LEADER 04046nam 2200565 a 450 001 9911006786803321 005 20241120174723.0 010 $a1-68015-788-4 010 $a0-89871-869-4 024 7 $aDC07 035 $a(CKB)2430000000023479 035 $a(CaBNVSL)gtp00544281 035 $a(SIAM)9780898718690 035 $a(SSID)ssj0000527657 035 $a(PQKBManifestationID)12188325 035 $a(PQKBTitleCode)TC0000527657 035 $a(PQKBWorkID)10527088 035 $a(PQKB)10949772 035 $a(PPN)189758503 035 $a(EXLCZ)992430000000023479 071 50$aDC07$bSIAM 100 $a20101020d2003 fy 0 101 0 $aeng 135 $aurbn||||m|||a 181 $ctxt 182 $cc 183 $acr 200 10$aIntroduction to shape optimization $etheory, approximation, and computation /$fJ. Haslinger, R.A.E. Màˆkinen 210 $aPhiladelphia, Pa. $cSociety for Industrial and Applied Mathematics (SIAM, 3600 Market Street, Floor 6, Philadelphia, PA 19104)$d2003 215 $a1 electronic text (xviii, 273 p.) $cill., digital file 225 1 $aAdvances in design and control ;$v7 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a0-89871-536-9 320 $aIncludes bibliographical references (p. 263-270) and index. 327 $aWhy the mathematical analysis is important -- A mathematical introduction to sizing and shape optimization -- Sensitivity analysis -- Numerical minimization methods -- On automatic differentiation of computer programs -- Fictitious domain methods in shape optimization -- Applications in elasticity -- Fluid mechanical and multidisciplinary applications -- Appendix A: Weak formulations and approximations of elliptic equations and inequalities -- Appendix B: On parametrizations of shapes and mesh generation. 330 3 $aThe efficiency and reliability of manufactured products depend on, among other things, geometrical aspects; it is therefore not surprising that optimal shape design problems have attracted the interest of applied mathematicians and engineers. This self-contained, elementary introduction to the mathematical and computational aspects of sizing and shape optimization enables readers to gain a firm understanding of the theoretical and practical aspects so they may confidently enter this field. Introduction to Shape Optimization: Theory, Approximation, and Computation treats sizing and shape optimization comprehensively, covering everything from mathematical theory (existence analysis, discretizations, and convergence analysis for discretized problems) through computational aspects (sensitivity analysis, numerical minimization methods) to industrial applications. Applications include contact stress minimization for elasto-plastic bodies, multidisciplinary optimization of an airfoil, and shape optimization of a dividing tube. By presenting sizing and shape optimization in an abstract way, the authors are able to use a unified approach in the mathematical analysis for a large class of optimization problems in various fields of physics. Audience: the book is written primarily for students of applied mathematics, scientific computing, and mechanics. Most of the material is directed toward graduate students, although a portion of it is suitable for senior undergraduate students. Readers are assumed to have some knowledge of partial differential equations and their numerical solution, as well as modern programming language such as C++ Fortran 90. 410 0$aAdvances in design and control ;$v7. 606 $aStructural optimization$xMathematics 615 0$aStructural optimization$xMathematics. 676 $a624.1/7713 700 $aHaslinger$b J$058886 701 $aMàˆkinen$b R. A. E$01825470 712 02$aSociety for Industrial and Applied Mathematics. 801 0$bCaBNVSL 801 1$bCaBNVSL 801 2$bCaBNVSL 906 $aBOOK 912 $a9911006786803321 996 $aIntroduction to shape optimization$94393157 997 $aUNINA