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  • 1
    Electronic Resource
    Electronic Resource
    Second-order necessary conditions for domain optimization problems in elastic structures, part 2: Surface traction dependent on the shape (1992)
    Springer
    Journal of optimization theory and applications 72 (1992), S. 383-401 
    Details
    ISSN: 1573-2878
    Keywords: Domain optimization ; optimal shape design ; elastic structures ; adjoint variables ; first-order and second-order necessary conditions
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The second-order sensitivity analysis for a domain optimization problem is studied for a linear elastic structure. In the primary elastic structure considered, the surface traction, a part of the boundary conditions, depends not only on the position but also on the shape of the structure. The first variation and the second variation of the objective functional are calculated in terms of the solution, the first variation of the solution for the primal elastic system, and of the adjoint variable introduced. Moreover, the first-order and the second-order necessary optimality conditions are derived for the structure under a hydrostatic pressure. As an illustrative problem, a mean compliance design is treated.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00940524
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Second-order necessary conditions for domain optimization problems in elastic structures, part 1: Surface traction given as a field (1992)
    Springer
    Journal of optimization theory and applications 72 (1992), S. 355-382 
    Details
    ISSN: 1573-2878
    Keywords: Domain optimization ; optimal shape design ; elastic structures ; adjoint variables ; first-order and second-order necessary conditions
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this paper, domain optimization problems for both linear and nonlinear elastic structures are studied. The first variation and the second variation of the objective function are calculated in terms of the solution, of the first variation of the solution for the primal elastic system, and of the adjoint variables introduced. The adjoint variables obey a (fictitious) linear elastic system in contrast with the nonlinear adjoint systems introduced by Dems and Mróz, and by Dems and Haftka. From these results, the first-order and the second-order necessary conditions that an optimal domain should satisfy are immediately derived.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00940523
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    Second-order necessary conditions in a domain optimization problem (1990)
    Springer
    Journal of optimization theory and applications 65 (1990), S. 223-244 
    Details
    ISSN: 1573-2878
    Keywords: Domain optimization ; shape optimal design ; distributed-parameter systems ; boundary-value problems ; first and second variations ; first-order and second-order necessary conditions
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Second-order necessary conditions of the Kuhn-Tucker type for optimality in a domain optimization problem are studied. The second variation, corresponding to a boundary variation, of the solution to a boundary-value problem is shown to exist and is given as the solution of a boundary-value problem of the same type. The boundary data are shown to be given in terms of the solution and the first variation of the solution. From these results, the second variation of the objective function is calculated to derive second-order necessary conditions of the Kuhn-Tucker type.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01102343
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