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  • 1985-1989  (6)
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Year
  • 1
    Electronic Resource
    Electronic Resource
    A variational inequality approach to constrained control problems for parabolic equations (1988)
    Springer
    Applied mathematics & optimization 17 (1988), S. 185-201 
    Details
    ISSN: 1432-0606
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A distributed optimal control problem for parabolic systems with constraints in state is considered. The problem is transformed to control problem without constraints but for systems governed by parabolic variational inequalities. The new formulation presented enables the efficient use of a standard gradient method for numerically solving the problem in question. Comparison with a standard penalty method as well as numerical examples are given.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01448366
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  • 2
    Electronic Resource
    Electronic Resource
    Optimization of the domain in elliptic variational inequalities (1988)
    Springer
    Applied mathematics & optimization 18 (1988), S. 85-98 
    Details
    ISSN: 1432-0606
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract This paper is concerned with a nonsmooth shape optimization problem for the Signorini unilateral boundary-value problem. The necessary optimality conditions are derived. The results of computations are presented.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01443616
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  • 3
    Electronic Resource
    Electronic Resource
    On the existence of optimal shapes in contact problems — Perfectly plastic bodies (1986)
    Springer
    Computational mechanics 1 (1986), S. 293-299 
    Details
    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 The optimal shape design of a two-dimensional elastic perfectly plastic body (a punch) on a rigid frictionless foundation is analysed. The problem is to find the boundary part of the body where the unilateral boundary conditions are assumed in such a way that certain energy integral of the system in the equilibrium will be minimized. It is assumed that the material of the body is elastic perfectly plastic, obeying the Henckys law. The variational formulation in terms of stresses is utilized. The existence of optimal shapes is proved.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00273705
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  • 4
    Electronic Resource
    Electronic Resource
    Sensitivity analysis for optimal shape design problems (1989)
    Springer
    Structural and multidisciplinary optimization 1 (1989), S. 241-251 
    Details
    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 Various methods for performing the sensitivity analysis in solving optimal shape design problems are outlined. The methods are illustrated in detail in the finite setting of a unilateral boundary value problem of the Dirichlet-Signorini type. The methods are compared in several numerical examples.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01650954
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  • 5
    Electronic Resource
    Electronic Resource
    On optimal shape design of systems governed by mixed Dirichlet-Signorini boundary value problems (1986)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 8 (1986), S. 157-181 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: A problem for finding optimal shape for systems governed by the mixed unilateral boundary value problem of Dirichlet-Signorini-type is considered. Conditions for the solvability of the problem are stated when a variational inequality formulation and when a penalty method is used for solving the state problem in question. The asymptotic relation of design problems based on these two formulations is presented. The optimal shape design problem is discretized by means of finite element method. The convergence results for the approximation are proved. The discretized versions are then formulated as a non-linear programming problem. Results of practical computations of the problem in question are reported.
    Additional Material: 6 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670080111
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  • 6
    Electronic Resource
    Electronic Resource
    On numerical simulation of the continuous casting process (1988)
    Springer
    Journal of engineering mathematics 22 (1988), S. 335-354 
    Details
    ISSN: 1573-2703
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Technology
    Notes: Abstract In this paper a steady-state nonlinear parabolic-type model, which simulates the multiphase heat transfer during solidification in continuous casting, is presented. An enthalpy formulation is used and we apply a FE-method in space and an implicit Euler method in time. A detailed solution algorithm is presented. We compute the temperature distributions in the strand when the boundary conditions (mold/spray cooling) on the strand surface are known. The numerical model gives thereby a good basis for the testing of new designs of continuous-casting machines. An application of the model to continuous casting of billets is presented.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00058513
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