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  • 1
    Electronic Resource
    Electronic Resource
    Substructured macro elements based on locally blended interpolation (1977)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 11 (1977), S. 1405-1421 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In this paper we describe a new class of locally refined macro finite elements which are especially amenable to the use of substructuring techniques for the efficient solution of the resulting idealization. The tools and guidelines illustrated by the examples of modelling crack tips, point load singularities and singularities at re-entrant corners should enable an analyst to construct other such blended macro elements specifically tailored to his particular class of problems. The use of such substructured macro elements in finite element calculations permits substantial reduction in the manual effort of data preparation and the computational cost of numerical solution.
    Additional Material: 18 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620110906
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Blended infinite elements for paraboblic boundary value problems (1978)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 12 (1978), S. 1841-1851 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A common method for numerically approximating two-point parabolic boundary value problems of the form ut = L[u]+f(u) defined of the semi-infinite strip S = [0, 1]×[0, ∞] is to first discretize the spatial operator in the differential equation and then solve for the time evolution. Such an approach typically involves solving a system of algebriaic equations at a sequence of time steps. In this paper we take a different approach and subdivide S into a collection of semi-infinite substrips Si = [xi, xi+1]×[0, ∞], and use blending function techniques to derive finite parameter functions ei(x, t) defined on Si. Spectral matching methods are used in deriving ei to ensure that (u - ei) can be made small on Si. Galerkin's method, with associated integration sover the entire space-time domain S, is then used to generate approximations to u(x, t) based upon the so defined infinite element (ei, Si). Approximations are hence found for all (x, t) in S by solving one well structed system of algebraic equations. We apply the method to several linear and non-linear problms.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620121206
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    Punch stretching of sheet metal and differential equations on manifolds (1988)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 25 (1988), S. 269-282 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The goal of mathematical modelling of sheet metal forming processes is to provide predictive tools for use in the design of stamping processes and the selection of sheet materials. Most current approaches to finite element modelling of large deformation, elastic-plastic sheet metal forming problems use a rate form of the virtual work (equilibrium) equations, and a single-field finite element representation of the displacement components. Called the incremental method, this approach does not produce approximations which satisfy the discrete equilibrium equations at all times, and consequently it demands small time steps to insure stability and numerical accuracy. This paper describes a variant of the mixed method in which displacements, stresses, effective strain and pressures are all given separate finite element representations. The equilibrium equations in non-rate form are discretized to produce a system of algebraic equations which are coupled with the constitutive equations and then integrated using state-of-the-art numerical software. When used to model rate sensitive sheet materials in hydrostatic bulging, plane strain punch stretching and hemispherical punch stretching, the new approach proved to be between 6 and 26 times as fast as the old incremental method.
    Additional Material: 9 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620250120
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  • 4
    Electronic Resource
    Electronic Resource
    DEM: A new computational approach to sheet metal forming problems (1986)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 23 (1986), S. 847-862 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Many current approaches to finite element modelling of large deformation elastic - plastic forming problems use a rate form of the virtual work (equilibrium) equations, and a finite element representation of the displacement components. Called the incremental method, this approach produces a three-field formulation in which displacements, stresses and effective strain are dependent variables. Next, the formulation is converted to a one-field displacement formulation by an algebraic time discretization which uses a low order explicit time-stepping procedure to integrate the equations. This approach does not produce approximations which satisfy the discrete equilibrium equations at all times and, moreover, the advantage of the single-field algebraic formulation is realized at the expense of very small time steps needed to produce stability and accuracy in the numerical calculations.This paper describes a variant of the mixed method in which all three field variables (displacements, stresses and effective strain) are given finite element representations. The discrete equilibrium equations then generate a nonlinear system of algebraic equations whose solutions represent a manifold, while the constitutive equations form a system of ordinary differential equations. A commercially available, variable time step/variable order code is then used to integrate this differential/algebraic system. When applied to the problem of hydrostatic bulging of a membrane, the new approach requires far less computer time than the incremental method.
    Additional Material: 6 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620230507
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  • 5
    Electronic Resource
    Electronic Resource
    Automatic triangulation of arbitrary planar domains for the finite element method (1974)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 8 (1974), S. 679-696 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The object of this paper is to describe a new algorithm for the semi-automatic triangulation of arbitrary, multiply connected planar domains. The strategy is based upon a modification of a finite element mesh genration algorithm recently developed. 1 The scheme is designed for maximum flexibility and is capable of generating meshes of triangular elements for the decomposition of virtually any multiply connected planar domain. Moreover, the desired density of elements in various regions of the problem domain is specified by the user, thus allowing him to obtain a mesh decomposition appropriate to the physical loading and/or boundary conditions of the particular problem at hand. Several examples are presented to illustrate the applicability of the algorithm. An extension of the algorithm to the triangulation of shell structures is indicated.
    Additional Material: 19 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620080402
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  • 6
    Electronic Resource
    Electronic Resource
    An apporach to automatic three-dimensional finite element mesh generation (1985)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 21 (1985), S. 329-347 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Recently developed solid modelling systems for the design of complex physical solids using interactive computer graphics offer the exciting possibility of an integrated design/analysis system. Called geometric modellers, these systems build complex solids from primitive solids (cubes, cylinders, spheres, solid patches, etc.) and macro solids (combination of primitives)3, 4, 8, 16, 18, 25, 38. To provide an effective structural analysis capability for these systems, methods must be devised to ease the burden of discretizing the solid geometry into a user controlled (usually locally graded) finite element mesh. The purpose of this paper is to describe an interactive solid mesh generation system capable of generating valid meshes of well-proportional tetrahedral finite elements for the decomposition of multiply connected solid structures. The system uses a semi-automatic node insertion procedure to locate element node points within and on the surface of a structure. An independent automatic three-dimensional triangulator then accepts these nodes as input and connects them to form a valid finite element mesh oftetrahedral elements. Although this report makes use of a modeller based on a constructive solid geometry representation (a so-called CSG modeller), the mesh generation strategy elaborated herein is completely general and makes no particular use of the CSG representation.
    Additional Material: 20 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620210210
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  • 7
    Electronic Resource
    Electronic Resource
    A new class of transitional blended finite elements for the analysis of solid structuresPresented at the SIAM 30th Anniversary Meeting, Stanford University, 19-23 July 1982. (1984)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 20 (1984), S. 241-253 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Recently developed computer aided design systems for the design and modification of complex physical solids using interactive computer graphics offer the exciting possibility of an integrated design/analysis system. Called geometric modellers, these systems build complex solids from primitive solids (cubes, cylinders, spheres, etc.) and macro solids (combinations of primitives). To provide an effective finite element analysis capability for these systems, methods must be devised to ease the burden of discretizing the solid geometry into a user controlled finite element mesh. In this paper we describe a new class of transitional blended finite elements which make substantially simpler the task of finite element mesh generation and local mesh refinement. Computational experience indicates that numerical accuracy is not compromised by use of these flexible elements.
    Additional Material: 19 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620200205
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  • 8
    Electronic Resource
    Electronic Resource
    Design of optimal process parameters for non-isothermal forging (1994)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 37 (1994), S. 155-177 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper presents a state space model and an optimal design scheme for non-isothermal metal forming processes. By selecting nodal velocity and temperature as the state variables, a non-isothermal state equation with coupled deformation and thermal terms is established. Based on this state space model, a control design scheme is developed to obtain the optimal die velocity and initial die temperature which will ensure that the effective strain-rate and temperature satisfy the design requirements. A titanium alloy engine disk forging is used to demonstrate two design examples. The results show that the proposed model and design scheme behave well for different design requirements.
    Additional Material: 11 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620370111
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  • 9
    Electronic Resource
    Electronic Resource
    State-space representation and optimal control of non-linear material deformation using the finite element method (1993)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 36 (1993), S. 1967-1986 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A state-space model for representing the non-linear material deformation and an optimal control scheme for obtaining desired process conditions in the deforming material are presented in this paper. The formulation is general for various metal-forming processes including forging and extrusion operations. The state variables selected in the formulation are the die/billet contact nodal velocities and the nodal velocities of the critical finite elements of the billet. The control input is the ram velocity, which is determined by using the linear quadratic regulator (LQR) theory to maintain desired strain rates within the selected finite elements. The influence of an optimally designed ram velocity on the deforming material is studied using performance measures. This paper includes the development of the state-space model from non-linear finite element formulation, optimal control strategy and numerical example cases with discussions.
    Additional Material: 16 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620361202
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  • 10
    Electronic Resource
    Electronic Resource
    p-ADAPTIVITY IN THE TIME DOMAIN USING MVpq MULTIVALUE TIME-MARCHING INTEGRATORS (1997)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 40 (1997), S. 2343-2367 
    Details
    ISSN: 0029-5981
    Keywords: transient ; time-marching ; single-step ; hierarchical ; p-adaptivity ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A unified set of MVpq multivalue algorithms for a single-step time-marching scheme is presented for the transient diffusion equation. These MVpq algorithms include the well-known SSij single-step algorithms as a special case. Non-uniform integrators are introduced in which discrete equations in the o.d.e. set each separately use a different order of integrator. Hierarchical variables are used in the time domain, firstly to facilitate non-uniform integrators and secondly to permit variable length timesteps. This paper is the first in a series. In the sequel (Part 2)17 error estimates are introduced and the non-uniform integrator concept is utilized to implement p-adaptivity in time. © 1997 by John Wiley & Sons, Ltd.
    Additional Material: 15 Ill.
    Type of Medium: Electronic Resource
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