Fundamentals of Structural Optimization (III)

Game-Theory Methods
Erscheinungsjahr 2027
ISBN: 978-3-032-42655-0
Verlag: Springer

Buch, Englisch, 202 Seiten, Format (B × H): 155 mm x 235 mm

Reihe: Mathematical Engineering

develops a unified, Lie-algebraic and geometric framework for modeling and solving competitive and uncertainty-aware optimization problems as structured games. It shows how static and differential lattice games on semisimple Lie groups can be translated—via mirroring and Lie expansion/retraction—into computable spectral problems. The volume explains when equilibrium selection is governed by eigenvalues (commuting/reference regimes) versus when it is governed by singular values (noncommuting, nonlinear, heterogeneous settings). It further introduces Green–Zerna metrics and Milnor curvature to interpret how Hamiltonian flow sensitivity produces geometric incompatibilities, and provides an asymptotic reduction pathway from differential games to terminal static interaction problems. Finally, it connects the methodology to engineering relevance through heterogeneous games and bilevel structural optimization, where design parameters parameterize lower-level game dynamics and the upper level optimizes the resulting equilibrium value.

Zielgruppe

Research

Autoren/Hrsg.

Kobelev, Vladimir

Fachgebiete

• Technische Wissenschaften Technik Allgemein Mathematik für Ingenieure

Inhaltsverzeichnis

Scaling Methods. Optimality of Michell Structures and membrane shells.- One-Dimensional Variational Methods. Optimization of twisted spherical shell.- Methods of Domain Variations for Shape Optimization.- Methods of Local Variations. Topological derivatives and Bubble Methods.- Methods of Tensor Transformations for Anisotropic Medium.- Methods of Differential Geometry. Optimal distributions of the residual stresses.- Integral Equation Methods. Optimization of stiffeners and needle-shaped inclusions.- Isoperimetric Inequalities. Structural optimization problems of stability.

Über Autor(innen)

Vladimir Kobelev, Ph.D., Dr rer nat habil, received the Dipl Physics and Ph.D. degrees from the Department of Aerophysics and Space Research, Moscow Institute of Physics and Technology, Dolgoprudny, Russia. Since 2000, he has been an APL professor with the Department of Mechanical Engineering, Universität Siegen, Siegen, Germany. He is the author of the books, “Durability of Springs,” , "Fundamentals of Spring Mechanics", "Federntechnologie", " “Design and Analysis of Composite Structures for Automotive Applications,” “Fundamentals of Structural Optimization (I),” and “Fundamentals of Structural Optimization (II).”