Buch, Englisch, Band 188, 212 Seiten, Format (B × H): 160 mm x 241 mm, Gewicht: 512 g
Buch, Englisch, Band 188, 212 Seiten, Format (B × H): 160 mm x 241 mm, Gewicht: 512 g
Reihe: Studies in Systems, Decision and Control
ISBN: 978-3-030-05431-1
Verlag: Springer International Publishing
The book presents new results and applications of the topological derivative method in control theory, topology optimization and inverse problems. It also introduces the theory in singularly perturbed geometrical domains using selected examples. Recognized as a robust numerical technique in engineering applications, such as topology optimization, inverse problems, imaging processing, multi-scale material design and mechanical modeling including damage and fracture evolution phenomena, the topological derivative method is based on the asymptotic approximations of solutions to elliptic boundary value problems combined with mathematical programming tools. The book presents the first order topology design algorithm and its applications in topology optimization, and introduces the second order Newton-type reconstruction algorithm based on higher order topological derivatives for solving inverse reconstruction problems. It is intended for researchers and students in applied mathematics and computational mechanics interested in the mathematical aspects of the topological derivative method as well as its applications in computational mechanics.
Zielgruppe
Research
Autoren/Hrsg.
Fachgebiete
- Mathematik | Informatik Mathematik Mathematik Interdisziplinär Systemtheorie
- Technische Wissenschaften Maschinenbau | Werkstoffkunde Technische Mechanik | Werkstoffkunde Statik, Dynamik, Kinetik, Kinematik
- Technische Wissenschaften Elektronik | Nachrichtentechnik Nachrichten- und Kommunikationstechnik Regelungstechnik
Weitere Infos & Material
Introduction.- Theory in Singularly Perturbed Geometrical Domains.- Steklov-Poincare´ Operator for Helmholtz Equation.- Topological Derivatives for Optimal Control Problems.- Optimality Conditions with Topological Derivatives.- A Gradient-Type Method and Applications.- Synthesis of Compliant Thermomechanical Actuators.- Synthesis of Compliant Piezomechanical Actuators.- Asymptotic Analysis of Variational Inequalities.- A Newton-Type Method and Applications.- The Electrical Impedance Tomography Problem.
