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The 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. In
contrast to existing texts on structural optimization, Introduction
to Shape Optimization: Theory, Approximation, and Computation
treats sizing and shape optimization in a comprehensive way,
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. Some of the
applications included are 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.
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