Shape Optimization Problems
Springer Verlag, Singapore
978-981-15-7620-1 (ISBN)
The structure of the book is shown in the Preface. The theorems are built up using mathematical results. Therefore, a mathematical style is introduced, consisting of definitions and theorems to summarize the key points. This method of expression is advanced as provable facts are clearly shown. If something to be investigated is contained in the framework of mathematics, setting up a theory using theorems prepared by great mathematicians is thought to be an extremely effective approach. However, mathematics attempts to heighten the level of abstraction in order to understand many things in a unified fashion. This characteristic may baffle readers with an engineering background. Hence in this book, an attempt has been made to provide explanations in engineering terms, with examples from mechanics, after accurately denoting the provable facts using definitions and theorems.
Preface.- Notation.- Chapter 1: Basics of Optimal Design.- Chapter 2: Basics of Optimization Theory.- Chapter 3: Basics of Mathematical Programming.- Chapter 4: Basics of Variational Principles and Functional Analysis.- Chapter 5: Boundary Value Problems of Partial Differential Equations.- Chapter 6: Fundamentals of Numerical Analysis.- Chapter 7: Abstract Optimum Design Problem.- Chapter 8: Topology Optimization Problem of Density Variation Type.- Chapter 9: Shape Optimization Problems of Domain Variation Type.- Answers to Practice Problems.- Afterword.- References.- Index.
“The book is written clearly. Key points of the presentation are summarized, and the theorems are formulated using well-known mathematical results. … The book is appropriate for use in a graduate course or for self-study. Each chapter ends with a diverse list of exercises. Again, the solutions to these exercises can be found at the end of the book. This book will be a valuable resource for engineering graduate students or experts on structural optimization problems and related areas.” (Andrzej M. Myśliński, Mathematical Reviews, March, 2022)
Erscheinungsdatum | 11.10.2021 |
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Reihe/Serie | Springer Optimization and Its Applications ; 164 |
Zusatzinfo | 3 Illustrations, color; 199 Illustrations, black and white; XXIII, 646 p. 202 illus., 3 illus. in color. |
Verlagsort | Singapore |
Sprache | englisch |
Maße | 155 x 235 mm |
Themenwelt | Mathematik / Informatik ► Mathematik ► Analysis |
Mathematik / Informatik ► Mathematik ► Angewandte Mathematik | |
Naturwissenschaften ► Physik / Astronomie ► Theoretische Physik | |
Schlagworte | Boundary Value Problem of Partial Differential Equation • Non-parametric Shape Optimization Problem • Numerical analysis • Optimization Theory / Mathematical Programming • Variational Calculus / Functional Analysis |
ISBN-10 | 981-15-7620-3 / 9811576203 |
ISBN-13 | 978-981-15-7620-1 / 9789811576201 |
Zustand | Neuware |
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