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  • Engineering  (929)
  • Wiley-Blackwell  (929)
  • American Physical Society
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  • 1
    Electronic Resource
    Electronic Resource
    A posteriori pointwise upper bound error estimates in the finite element method (1993)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 36 (1993), S. 1279-1298 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An error estimate for the finite element method is presented in this paper. The error is identified as the response to a set of residual forces, and a complementary analysis provides an upper bound estimate of the global energy of the error. The inequality proposed by Babuška and Miller1 is then employed to bound the error in stress and displacement at a point. The formula is derived for two-dimensional elasticity, but the procedure is general; and can be applied to three-dimensional and other problems. Numerical experiments using the procedure are carried out and the results are given for the four-node bilinear compatible element and plane stress.
    Additional Material: 19 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620360803
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  • 2
    Electronic Resource
    Electronic Resource
    Vibration problems using isoparametric shell elements (1972)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 5 (1972), S. 142-145 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Additional Material: 1 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620050114
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  • 3
    Electronic Resource
    Electronic Resource
    Frequency analysis of thick orthotropic plates on elastic foundation using a high precision triangular plate bending element (1979)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 14 (1979), S. 531-544 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A high precision triangular thick orthotropic plate bending element on an elastic foundation is developed for the free vibration analysis of thick plates on elastic foundation. The element has three nodes with twelve degrees-of-freedom per node, and takes into account the shear deformation and rotatory inertia. The accuracy of the element is established by comparison of the natural frequencies of certain thick and thin plates, determined from a consistent mass matrix formulation, with available results.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620140406
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  • 4
    Electronic Resource
    Electronic Resource
    A linear finite element approach to the solution of the variational inequalities arising in contact problems of structural dynamics (1982)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 18 (1982), S. 1505-1520 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The present paper deals with the theoretical and numerical treatment of dynamic unilateral problems. The governing equations are formulated as an equivalent variational inequality expressing D' Alembert's principle in its inequality form. The discretization with respect to time and space leads to a static nonlinear programming problem which is solved by an appropriate algorithm. Some properties of dynamic unilateral problems are outlined and the influence of several parameters on the solution is investigated by means of numerical examples.
    Additional Material: 9 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620181006
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  • 5
    Electronic Resource
    Electronic Resource
    On the numerical solution of a class of problems in a linear first strain-gradient theory of elasticity (1970)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 2 (1970), S. 159-174 
    Details
    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 general discrete models for the analysis of boundary-value problems in the first strain-gradient theory of elasticity. Extensions of the finite element method are constructed for this purpose, and general equations of motion are derived for finite elements of a class of micro-polar materials which are characterized by strain energy functions involving strains and second gradients of strains or displacements. The notion of generalized nodal doublets is introduced. The problem of a composite consisting of a strain-gradient sensitive microlayer embedded between semi-infinite bodies is examined as an example problem. Some of the results are compared with available exact solutions.
    Additional Material: 7 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620020203
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  • 6
    Electronic Resource
    Electronic Resource
    A model of binary alloy solidification (1984)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 20 (1984), S. 1067-1084 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A linear model for the solidification of a dilute binary alloy is presented. In this model the solidus and liquidus curves are linear. As a consequence internal energy depends linearly upon temperature and concentration. The formulation is a generalization of the well-known enthalpy method to treat a phase change problem involving coupled heat and mass transfer. Both analytic and numerical formulations are given. Results from the latter are presented and compared with an explicit solution of Rubinstein for a Stefan-like problem posed in a semi-infinite slab. Some remarks on the behaviour of the explicit solution are given.
    Additional Material: 5 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620200609
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  • 7
    Electronic Resource
    Electronic Resource
    A posteriori estimates of the solution error caused by discretization in the finite element, finite difference and boundary element methods (1987)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 24 (1987), S. 1921-1939 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A theory is described which guarantees an upper and lower bound estimate of the discretization error in numerical solutions of elliptic boundary value problems. This method gives bounded global estimates of the error in the energy norm. Pointwise estimates of the error in the solution variable or its derivatives can then be obtained if the numerical solution is exhibiting pointwise monotonic convergence.The versatility of this method is illustrated by its application to numerical solutions from finite element, finite difference and boundary element methods.
    Additional Material: 8 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620241008
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  • 8
    Electronic Resource
    Electronic Resource
    Pure moment loading of axisymmetric finite element models (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 5 (1973), S. 459-463 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A method of loading axisymmetric finite element models by application of a uniform circumferentially distributed moment is presented herein. Operationally, this is accomplished by changing the radius of curvature of some reference point in the axisymmetric model. The radius change gives rise to hoop strains, which are used in an ‘initial strain’ method to actually load the model. The resulting pure axisymmetric moment is computed by integrating the hoop stresses thus generated over a cross-sectional cut through the axisymmetric model. For non-linear problems, the procedure just described can be performed incrementally. Several numerical examples are presented herein to illustrate the method, such as bending of a curved bar, sharp folding of a thin sheet and bending of a toroidal tube until the cross-section is flattened.
    Additional Material: 1 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620050403
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  • 9
    Electronic Resource
    Electronic Resource
    Direct solution of two linear systems of equations forming coupled tridiagonal-type matrices (1977)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 11 (1977), S. 1049-1052 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Additional Material: 1 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620110612
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  • 10
    Electronic Resource
    Electronic Resource
    Solution of non-linear differential equations by discrete least squares (1978)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 12 (1978), S. 597-612 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A general-purpose technique has been developed for solving non-linear partial differential equations. A set of approximating functions with undetermined parameters is used to evaluate the differential equation and boundary conditions at discrete points, forming a set of residuals to be minimized. The parameters which minimize the sum of squared residuals are determined by a non-linear least-squares minimization technique. Initial value problems are solved by integrating the equations with respect to time at the fitting points by a predictor-corrector algorithm. The resulting formulation is independent of the form of the problem and the approximating functions, so that a broad class of problems may be solved with a single computer program. The technique is applied to several boundary and initial value problems in one and two spatial dimensions. The tecnique is applied to several boundary and initial value problems in one and two spatial dimensions.
    Additional Material: 5 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620120405
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