Introduction to Shape Optimization is popular PDF and ePub book, written by Jan Sokolowski in 2012-12-06, it is a fantastic choice for those who relish reading online the Mathematics genre. Let's immerse ourselves in this engaging Mathematics book by exploring the summary and details provided below. Remember, Introduction to Shape Optimization can be Read Online from any device for your convenience.
Introduction to Shape Optimization Book PDF Summary
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.
Detail Book of Introduction to Shape Optimization PDF
- Author : Jan Sokolowski
- Release : 06 December 2012
- Publisher : Springer Science & Business Media
- ISBN : 9783642581069
- Genre : Mathematics
- Total Page : 254 pages
- Language : English
- PDF File Size : 10,6 Mb
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