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  • 1
    Electronic Resource
    Electronic Resource
    An accurate scalar potential finite element method for linear, two-dimensional magnetostatics problems (1983)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 19 (1983), S. 725-737 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: We have assessed the accuracy of a commercially available computer software package for finite element method calculations of magnetostatic fields. The computer program, MSC/NASTRAN,Available from the MacNeal-Schwendler Corporation, Los Angeles, CA 90041, U.S.A. is well known for its wide applicability in structural analysis and heat transfer problems. We exploit the fact that the differential equations of magnetostatics are identical to those for heat transfer if the magnetic field problem is formulated with the reduced scalar potential.1 Consequently, the powerful, optimized numerical routines of NASTRAN can immediately be applied to two- and three-dimensional linear magneto-statics problems. Application of the NASTRAN reduced scalar potential approach to a ‘worst case’ two-dimensional problem for which an analytic solution is available has yielded much better accuracy than was recently reported2 for a reduced scalar potential calculation using a different finite element program. Furthermore, our method exhibits completely satisfactory performance with regard to computational expense and accuracy for a linear electromagnet with an air gap. Our analysis opens the way for large three-dimensional magnetostatics calculations at far greater economy than is possible with the more commonly used vector potential and boundary integral methods.
    Additional Material: 12 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620190507
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  • 2
    Electronic Resource
    Electronic Resource
    Quadratic reduction for the eigenproblem (1980)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 15 (1980), S. 911-923 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A quadratic method is presented for solving the eigenvalue problem of a structural system having a large number of degrees-of-freedom. The eigenproblem is reduced to a smaller problem by condensing the system stiffness and mass using Guyan reduction. Application of a set of corrective displacements to the reduced system subsequently leads to an eigenproblem of quadratic form involving an additional mass term. To obtain the solution to the reduced problem, inverse iteration with spectrum shifts based on the eigenvalues of the Guyan problem is used. The resulting eigenvalues and mode shapes represent a corrected Guyan approximation to the solution of the unreduced system. In addition, it is shown that the amount of improvement over the Guyan solution can be approximated by employing a first-order error analysis procedure. Numerical examples of vibrations of a bar, a beam and a plate demonstrate that the solutions obtained from the quadratic reduction procedure are very accurate and require relatively little additional computational effort in comparison with the solutions of the corresponding linear eigen-problem. The relationship of the present method to that proposed by Przemieniecki is illustrated by an example.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620150609
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    Numerical evaluation of stress intensity factor and J integral in three-point bend specimen (1984)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 20 (1984), S. 15-24 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The present paper attempts to evaluate the fracture mechanics parameters, the stress intensity factor (K) and Rice's energy integral (J) in plane strain conditions for three-point bend specimens. Both the parameters have been evaluated by the FEM using higher order isoparametric elements (i.e. quadratic elements). The crack tip elastic singularity (1/√r) has been taken into account by the use of the special crack tip elements of degenerate triangular element type as well as the fine eight-noded isoparametric plane elements. The stress distribution has been compared with the Westergaard solution in the vicinity of the crack. The K and J values have also been-compared with the theoretical results.
    Additional Material: 11 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620200103
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  • 4
    Electronic Resource
    Electronic Resource
    Computable finite element error bounds for Poisson's equation (1977)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 11 (1977), S. 593-597 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Theoretical error bounds of the form are often available for finite element solutions U of elliptic problems. In this form the estimates give the order of convergence of the method but are of little practical value for estimating the size of the error because the magnitudes of the constant K and the theoretical solution u are unknown. An exception occurs in the case of the equation ∂2u/∂x2 + ∂2u/∂y2 + f = 0 in a rectangle where the Ritz-Galerkin finite element solution involves piecewise linears over a regular triangular grid. In this case where α = 1 and Barnhill and Gregory1 have obtained the theoretical value 0·93√2 for K. In this note calculations are carried out for a variety of problems and the quantity K* = ∥u - U∥E/h∥f∥L2 measured and compared with K. The values of K* obtained fit into a well defined pattern from which we conclude that the theoretical constant K is of the correct order of magnitude.
    Additional Material: 1 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620110315
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  • 5
    Electronic Resource
    Electronic Resource
    Finite element analysis of multicomponent two-phase flows with interphase mass and momentum transport (1994)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 18 (1994), S. 821-842 
    Details
    ISSN: 0271-2091
    Keywords: Free-surface ; Interphase mass transfer ; Finite element two-phase flow ; Coating ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The application of the finite element method to multiphase flow problems with interphase mass and heat transfer is described. A general forinulation is used that determines the position of the interfacial boundary and allows for multiple solvents, differential volatilities and concentration- and temperature-dependent thermophysical properties. Species phase change and the dramatic volume change that acompanies interphase mass transfer make implementation of the theory challening, since these events lead to discontinuous velocities and concentrations at phase boundaries. These discontinuities are especially large in processes involving rapid evaporation or condensation. As examples we examine the effects of rapid drying on film and fibre formation of sol--gel materials, which are often laden with volatile species.
    Additional Material: 10 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650180903
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  • 6
    Electronic Resource
    Electronic Resource
    APPLICATION OF TOPOLOGICAL OPTIMIZATION TECHNIQUES TO STRUCTURAL CRASHWORTHINESS (1996)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 39 (1996), S. 1383-1403 
    Details
    ISSN: 0029-5981
    Keywords: crashworthiness ; homogenization ; topology design ; automotive structure optimization ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The topological optimization of components to maximize crash energy absorption for a given volume is considered. The crash analysis is performed using a DYNA3D finite element analysis. The original solid elements are replaced by ones with holes, the hole size being characterized by a so-called density (measure of the reduced volume). A homogenization method is used to find elastic moduli as a function of this density. Simpler approximations were developed to find plastic moduli and yield stress as functions of density.Optimality criteria were derived from an optimization statement using densities as the design variables. A resizing algorithm was constructed so that the optimality criteria are approximately satisfied. A novel feature is the introduction of an objective function based on strain energies weighted at specified times. Each different choice of weighting factors leads to a different structure, allowing a range of design possibilities to be explored.The method was applied to an automotive body rear rail. The original design and a new design of equal volume with holes were compared for energy absorption.
    Additional Material: 25 Ill.
    Type of Medium: Electronic Resource
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  • 7
    Electronic Resource
    Electronic Resource
    Geometrically based, automatic generator for irregular triangular networks (1993)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 9 (1993), S. 555-566 
    Details
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The network generation method described herein produces two-dimensional irregular triangular grids in which element area is proportional to some scalar density function defined over the domain. This density function can reflect arbitrarily chosen properties of the geometry or flow. After the initial generation, various adjustment utilities and an interactive (graphic-based) editor ensures that the resultant triangular elements are well shaped. Some of these utilities can be used with adaptive refinement schemes.
    Additional Material: 10 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cnm.1640090703
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  • 8
    Electronic Resource
    Electronic Resource
    Local refinement techniques for elliptic problems on cell-centered grids; II. Optimal order two-grid iterative methods (1994)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Linear Algebra with Applications 1 (1994), S. 337-368 
    Details
    ISSN: 1070-5325
    Keywords: Local refinement ; Preconditioning ; Two-grid method ; Cell-centered grids ; Finite differences ; Elliptic problem ; Optimal rate of convergence ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Two preconditioning techniques for solving difference equations arising in finite difference approximation of elliptic problems on cell-centered grids are studied. It is proven that the BEPS and the FAC preconditioners are spectrally equivalent to the corresponding finite difference schemes, including a nonsymmetric one, which is of higher-order accuracy. Numerical experiments that demonstrate the fast convergence of the preconditioned iterative methods (CG and GCG-LS in the nonsymmetric case) are presented.
    Additional Material: 3 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nla.1680010403
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  • 9
    Electronic Resource
    Electronic Resource
    On the eigenvalues basic to the analytical solution of convective heat transfer with axial diffusion effects (1995)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 11 (1995), S. 287-296 
    Details
    ISSN: 1069-8299
    Keywords: eigenvalues ; integral transforms ; analytical methods ; convection ; Sturm-Liouville system ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The integral transform method is employed in the analytical solution of the non-classical eigenvalue problem that appears in connection with the analysis of forced convection in ducts, including the effect of fluid heat diffusion in the axial direction. The related eigenfunctions are expanded in terms of eigenfunctions from a simpler auxiliary eigenvalue problem, and the original eigenvalues are determined from the associated matrix eigensystem analysis. Convergence rates of the proposed solutions are illustrated and reference results established for different values of the governing parameters.
    Additional Material: 4 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cnm.1640110402
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  • 10
    Electronic Resource
    Electronic Resource
    A simple class of finite elements for plate and shell problems. I: Elements for beams and thin flat plates (1992)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 35 (1992), S. 955-977 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This is the first paper of a pair which together discuss the development of a class of overlapping hinged bending finite elements which are suitable for the analysis of thin-shell, plate and beam structures. These elements rely on a simple physical analogy, involving overlapping hinged facets. They are based on quadratic overlapping assumed displacement functions. Only translational nodal degrees of freedom are necessary, which is a significant simplification over most other currently available beam, plate and shell finite elements which employ translational, rotational and higher-order nodal variables. In this paper the hinged bending element concept is introduced, and the hinged beam bending (HBB) and hinged plate bending (HPB) elements are formulated. In paper II these concepts are extended to develop a hinged shell bending (HSB) element. The HSB element can be readily combined with the constant strain triangular (CST) plane stress finite element for the modelling of thin-shell structures.
    Additional Material: 17 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620350502
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