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  • 1
    Electronic Resource
    Electronic Resource
    Shape optimal design of elastic planar frames with non-linear response (1995)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 38 (1995), S. 3227-3242 
    Details
    ISSN: 0029-5981
    Keywords: planar-frames ; non-linear elasticity ; shape optimal design ; Bezier curves ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper describes an approach to shape optimal design of elastic planar frames with non-linear response. The foundation of the proposed approach forms an appropriate strategy of shape representation of the structure, based on the design element technique. A frame structure is treated as to be assembled from several frame design elements, which in turn may consist of several appropriately joined beam finite elements. The shape of each frame design element is defined by convenient functions involving Bezier blending polynomials. The original formulation of the beam finite element, proposed by Saje, is modified in order to fit nicely into the context of the frame design element technique. The formulation of the shape optimal design problem in a form of a problem of non-linear mathematical programming and its solution by employing gradient-based methods of mathematical programming are discussed briefly. The theory is illustrated with two numerical examples.
    Additional Material: 6 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620381904
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  • 2
    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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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    Incremental objectivity in cyclic shearing deformations (1996)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 12 (1996), S. 863-871 
    Details
    ISSN: 1069-8299
    Keywords: objectivity ; kinematics ; computational mechanics ; large deformations ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In this paper, an example problem is presented that illustrates the importance of strong objectivity in kinematic algorithms for large-deformation finite element applications. The example problem involves cyclic simple shearing of a hypoelastic material, wherein the increments of stretch and of rotation are of comparable magnitude. It is demonstrated that two kinematic algorithms that are in common use, and which are only weakly objective, give rise to an accumulative error in the normal stress components. The error is surprisingly large, even for very small strain increments. This behaviour arises due to a coupling between the stretch and rotation increments that is exhibited by weakly objective algorithms, and is perhaps especially serious in the context of models for jointed rock and other frictional materials, in which the shear response may depend strongly on the normal components of stress.
    Additional Material: 3 Ill.
    Type of Medium: Electronic Resource
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    Paper (German National Licenses)
  • 4
    Electronic Resource
    Electronic Resource
    The use of bubble functions for the post-local buckling of plate assemblies by the finite strip method (1995)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 38 (1995), S. 955-968 
    Details
    ISSN: 0029-5981
    Keywords: bubble functions ; elasticity ; finite strips ; I-sections ; non-linear analysis ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The finite strip displacement functions for post-local buckling are augmented with so-called bubble functions, which are extra modes associated with internal or nodeless degrees of freedom. A non-linear finite strip method of analysis including bubble functions is described for the post-local buckling of geometrically imperfect plate assemblies. It is shown that the use of bubble functions improves significantly the convergence of the method. The non-linear finite strip method is then used to study channel and I-section members in compression and bending.
    Additional Material: 9 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620380606
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  • 5
    Electronic Resource
    Electronic Resource
    A C0 EIGHT-NODE MEMBRANE-SHEAR-BENDING ELEMENT FOR GEOMETRICALLY NON-LINEAR (STATIC AND DYNAMIC) ANALYSIS OF LAMINATES (1996)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 39 (1996), S. 3453-3474 
    Details
    ISSN: 0029-5981
    Keywords: plate ; finite element ; locking ; non-linear ; buckling ; vibrations ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A new eight-node C0 membrane-plate quadrilateral finite element is presented to analyse static and dynamic moderately large deflections of moderately thick laminates. The finite element is based on the Reissner- Mindlin plate theory and on previous works for the shear-bending (plate) part, which has been described in a previous paper, Reference 10. In the paper, the novelty is in the way of improving isoparametric membrane response without adding zero-energy modes, and the moderately large deflection static and dynamic analysis of laminates based on von Karman's assumptions. Finally, some numerical simulations are presented in statics and in dynamics for laminates, including buckling analysis and membrane-plate coupling effects. Among a large variety of finite elements which have been proposed during the two last decades, interest in the present element lies in its simplicity implementation, its efficiency without any correction factors and spurious energy modes, and (also) the fact it is fully standard from an engineering view point.
    Additional Material: 10 Ill.
    Type of Medium: Electronic Resource
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    Paper (German National Licenses)
  • 6
    Electronic Resource
    Electronic Resource
    A patch test for mesh alignment effects in localized failure (1995)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 11 (1995), S. 1015-1024 
    Details
    ISSN: 1069-8299
    Keywords: localization ; volumetric locking ; pressure formulation ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Computation of failure mechanisms is of paramount importance for engineers assessing safety of structures. However, computation of failure loads and mechanisms presents numerical difficulties leading to wrong answers, especially in the case where failure consists in localization of plastic deformation or damage in localized zones. Here, the results depend on factors like mesh alignment and element distortion. The paper addresses the problem of designing a suitable patch test to assess element performance under localized failure. It will be shown how predictions of this test provide a reliable answer to the question of whether a particular element will or will not be suitable for such failure computations.
    Additional Material: 7 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cnm.1640111207
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  • 7
    Electronic Resource
    Electronic Resource
    Calculation of fully developed flows of complex fluids in pipes of arbitrary shape, using a mapped circular domain (1995)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 11 (1995), S. 813-820 
    Details
    ISSN: 1069-8299
    Keywords: non-circular ducts ; mapping functions ; non-Newtonian fluids ; Levenberg-Marquardt algorithm ; velocity contour values ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The problem of determination of fully developed duct flows of arbitrary shape is considered for fluids obeying various constitutive equations. A numerical method based on the transformation of the physical flow (simply connected) domain into a mapped circular domain is set up. The numerical determination of the unknown transformation between the two domains leads to knowledge of the velocities and stresses in the duct, starting from circular contour values of the velocity in the mapped computational domain. Different constitutive equations are investigated for several flow geometries. The comparisons with existing analytical solutions are found to be consistent for all the geometries tested. The method may provide a useful tool for determination, in steady flow conditions, of the flow characteristics for various types of ducts and constitutive equations.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cnm.1640111005
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    Paper (German National Licenses)
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  • 8
    Electronic Resource
    Electronic Resource
    A second order finite element method for the solution of the transonic Euler and Navier-Stokes equations (1995)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 20 (1995), S. 671-693 
    Details
    ISSN: 0271-2091
    Keywords: airfoil ; artificial viscosity ; upwinding ; 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 numerical solution of the compressible Euler and Navier-Stokes equations in primitive variables form requires the use of artificial viscosity or upwinding. Methods that are first-order-accurate are too dissipative and reduce the effective Reynolds number substantially unless a very fine grid is used. A first-order finite element method for the solution of the Euler and Navier-Stokes equations can be constructed by adding Laplacians of the primitive variables to the governing equations. Second-order schemes may require a fourth-order dissipation and higher-order elements. A finite element approach is proposed in which the fourth-order dissipation is recast as the difference of two Laplacian operators, allowing the use of bilinear elements. The Laplacians of the primitive variables of the first-order scheme are thus balanced by additional terms obtained from the governing equations themselves, tensor identities or other forms of nodal averaging. To demonstrate formally the accuracy of this scheme, an exact solution is introduced which satisfies the continuity equation identically and the momentum equations through forcing functions. The solutions of several transonic and supersonic inviscid and laminar viscous test cases are also presented and compared to other available numerical data.
    Additional Material: 17 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650200802
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  • 9
    Electronic Resource
    Electronic Resource
    A DIRECTIONALLY ADAPTIVE METHODOLOGY USING AN EDGE-BASED ERROR ESTIMATE ON QUADRILATERAL GRIDS (1996)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 23 (1996), S. 673-690 
    Details
    ISSN: 0271-2091
    Keywords: Euler equations ; directionally adaptive meshes ; edge-based error estimate ; structured grids ; mesh movement ; finite element method ; high-speed flows ; 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 present paper describes a directionally adaptive finite element method for high-speed flows, using an edge-based error estimate on quadrilateral grids. The error of the numerical solution is estimated through its second derivatives and the resulting Hessian tensor is used to define a Riemannian metric. An improved mesh movement strategy, based on a spring analogy, but with no orthogonality constraints, is introduced to equidistribute the lengths of the edges of the elements in the defined metric. The grid adaptation procedure is validated on an analytical test case and the efficiency of the overall methodology is investigated on supersonic and hypersonic benchmarks.
    Additional Material: 21 Ill.
    Type of Medium: Electronic Resource
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    Paper (German National Licenses)
  • 10
    Electronic Resource
    Electronic Resource
    A little more on stabilized Q1Q1 for transient viscous incompressible flow (1995)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 21 (1995), S. 837-856 
    Details
    ISSN: 0271-2091
    Keywords: stabilized finite elements ; projection method ; approximate projections ; equal-order interpolation ; 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: In an attempt to overcome some of the well-known ‘problems’ with the Q1P0 element, we have devised two ‘stabilized’ versions of the Q1Q1 element, one based on a semi-implicit approximate projection method and the other based on a simple forward Euler technique. While neither one conserves mass in the most desirable manner, both generate a velocity field that is usually ‘close enough’ to divergence-free. After attempting to analyse the two algorithms, each of which includes some ad hoc ‘enhancements’, we present some numerical results to show that they both seem to work well enough. Finally, we point out that any projection method that uses a ‘pressure correction’ approach is inherently limited to time-accurate simulations and, even if treated fully implicitly, is inappropriate for seeking steady states via large time steps.
    Additional Material: 8 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650211005
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    Paper (German National Licenses)
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