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Books > Reference & Interdisciplinary > Communication studies > Information theory > Cybernetics & systems theory
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Introduction to Shape Optimization - Shape Sensitivity Analysis (Paperback, Softcover reprint of the original 1st ed. 1992)
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Introduction to Shape Optimization - Shape Sensitivity Analysis (Paperback, Softcover reprint of the original 1st ed. 1992)
Series: Springer Series in Computational Mathematics, 16
Expected to ship within 10 - 15 working days
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This book is motivated largely by a desire to solve shape
optimization prob lems that arise in applications, particularly in
structural mechanics and in the optimal control of distributed
parameter systems. Many such problems can be formulated as the
minimization of functionals defined over a class of admissible
domains. Shape optimization is quite indispensable in the design
and construction of industrial structures. For example, aircraft
and spacecraft have to satisfy, at the same time, very strict
criteria on mechanical performance while weighing as little as
possible. The shape optimization problem for such a structure
consists in finding a geometry of the structure which minimizes a
given functional (e. g. such as the weight of the structure) and
yet simultaneously satisfies specific constraints (like thickness,
strain energy, or displacement bounds). The geometry of the
structure can be considered as a given domain in the
three-dimensional Euclidean space. The domain is an open, bounded
set whose topology is given, e. g. it may be simply or doubly
connected. The boundary is smooth or piecewise smooth, so boundary
value problems that are defined in the domain and associated with
the classical partial differential equations of mathematical
physics are well posed. In general the cost functional takes the
form of an integral over the domain or its boundary where the
integrand depends smoothly on the solution of a boundary value
problem."
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