Optimization of conducting structures by using the homogenization method
作者： J. Haslinger , A. Hillebrand , T. Kärkkäinen , M. Miettinen
DOI: 10.1007/S00158-002-0223-1
关键词: Homogenization (chemistry) 、 Engineering design process 、 Control variable 、 Mathematical optimization 、 Optimization problem 、 Mathematics 、 Well-posed problem 、 Heat transfer 、 Applied mathematics 、 Thermal conduction 、 Numerical analysis
摘要: Approximation and numerical realization of a class optimization problems with control variables represented by coefficients linear elliptic state equations is considered. Convergence analysis well-posed performed using one- two-level approximation strategies. The latter utilized in an layout problem for two conductive constituents, which the necessary steps to transfer into computational form are described some experiments given.
springer.com
sci-hub.se 参考文章(12)
Martin P. Bendsøe, Optimization of structural topology, shape, and material ,(1995)
S. M. Kozlov, Vasiliĭ Vasilʹevich Zhikov, O. A. Oleĭnik, Homogenization of Differential Operators and Integral Functionals ,(1994)
T. Burns, A. Cherkaev, Optimal distribution of multimaterial composites for torsional beams Structural Optimization. ,vol. 13, pp. 4- 11 ,(1997) , 10.1007/BF01198369
M. P. Bendsøe, A. Ben-Tal, J. Zowe, Optimization methods for truss geometry and topology design Structural Optimization. ,vol. 7, pp. 141- 159 ,(1994) , 10.1007/BF01742459
G. Allaire, S. Aubry, On optimal microstructures for a plane shape optimization problem Structural Optimization. ,vol. 17, pp. 86- 94 ,(1999) , 10.1007/BF01195933
B. Maar, V. Schulz, Interior point multigrid methods for topology optimization Structural and Multidisciplinary Optimization. ,vol. 19, pp. 214- 224 ,(2000) , 10.1007/S001580050104
Martin Philip Bendsoe, Noboru Kikuchi, None, Generating optimal topologies in structural design using a homogenization method Applied Mechanics and Engineering. ,vol. 71, pp. 197- 224 ,(1988) , 10.1016/0045-7825(88)90086-2
Robert V. Kohn, Gilbert Strang, Optimal design and relaxation of variational problems, I Communications on Pure and Applied Mathematics. ,vol. 39, pp. 113- 137 ,(1986) , 10.1002/CPA.3160390107
K. A. Lurie, A. V. Cherkaev, Exact estimates of conductivity of composites formed by two isotropically conducting media taken in prescribed proportion Proceedings of The Royal Society A: Mathematical, Physical and Engineering Sciences. ,vol. 99, pp. 71- 87 ,(1984) , 10.1017/S030821050002597X
K. Schittkowski, C. Zillober, R. Zotemantel, Numerical comparison of nonlinear programming algorithms for structural optimization Structural Optimization. ,vol. 7, pp. 1- 19 ,(1994) , 10.1007/BF01742498