Shape Optimization Problems

This book provides theories on non-parametric shape optimization problems, with an emphasis on readers with an engineering background. It discusses topology optimization problems, where the optimum shape is sought by making a hole in the domain, and shape optimization problems of domain variation type, where the optimum shape is obtained based on domain variation. The theorems are built up using mathematical results, but an engineering style is introduced with examples from mechanics to explain the key points.

\n Format: Hardback
\n Length: 646 pages
\n Publication date: 01 October 2020
\n Publisher: Springer Verlag, Singapore
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This book delves into the realm of non-parametric shape optimization, catering to readers with an engineering background. Non-parametric shape optimization pertains to the identification of shapes for domains where boundary value problems of partial differential equations are defined. In these problems, optimal shapes are derived from arbitrary forms without pre-assigned geometrical parameters. Specifically, topology optimization problems involve seeking shapes by creating holes within the domain, while shape optimization problems of domain variation type focus on obtaining optimum shapes based on variations within the domain.

To address these complex challenges, software solutions have been developed and employed to seek practical optimum shapes. However, a notable gap exists in the literature: there are no books that comprehensively explain these theories from their foundational principles. This book aims to bridge that gap by presenting a structured approach. The theorems are built upon mathematical results, employing a mathematical style that encompasses definitions and theorems to summarize the key points. This method of expression is further enhanced by demonstrating the veracity of the presented facts through clear proofs.

Recognizing the characteristic of mathematics to elevate abstraction for a unified understanding of various phenomena, this book endeavors to provide explanations in engineering terms, drawing upon examples from the field of mechanics. By employing a combination of mathematical rigor and engineering practicality, this book seeks to cater to readers with diverse backgrounds, including those with an engineering orientation.

\n Weight: 1200g\n
Dimension: 165 x 242 x 39 (mm)\n
ISBN-13: 9789811576171\n
Edition number: 1st ed. 2020\n