1988), S. 1908-1908 
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    Keywords: Engineering ; Engineering General
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  • 184
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    International Journal for Numerical Methods in Engineering 26 (1988), S. ii 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
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  • 185
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    International Journal for Numerical Methods in Engineering 26 (1988), S. 1913-1924 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Applications of the boundary element method for two- and three-dimensional structural shape optimization are presented. The displacements and stresses are computed using the boundary element method. Sub-structuring is used to isolate the portion of the structure undergoing geometric change. The corresponding non-linear programming problem for the optimization is solved by the generalized reduced gradient method. B-spline curves and surfaces are introduced to describe the shape of the design. The control points on these curves or surfaces are selected as design variables. The design objective may be either to minimize the weight or a peak stress of the component by determining the optimum shape subject to geometrical and stress constraints. The use of substructuring allows for problem solution without requiring traditional simplifications such as linearization of the constraints. The method has been successfully applied to the structural shape optimization of plane stress, plane strain and three-dimensional elasticity problems.
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  • 186
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    International Journal for Numerical Methods in Engineering 26 (1988), S. 2049-2060 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In this paper a discrete element matrix formulation for the analysis of linear and non-linear bifurcation problems of some elastic structures is introduced. This, combined with a discrete perturbation technique, is implemented into a computer code to solve buckling and initial postbuckling problems of elastic struts.
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  • 187
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    International Journal for Numerical Methods in Engineering 26 (1988), S. 2211-2226 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A substructure synthesis formulation is presented that permits use of established flexible multibody dynamic analysis computer codes to account for structural geometric non-linear effects. Large relative displacement is permitted between points within bodies that undergo small strain elastic deformation. Components are divided into substructures, on each of which the theory of linear elasticity relative to a body reference frame is adequate to describe deformation and its coupling with system motion. Normal vibration and static correction deformation modes are used to account for elastic deformation within each substructure. Compatibility conditions are derived and imposed as constraint equations at boundary points between substructures. System equations of motion that include geometric non-linear effects of large rotation, in terms of generalized co-ordinates of a reference frame for each substructure and a set of deformation modes that are defined within the substructure, are assembled. The method is implemented in an industry standard flexible multibody dynamics code, with minimal modification. Use of the formulation is illustrated on the classical problem of a spinning beam with geometric stiffening and on a space structure that experiences large deformation.
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    International Journal for Numerical Methods in Engineering 26 (1988), S. 1345-1364 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An eighteen-node, three-dimensional, solid element with 54 degrees of freedom is presented for the finite element analysis of thin plates and shells. The element is based on the Hellinger-Reissner principle with independent strain. The assumed independent strain is divided into higher and lower terms. The stiffness matrix associated with the higher order independent strain plays the role of stabilization matrix. A modified stress-strain relation decoupling inplane and normal strain is used to incorporate thin shell behaviour. Numerical results demonstrate that, with a properly chosen set of assumed strain, this element is effectively free of locking even for very thin plates and shells.
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    International Journal for Numerical Methods in Engineering 26 (1988), S. 1449-1466 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The incremental holonomic boundary-value problem in elastoplasticity has been shown to be characterized by a variational inequality. The problem may be approximated, however, by a perturbed minimization problem, characterized by a variational equality. This formulation is used as the basis for constructing finite element approximations of the original boundary-value problem, leading to a system of non-linear algebraic equations. Procedures for solving these equations are described and numerical results are presented and compared with those obtained using a conventional approach.
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    International Journal for Numerical Methods in Engineering 26 (1988), S. 1433-1447 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The new method involving the combined use of the Laplace transform and the finite difference method is applicable to the problem of time-dependent heat flow systems. The present method removes the time derivatives from the governing differential equation using the Laplace transform and then solves the associated equation with the finite difference method. The transformed temperature is inverted numerically by the method of Honig and Hirdes to obtain the result in the physical quantities. The present results are compared in tables with exact solutions and those obtained from the combined use of the Laplace transform and the finite element method. It is found that the present method is reliable and efficient.
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    International Journal for Numerical Methods in Engineering 26 (1988), S. 1467-1469 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    International Journal for Numerical Methods in Engineering 26 (1988), S. 1507-1523 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The variational-asymptotic formulation for the edge layer problem is implemented by mixed-hybrid finite elements. This approach is used to analyse the stress singularity at the free edge in composite laminates. Results indicate that the stress singularity (as r → 0) is very closely approximated by log r instead of r-α.
    Additional Material: 10 Ill.
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  • 193
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    International Journal for Numerical Methods in Engineering 26 (1988), S. 1541-1549 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A new numerical formulation is proposed in this investigation for the solution of parabolic differential equations. The time step parameter λ = 2Δτ/(Δχ)2 under consideration is as large as 2000 such that only a few time steps are needed for the entire regime of transient heat conduction. Along with the formulation, a time scaling transformation is introduced to produce an accurate result for the beginning of a transient process. Although the present formulation makes reference only to the transient heat conduction problem, the idea is equally applicable to parabolic differential equations for other physical phenomena such as transformed boundary layer flow equations.
    Additional Material: 5 Ill.
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  • 194
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    International Journal for Numerical Methods in Engineering 26 (1988), S. 1551-1566 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An alternative formulation of Kirchhoff's equations is given which is amenable to a standard C0 finite element discretization. In this formulation, the potential energy of the plate is formulated entirely in terms of rotations, whereas the deflections are the outcome of a subsidiary problem. The nature of the resulting equations is such that C0 interpolation can be used on both rotations and deflections. In particular, general classes of triangular and quadrilateral isoparametric elements can be used in conjunction with the method. Unlike other finite element methods which are based on three-dimensional or Mindlin formulations, the present approach deals directly with Kirchhoff's equations of thin plate bending. Excellent accuracy is observed in standard numerical tests using both distorted and undistorted mesh patterns.
    Additional Material: 6 Ill.
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  • 195
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    International Journal for Numerical Methods in Engineering 26 (1988), S. 1579-1595 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A general method for shape design sensitivity analysis as applied to plane elasticity problems is developed with a direct boundary integral equation formulation, using the material derivative concept and adjoint variable method. The problem formulation is very general and a complete consideration is given to describing the boundary variation by including the tangential component of the velocity field. The method is then applied to obtain the sensitivity formula for a general stress constraint imposed over a small part of the boundary. The accuracy of the design sensitivity analysis is studied with a fillet and an elastic ring design problem. Among the several numerical implementations tested, the second order boundary elements with a cubic spline representation of the moving boundary have shown the best accuracy. A smooth characteristic function is found to be better than a plateau function for localization of the stress constraint. Optimal shapes for the two problems are presented to show numerical applications.
    Additional Material: 13 Ill.
    Type of Medium: Electronic Resource
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  • 196
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    International Journal for Numerical Methods in Engineering 26 (1988), S. 1597-1613 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An incremental Total Lagrangian Formulation for curved beam elements that includes the effect of large rotation increments is developed. A complete and symmetric tangent stiffness matrix is obtained and the numerical results show, in general, an improvement over the standard formulation where the assumption of infinitesimal rotation increments is made in the derivation of the tangent stiffness matrix.
    Additional Material: 6 Ill.
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  • 197
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    International Journal for Numerical Methods in Engineering 26 (1988), S. 1631-1643 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A finite element solution for two-dimensional contact between elastic bodies is presented. Equations of constraint and equilibrium governing ‘sticking’ and ‘sliding’ contact are imposed at mesh contact boundaries and incorporated in the usual displacement solution routine. The method allows sliding over curved bodies and the dynamic coefficient of friction between the bodies is included in a direct (non-iterative) solution at each loading stage.A progressive loading approach is implemented whereby full loads are initially applied. If a change in the contact boundary condition occurs, then scaling (reduction) of loads and displacements is undertaken until the first new boundary constraint becomes just operative again. The remainder of the load is then applied with a modified stiffness matrix and the process is repeated. Finally the mesh is fully loaded and the contact boundary conditions are satisfied.Sample problems include comparison of the finite element results with classical solutions from the literature.
    Additional Material: 16 Ill.
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  • 198
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    International Journal for Numerical Methods in Engineering 26 (1988), S. 1665-1682 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A new fundamental solutions method for the numerical solution of two-dimensional biharmonic problems is described. In this method, which is based on the Almansi representation of a biharmonic function in the plane, the approximate solution is expressed in terms of fundamental solutions of Laplace's equation, and is determined by a least squares fit of the boundary conditions. The results of numerical experiments which demonstrate the efficacy of the method are presented.
    Additional Material: 2 Ill.
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  • 199
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    International Journal for Numerical Methods in Engineering 26 (1988), S. 1684-1684 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
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  • 200
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 26 (1988), S. 1689-1692 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
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