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  • Articles  (18)
  • sensitivity analysis  (18)
  • Wiley-Blackwell  (18)
  • American Geophysical Union
  • Wiley
  • Mathematics  (18)
  • 1
    Electronic Resource
    Electronic Resource
    An inverse solution procedure for material parameters identification in large plastic deformations (1996)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 12 (1996), S. 161-173 
    Details
    ISSN: 1069-8299
    Keywords: inverse identification ; non-linear behaviour ; material parameters ; sensitivity analysis ; finite elements ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The identification of materials rheological behaviour in the non-linear range is based on experimental tests. When using direct identification methods, one faces the problem of the interpretation of the experimental tests, which requires the assumption of deformation homogeneity and therefore the use of approximation methods. Since this assumption is often not satisfied in the case of non-linear behaviour, material parameters are not assessed precisely. In the paper, an inverse identification method is proposed to avoid the problems raised by interpretation of the experimental tests and to determine material parameters more accurately. The algorithm developed consists of both an optimization method and a finite element method. This method is applied to the inverse identification of viscoplastic parameters of an aluminium alloy, with an investigation on the effect of the initial guess and errors in experimental data on the identified values.
    Additional Material: 5 Ill.
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  • 2
    Electronic Resource
    Electronic Resource
    OPTIMAL DESIGN FOR NON-STEADY-STATE METAL FORMING PROCESSES - I. SHAPE OPTIMIZATION METHOD (1996)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 39 (1996), S. 33-50 
    Details
    ISSN: 0029-5981
    Keywords: finite element method ; shape optimization ; sensitivity analysis ; forming process ; optimal design ; forging ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: We suggest a shape optimization method for a non-linear and non-steady-state metal forming problem. It consists in optimizing the initial shape of the part as well as the shape of the preform tool during a two-step forging operation, for which the shape of the second operation is known. Shapes are described using spline functions and optimal parameter values of the splines are searched in order to produce, at the end of the forging sequence, a part with a prescribed geometric accuracy, optimal metallurgical properties and for a minimal production cost. The finite element method, including numerous remeshing operations, is used for the simulation of the process. We suggest using a least-squares-type algorithm for the unconstrained optimization method (based on external penalty) for which we describe the calculation of the derivatives of the objective function. We show that it can reduce to calculations which are equivalent to the derivative calculations of steady-state processes and to evolution equations. Therefore, the computational cost of such an optimization is quite reasonable, even for complex forging processes. Lastly, in order to reduce the errors due to the numerous remeshings during the simulation, we introduce error estimation and adaptive remeshing methods with respect to the calculation of derivatives.
    Additional Material: 6 Ill.
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  • 3
    Electronic Resource
    Electronic Resource
    SENSITIVITY ANALYSIS FOR BOUNDARY ELEMENT ERROR ESTIMATION AND MESH REFINEMENT (1996)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 39 (1996), S. 2907-2920 
    Details
    ISSN: 0029-5981
    Keywords: sensitivity analysis ; error estimates ; mesh refinement ; hypersingular integrals ; boundary element method ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The subject of this paper is the sensitivity analysis of approximate boundary element solutions with respect to the positions of the collocation points. The direct differentiation approach is considered here and the analysis is performed analytically. Since only the collocation points are perturbed, the shape of the body and the corresponding discretization remain unaltered. This aspect makes the present work quite different in spirit with respect to earlier analyses on shape sensitivities. Sensitivities of approximate BEM solutions with respect to the positions of collocation points are shown to be related to the residual of hypersingular integral equations. Numerical results confirm that the present approach can be seen as the analytical counterpart of an adaptive scheme for mesh refinement presented by the same author in some recent papers. Some other advantages of the present approach over the former one are also outlined.
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  • 4
    Electronic Resource
    Electronic Resource
    An optimization approach for stream function solution of potential flows around immersed bodies (1998)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 14 (1998), S. 253-269 
    Details
    ISSN: 1069-8299
    Keywords: potential flow ; optimization approach ; sensitivity analysis ; adjoint variable method ; finite elements ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Potential flow problems around immersed bodies have been treated by an optimization approach. When the stream function is used as the field variable, the boundary values may not be known a priori and may be taken as the decision parameters to minimize integral objective functionals. The circulation integrals around the immersed bodies or the Kutta condition at the trailing edges of the bodies may be used to construct the objective function of optimization. The sensitivity analysis needed for the minimization process is performed by the adjoint variable method, while the numerical solutions of the primary (flow) and adjoint equations have been obtained by the finite element method. Having checked the present method with exact solutions and the classical superposition method, several flow problems involving one or more immersed bodies with or without circulation are investigated numerically. © 1998 John Wiley & Sons, Ltd.
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  • 5
    Electronic Resource
    Electronic Resource
    Design sensitivity and constraint approximation methods for optimization in non-linear analysis (1997)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 13 (1997), S. 999-1008 
    Details
    ISSN: 1069-8299
    Keywords: optimization ; sensitivity analysis ; constraint approximation ; non-linear analysis ; finite element method ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: For the finite element non-linear analysis of engineering problems combined with an optimization method, two techniques - a semi-analytical sensitivity method and bi-point constraint approximation - have been proposed. To validate the proposed methods, a raft foundation on a soil medium has been analysed and the results have been compared. From the numerical results, it has been found that, for non-linear analysis, the semi-analytical sensitivity method is more efficient than the finite difference method and the bi-point approximation gives results which compare favourably with the finite element results. © 1997 John Wiley & Sons, Ltd.
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  • 6
    Electronic Resource
    Electronic Resource
    Tangential derivative of singular boundary integrals with respect to the position of collocation points (1998)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 41 (1998), S. 1255-1275 
    Details
    ISSN: 0029-5981
    Keywords: sensitivity analysis ; singular boundary integral equations ; hypersingular integrals ; boundary element method ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper investigates the evaluation of the sensitivity, with respect to tangential perturbations of the singular point, of boundary integrals having either weak or strong singularity. Both scalar potential and elastic problems are considered. A proper definition of the derivative of a strongly singular integral with respect to singular point perturbations should accommodate the concomitant perturbation of the vanishing exclusion neighbourhood involved in the limiting process used in the definition of the integral itself. This is done here by esorting to a shape sensitivity approach, considering a particular class of infinitesimal domain perturbations that ‘move’ individual points, and especially the singular point, but leave the initial domain globally unchanged. This somewhat indirect strategy provides a proper mathematical setting for the analysis. Moreover, the resulting sensitivity expressions apply to arbitrary potential-type integrals with densities only subjected to some regularity requirements at the singular point, and thus are applicable to approximate as well as exact BEM solutions. Quite remarkable is the fact that the analysis is applicable when the singular point is located on an edge and simply continuous elements are used. The hypersingular BIE residual function is found to be equal to the derivative of the strongly singular BIE residual when the same values of the boundary variables are substituted in both SBIE and HBIE formulations, with interesting consequences for some error indicator computation strategies. © 1998 John Wiley & Sons, Ltd.
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  • 7
    Electronic Resource
    Electronic Resource
    SIMULTANEOUS OPTIMIZATION OF SHAPE AND FLOW PARAMETERS FOR COMBINED FREE AND FORCED CONVECTION IN VERTICAL CHANNELS (1997)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 40 (1997), S. 551-563 
    Details
    ISSN: 0029-5981
    Keywords: sensitivity analysis ; simultaneous optimization ; mixed convection ; finite element method ; material derivative concept ; adjoint variable method ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Simultaneous optimization of shape and flow parameters is performed for a combined free and forced convection flow through vertical rectangular channels with moving walls. The laminar flow is assumed to be fully developed in the axial direction. The wall velocity, the axial pressure gradient and the channel height in the transverse plane are taken as the optimization parameters. The sensitivity expressions of both the objective function and the flow rate constraint of optimization are obtained in terms of the relevant physical variables, as well as adjoint variables which satisfy additional p.d.e.'s. All equations are discretized using the finite element method. Numerical results are provided for the present constrained optimization problem for various values of the problem parameters which include the moving wall segment size and the Rayleigh number. The results indicate that with increased Rayleigh number the optimal values of the wall velocity and the axial pressure gradient are increased, while the optimal value of the channel height is decreased. General sensitivity expressions are also presented in the appendix which might be utilized for arbitrary boundary variations along with arbitrary optimization objectives in other investigations. © 1997 by John Wiley & Sons, Ltd.
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  • 8
    Electronic Resource
    Electronic Resource
    Voigt-Reuss topology optimization for structures with linear elastic material behaviours (1997)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 40 (1997), S. 3033-3057 
    Details
    ISSN: 0029-5981
    Keywords: topology optimization ; structural design ; concept design ; mixing rules ; sensitivity analysis ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The desired results of variable topology material layout computations are stable and discrete material distributions that optimize the performance of structural systems. To achieve such material layout designs a continuous topology design framework based on hybrid combinations of classical Reuss (compliant) and Voigt (stiff) mixing rules is investigated. To avoid checkerboarding instabilities, the continuous topology optimization formulation is coupled with a novel spatial filtering procedure. The issue of obtaining globally optimal discrete layout designs with the proposed formulation is investigated using a continuation method which gradually transitions from the stiff Voigt formulation to the compliant Reuss formulation. The very good performance of the proposed methods is demonstrated on four structural topology design optimization problems from the literature. © 1997 John Wiley & sons, Ltd.
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  • 9
    Electronic Resource
    Electronic Resource
    Sensitivity computation and shape optimization for a non-linear arch model with limit-points instabilities (1998)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 42 (1998), S. 15-48 
    Details
    ISSN: 0029-5981
    Keywords: shape optimization ; sensitivity analysis ; non-linear arch ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A shape optimization method for geometrically non-linear structural mechanics based on a sensitivity gradient is proposed. This gradient is computed by means of an adjoint state equation and the structure is analysed with a total Lagrangian formulation. This classical method is well understood for regular cases, but standard equations have to be modified for limit points and simple bifurcation points. These modifications introduce numerical problems which occur at limit points. Numerical systems are very stiff and the quadratic convergence of Newton-Raphson algorithm vanishes, then higher-order derivatives have to be computed with respect to state variables. A geometrically non-linear curved arch is implemented with a finite element method via a formal calculus approach. Thickness and/or shape for differentiable costs under linear and non-linear constraints are optimized. Numerical results are given for linear and non-linear examples and are compared with analytic solutions. © 1998 John Wiley & Sons, Ltd.
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  • 10
    Electronic Resource
    Electronic Resource
    SHAPE SENSITIVITY ANALYSIS FOR STEADY METAL-FORMING PROCESSES (1996)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 39 (1996), S. 1199-1217 
    Details
    ISSN: 0029-5981
    Keywords: sensitivity analysis ; shape optimization ; extrusion ; drawing ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper develops a numerical technique for determining the shape sensitivity parameters in steady metal- forming processes such as drawing and rolling. The adjoint method is applied to the discrete non-linear system of equations in the finite element model in order to determine the discrete matrix of sensitivity parameters. In this work, two specific cases are considered. The first case involves determining the sensitivity of the process power requirement to the process geometry and the second case involves determining the sensitivity of the internal state variable distribution in the final product to the process geometry. The process geometry is assumed to be characterized by a finite number of shape parameters. The internal state variable distribution in this case represents the resistance to plastic flow and is considered to be related to the quality of the final product. Numerical examples for a simple drawing process are presented to demonstrate the efficiency of the algorithm.
    Additional Material: 11 Ill.
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