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  • 1
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 13 (1997), S. 977-986 
    ISSN: 1069-8299
    Keywords: sequential function approximation ; interpolation functions ; optimization ; parallel direct search ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A computational method for the solution of differential equations is proposed. With this method an accurate approximation is built by incremental additions of optimal local basis functions. The parallel direct search software package (PDS), that supports parallel objective function evaluations, is used to solve the associated optimization problem efficiently. The advantage of the method is that, although it resembles adaptive methods in computational mechanics, an a priori grid is not necessary. Moreover, the traditional matrix construction and evaluations are avoided. Computational cost is reduced while efficiency is enhanced by the low-dimensional parallel-executed optimization and parallel function evaluations. In addition, the method should be applicable to a broad class of interpolation functions. Results and global convergence rates obtained for one- and two-dimensional boundary value problems are satisfactorily compared to those obtained by the conventional Galerkin finite element method. © 1997 John Wiley & Sons, Ltd.
    Additional Material: 3 Ill.
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  • 2
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 13 (1997), S. 999-1008 
    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.
    Additional Material: 4 Ill.
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  • 3
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 40 (1997), S. 777-796 
    ISSN: 0029-5981
    Keywords: finite element method ; force method ; reanalysis ; eigenvalue ; structural variation ; optimization ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper presents a force-based finite element method that involves eigen-space transformation of element stiffness matrices in the first analysis. In each subsequent analysis (‘reanalysis’) associated with structural variations, the solution obtained previously is modified making use of intrinsic properties of eigen solutions and avoiding the time-consuming task of solving a large system of equations. The structural variations may involve changes in material properties, birth or death of elements, or change in boundary conditions. Numerical examples are presented to compare the accuracy and computational efficiency of the proposed method with the displacement-based finite element method. © 1997 by John Wiley & Sons, Ltd.
    Additional Material: 12 Ill.
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  • 4
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 40 (1997), S. 655-687 
    ISSN: 0029-5981
    Keywords: crashworthiness ; multibody dynamics ; flexible structures ; simulation ; design ; optimization ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Different formulations based on multibody dynamics are shown to be suitable for the development of a methodology for the impact simulation and crashworthiness design of railway vehicles. The proposed design methodology comprises different computer-aided tools of increasing complexity and accuracy which can be used with greater advantage and efficiency in the different design stages of railway stock. In general, the crashworthiness design methods and associated multibody dynamic tools which are presented in this paper require information to be obtained from numerical or experimental crush tests of specific structural components, subassemblies and critical energy absorption devices normally located in car extremities. This hybrid feature lends to the present design process various efficiency gains as a result of a better understanding of the crash and different collapse mechanisms and ease of use. To access the merits of the present methodologies some new designs are discussed and the application of the proposed numerical tools is illustrated for different structural configurations of car extremities. A formulation for the sensitivity analysis and optimization of planar constrained mechanical systems is also presented. An example of crashworthiness design of an end underframe model of a railway car is solved to demonstrate the use of the methodology. © 1997 by John Wiley & Sons, Ltd.
    Additional Material: 26 Ill.
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  • 5
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 40 (1997), S. 1213-1230 
    ISSN: 0029-5981
    Keywords: metal forming ; preform design ; forging ; sensitivity analysis ; optimization ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An optimization algorithm for preform die shape design in metal-forming processes is developed in this paper. The preform die shapes are represented by cubic B-spline curves. The control points of the B-spline are used as the design variables. The optimization objective is to reduce the difference between the realized and desired final forging shapes. The sensitivities of the objective function with respect to the design variables are developed in detail. The numerical examples show that the optimization method and the sensitivity analysis developed in this paper are very useful and the design results are satisfactory. Importantly, the preform die shapes designed by this method are easily manufacturable and can be implemented in practical metal-forming operations. This optimization method and the sensitivity analysis can also be applied in the preform design of complex industrial metal-forming problems. © 1997 by John Wiley & Sons, Ltd.
    Additional Material: 11 Ill.
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  • 6
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 40 (1997), S. 1505-1524 
    ISSN: 0029-5981
    Keywords: linkages ; synthesis ; position problems ; optimization ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The present paper describes a procedure for the optimal dimensional synthesis of mechanisms which is based on the solution of non-linear position problems. Planar mechanisms are modelled very easily by means of finite elements of bi-hinged rod type. The judicious choice of constraint conditions makes possible the solution of classical position problems: initial, finite-displacement, deformed and static-equilibrium problems, as well as the main types of dimensional synthesis: path generation, functions, rigid body guidance, mixed, and multiple. A single synthesis error function applies to all these types, and moreover is general since it is valid for mechanisms of any configuration. This function is based on the idea that the best mechanism for the given synthesis conditions is the one that least needs to be deformed when it is obliged to satisfy them exactly, to which end the elastic deformation of the elements is permitted. © 1997 by John Wiley & Sons, Ltd.
    Additional Material: 6 Ill.
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  • 7
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 40 (1997), S. 165-188 
    ISSN: 0029-5981
    Keywords: engineering design ; optimization ; discrete variables ; numerical methods ; test problems ; evaluation of methods ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Continuous-discrete variable non-linear optimization problems are defined and categorized into six different types. These include a full range of problems from continuous to purely discrete and non-differentiable. Methods for solution of these problems are studied and their characteristics are catalogued. The branch and bound, simulated annealing and genetic algorithms are found to be the most general methods for solving discrete problems. After some enhancements, these and two other methods are implemented into a program for certain applications. Several example problems are solved to study performance of the methods. It is concluded that solution of the mixed variable non-linear optimization problems usually requires considerable more computational effort compared to the continuous variable optimization problems. In addition, there is no guarantee that the best solution has been obtained; however, good practical solutions are usually obtained. © 1997 by John Wiley & Sons, Ltd.
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  • 8
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 40 (1997), S. 1525-1550 
    ISSN: 0029-5981
    Keywords: adjoint problem ; discrete curvature ; finite element method ; free surface flow ; optimization ; quasi-Newton method ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Optimal shape design approach is applied to numerical computation of a model potential free boundary value problem. The problem is discretized using the finite element method. To test the approach the problem is formulated in both velocity potential and stream function formulation and four different finite element discretizations are used. Associated minimization problem is solved using the quasi-Newton method. Gradient of the cost function is computed by solving the algebraic adjoint equation. Gravity and surface tension forces are included in the model. Viability of the method is showed by solving problems with important effects of gravity and surface tension forces. © 1997 by John Wiley & Sons, Ltd.
    Additional Material: 8 Ill.
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