000 03875nam a22005295i 4500
001 978-3-642-35245-4
003 DE-He213
005 20200420221251.0
007 cr nn 008mamaa
008 121214s2013 gw | s |||| 0|eng d
020 _a9783642352454
_9978-3-642-35245-4
024 7 _a10.1007/978-3-642-35245-4
_2doi
050 4 _aTA349-359
072 7 _aTGMD
_2bicssc
072 7 _aTEC009070
_2bisacsh
072 7 _aSCI041000
_2bisacsh
082 0 4 _a620.1
_223
100 1 _aNovotny, Antonio Andr�e.
_eauthor.
245 1 0 _aTopological Derivatives in Shape Optimization
_h[electronic resource] /
_cby Antonio Andr�e Novotny, Jan Soko�owski.
264 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg :
_bImprint: Springer,
_c2013.
300 _aXII, 324 p. 68 illus.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aInteraction of Mechanics and Mathematics,
_x1860-6245
505 0 _aDomain Derivation in Continuum Mechanics -- Material and Shape Derivatives for Boundary Value Problems -- Singular Perturbations of Energy Functionals -- Configurational Perturbations of Energy Functionals -- Topological Derivative Evaluation with Adjoint States -- Topological Derivative for Steady-State Orthotropic Heat Diffusion Problems -- Topological Derivative for Three-Dimensional Linear Elasticity Problems -- Compound Asymptotic Expansions for Spectral Problems -- Topological Asymptotic Analysis for Semilinear Elliptic Boundary Value Problems -- Topological Derivatives for Unilateral Problems.
520 _aThe topological derivative is defined as the first term (correction) of the asymptotic expansion of a given shape functional with respect to a small parameter that measures the size of singular domain perturbations, such as holes, inclusions, defects, source-terms and cracks. Over the last decade, topological asymptotic analysis has become a broad, rich and fascinating research area from both theoretical and numerical standpoints. It has applications in many different fields such as shape and topology optimization, inverse problems, imaging processing and mechanical modeling including synthesis and/or optimal design of microstructures, sensitivity analysis in fracture mechanics and damage evolution modeling. Since there is no monograph on the subject at present, the authors provide here the first account of the theory which combines classical sensitivity analysis in shape optimization with asymptotic analysis by means of compound asymptotic expansions for elliptic boundary value problems. This book is intended for researchers and graduate students in applied mathematics and computational mechanics interested in any aspect of topological asymptotic analysis. In particular, it can be adopted as a textbook in advanced courses on the subject and shall be useful for readers interested in the mathematical aspects of topological asymptotic analysis as well as in applications of topological derivatives in computational mechanics.
650 0 _aEngineering.
650 0 _aMathematical physics.
650 0 _aComputer mathematics.
650 0 _aMechanics.
650 0 _aMechanics, Applied.
650 1 4 _aEngineering.
650 2 4 _aTheoretical and Applied Mechanics.
650 2 4 _aComputational Science and Engineering.
650 2 4 _aMathematical Applications in the Physical Sciences.
700 1 _aSoko�owski, Jan.
_eauthor.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783642352447
830 0 _aInteraction of Mechanics and Mathematics,
_x1860-6245
856 4 0 _uhttp://dx.doi.org/10.1007/978-3-642-35245-4
912 _aZDB-2-ENG
942 _cEBK
999 _c52626
_d52626