Overview
- Provides a survey of interactions between the calculus of variations and theoretical and applied mechanics
- Presents future research ideas, connecting foundational mathematical techniques to exciting potential applications
- Teaches a multidisciplinary audience how real-world phenomena can be seen through the lens of the calculus of variations
Part of the book series: Advances in Mechanics and Mathematics (AMMA, volume 46)
Part of the book sub series: Advances in Continuum Mechanics (ACM)
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Table of contents (12 chapters)
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Front Matter
Keywords
About this book
This volume provides a timely survey of interactions between the calculus of variations and theoretical and applied mechanics. Chapters have been significantly expanded since preliminary versions appeared in a special issue of the Journal of Optimization Theory and Applications (184(1), 2020) on “Calculus of Variations in Mechanics and Related Fields”. The variety of topics covered offers researchers an overview of problems in mechanics that can be analyzed with variational techniques, making this a valuable reference for researchers in the field. It also presents ideas for possible future areas of research, showing how the mastery of these foundational mathematical techniques can be used for many exciting applications. Specific topics covered include:
- Topology optimization
- Identification of material properties
- Optimal control
- Plastic flows
- Gradient polyconvexity
- Obstacle problems
- Quasi-monotonicity
Variational Views in Mechanics will appeal to researchers in mathematics, solid-states physics, and mechanical, civil, and materials engineering.
Editors and Affiliations
Bibliographic Information
Book Title: Variational Views in Mechanics
Editors: Paolo Maria Mariano
Series Title: Advances in Mechanics and Mathematics
DOI: https://doi.org/10.1007/978-3-030-90051-9
Publisher: Birkhäuser Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021
Hardcover ISBN: 978-3-030-90050-2Published: 09 February 2022
Softcover ISBN: 978-3-030-90053-3Published: 09 February 2023
eBook ISBN: 978-3-030-90051-9Published: 08 February 2022
Series ISSN: 1571-8689
Series E-ISSN: 1876-9896
Edition Number: 1
Number of Pages: XIV, 309
Number of Illustrations: 31 b/w illustrations, 63 illustrations in colour
Topics: Optimization, Classical and Continuum Physics, Functional Analysis