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  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Structural optimization 18 (1999), S. 12-23 
    ISSN: 0934-4373
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract The numerical treatment of shape optimization problems requires sophisticated software tools such as Computer Aided Design (CAD), the Finite Element Method (FEM) and a suitable Mathematical Programming (MP) algorithm. Efficiency of the overall procedure is guaranteed if these tools interact optimally. The theoretical and numerical effort for sensitivity analysis reflect the complexity of this engineering problem. In this paper we outline a general modelling concept for shape optimization problems. Hierarchical design models within Computer Aided Geometrical Design (CAGD) and the interaction of geometry and FEM lead to an efficient overall optimization procedure. Our concept has been derived, implemented and tested for shell structures but it is seen to be generally applicable. After a short introduction containing the state of the art we give an overview of the numerical tools used and outline the interaction of CAGD and FEM within the overall optimization procedure. The paper is mainly devoted to the hierarchical design space based on a hierarchical geometrical modelling. The major part of computational effort is consumed by sensitivity analysis related to the number of design variables. Therefore, this number should be limited and only few powerful design variables corresponding to the special interests of the considered problem should be defined. This procedure may lead to a considerable limitation of the design space. Based on a hierarchy in the geometrical model different types of design variables are introduced: design variables with global, regional and local influence. The new method is based on successive activation of these types of design variables. This procedure leads to a considerable reduction of computational time for the sensitivity analysis without loss of geometrical flexibility. A new method of geometrical refinement and a successive adaptively driven expansion and reduction of the design space is described. It is based on the degree elevation or degree reduction of parametric curves and surfaces, respectively. A numerical example illustrates the new method and the efficiency of the overall optimization procedure.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    Springer
    Structural and multidisciplinary optimization 11 (1996), S. 102-112 
    ISSN: 1615-1488
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract This paper presents a numerical performance comparison of a modern version of the well-established sequential quadratic programming (SQP) method and the more recent spherical approximation method (SAM). The comparison is based on the application of these algorithms to examples with nonlinear objective and constraint functions, among others: weight minimization problems in structural shape optimization. The comparison shows that both the SQP and SAM-algorithms are able to converge to accurate minimum weight values. However, because of the lack of a guaranteed convergence property of the SAM method, it exhibits an inability to consistently converge to a fine tolerance. This deficiency is manifested by the appearance of small oscillations in the neighbourhood of the solution.
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    Springer
    Structural and multidisciplinary optimization 18 (1999), S. 12-23 
    ISSN: 1615-1488
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract The numerical treatment of shape optimization problems requires sophisticated software tools such as Computer Aided Design (CAD), the Finite Element Method (FEM) and a suitable Mathematical Programming (MP) algorithm. Efficiency of the overall procedure is guaranteed if these tools interact optimally. The theoretical and numerical effort for sensitivity analysis reflect the complexity of this engineering problem. In this paper we outline a general modelling concept for shape optimization problems. Hierarchical design models within Computer Aided Geometrical Design (CAGD) and the interaction of geometry and FEM lead to an efficient overall optimization procedure. Our concept has been derived, implemented and tested for shell structures but it is seen to be generally applicable. After a short introduction containing the state of the art we give an overview of the numerical tools used and outline the interaction of CAGD and FEM within the overall optimization procedure. The paper is mainly devoted to the hierarchical design space based on a hierarchical geometrical modelling. The major part of computational effort is consumed by sensitivity analysis related to the number of design variables. Therefore, this number should be limited and only few powerful design variables corresponding to the special interests of the considered problem should be defined. This procedure may lead to a considerable limitation of the design space. Based on a hierarchy in the geometrical model different types of design variables are introduced: design variables with global, regional and local influence. The new method is based on successive activation of these types of design variables. This procedure leads to a considerable reduction of computational time for the sensitivity analysis without loss of geometrical flexibility. A new method of geometrical refinement and a successive adaptively driven expansion and reduction of the design space is described. It is based on the degree elevation or degree reduction of parametric curves and surfaces, respectively. A numerical example illustrates the new method and the efficiency of the overall optimization procedure.
    Type of Medium: Electronic Resource
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  • 4
    Electronic Resource
    Electronic Resource
    Springer
    Computational mechanics 22 (1998), S. 225-238 
    ISSN: 1432-0924
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract Many interesting tasks in technology need the solution of complex boundary value problems within the mathematical theory of elastoplasticity. Error controlled adaptive strategies should be used in order to achieve a prescribed accuracy of the computed solutions at minimum cost. Local error indicators in the primal form of the finite-element-method for Hencky- and Prandtl–Reußplasticity without and with nonlinear hardening are presented, controlling global errors of equilibrium, plastic strain rates, the yield condition and the numerical integration of the flow rule. A 2D finite element code was extended for the transfer of physical parameters between meshes and for a combined space and time adaptive strategy. All error indicators are tested with the benchmark example of a rectangular plane strain problem with a hole.
    Type of Medium: Electronic Resource
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  • 5
    Electronic Resource
    Electronic Resource
    Springer
    Structural and multidisciplinary optimization 11 (1996), S. 29-42 
    ISSN: 1615-1488
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract A variational formulation of shape design sensitivity analysis is outlined, starting from a differential geometry-based representation of continuum mechanics. A rigorous analysis using convected curvilinear coordinates yields a decomposition of all continuum mechanical functions into independent geometry and displacement mappings. Using this representation of geometry and displacements defined on a fixed parameter space, their influence on physical quantities can easily be separated. Consequently, the variations of continuum mechanical quantities with respect to either geometry or displacements can be performed similarly using the well-known linearization techniques in nonlinear mechanics. The proposed methodology for performing variational design sensitivity analysis is formulated for general nonlinear hyperelastic material behaviour using either the Lagrangian or Eulerian description. The differences and similarities of the formulation presented compared with the material derivative approach and the domain parametrization approach are highlighted and discussed.
    Type of Medium: Electronic Resource
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  • 6
    Electronic Resource
    Electronic Resource
    Springer
    Structural and multidisciplinary optimization 9 (1995), S. 46-51 
    ISSN: 1615-1488
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract The numerical solution of shape optimization problems is considered. The algorithm of successive optimization based on finite element techniques and design sensitivity analysis is applied. Mesh refinement is used to improve the quality of finite element analysis and the computed numerical solution. The norm of the variation of the Lagrange augmented functional with respect to boundary variation (residuals in necessary optimality conditions) is taken as an a posteriori error estimator for optimality conditions and the Zienkiewicz—Zhu error estimator is used to improve the quality of structural analysis. The examples presented show meaningful effects obtained by means of mesh refinement with a new error estimator.
    Type of Medium: Electronic Resource
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  • 7
    Electronic Resource
    Electronic Resource
    Springer
    Structural and multidisciplinary optimization 20 (2000), S. 12-21 
    ISSN: 1615-1488
    Keywords: Key words: hyperelasticity, history dependent materials, damage mechanics, structural optimization, design sensitivity analysis, tangent sensitivity
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract. In many practical problems, engineering structures under repeated loading exhibit softening material behaviour. The complex micromechanical processes yielding the observed loss of stiffness are often described phenomenologically on the macroscopic level by damage mechanics. A finite strain elastic constitutive model incorporating an isotropic damage mechanism was developed by Simo (1987). The additional theoretical and computational enhancements for utilizing this damage model and the associated finite element formulation for optimization purposes are outlined in this paper.¶The structural response and its sensitivity expressions at a given time and position depend on the response and the response sensitivities of all previous locations and times. The expressions for variational design sensitivity analysis within damage mechanics are fully stated and related to prior work on history dependent material behaviour such as Prandtl-Reuss elastoplasticity, see Barthold and Wiechmann (1997) and Wiechmann et al. (1997). The theoretical details and the corresponding finite element formulation were described in the paper by Firuziaan (1998).¶New problem functions based on the internal variables are shown to be adequate for controlling and optimizing the damage process.¶Numerical experiments illustrate the method proposed and the efficiency of the overall optimization procedure.
    Type of Medium: Electronic Resource
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  • 8
    Publication Date: 2003-12-01
    Electronic ISSN: 1617-7061
    Topics: Mathematics , Physics , Technology
    Published by Wiley
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