Variational Views in Mechanics

This book provides a comprehensive survey of interactions between the calculus of variations and theoretical and applied mechanics, covering topics such as topology optimization, identification of material properties, optimal control, plastic flows, gradient polyconvexity, obstacle problems, quasi-monotonicity, and variational views in mechanics. It is a valuable reference for researchers in mathematics, solid-states physics, and mechanical, civil, and materials engineering.

Format: Hardback
Length: 309 pages
Publication date: 09 February 2022
Publisher: Springer Nature Switzerland AG

This comprehensive volume offers a timely and insightful exploration of the intricate interplay between the calculus of variations and theoretical and applied mechanics. Since its initial publication in a special issue of the Journal of Optimization Theory and Applications {PHONE}), dedicated to "Calculus of Variations in Mechanics and Related Fields," the chapters have undergone substantial expansion, reflecting the ongoing advancements in this field. The diverse range of topics covered provides researchers with a comprehensive overview of mechanics problems that can be approached using variational techniques, making this an invaluable resource for scholars engaged in this domain. Furthermore, the book presents exciting ideas for potential future research directions, showcasing the immense potential of mastering these fundamental mathematical tools for a wide array of captivating applications.

Specifically, the book delves into various captivating topics, including:

Topology Optimization: This innovative approach involves designing optimal structures or shapes by minimizing or maximizing certain geometric properties. It finds applications in various fields, such as aerospace, automotive, and civil engineering, where efficiency, strength, and durability are critical.

Identification of Material Properties: The identification of material properties plays a crucial role in understanding the behavior of materials under different conditions. By employing variational techniques, researchers can accurately model and predict the mechanical properties of materials, enabling the development of more robust and sustainable structures.

Optimal Control: Optimal control is a mathematical framework that aims to find the optimal control policies for systems subject to constraints. It finds applications in diverse fields, including robotics, aerospace, and energy systems, where efficient and precise control is essential.

Plastic Flows: Plastic flows describe the deformation and flow of materials under stress or strain. By employing variational techniques, researchers can study the behavior of plastic materials, including their strength, stiffness, and ductility, which are crucial in various industries, such as automotive and aerospace.

Gradient Polyconvexity: Gradient polyconvexity is a mathematical concept that describes the behavior of functions defined on convex sets. It finds applications in optimization, control theory, and machine learning, where the minimization of objective functions is required.

Obstacle Problems: Obstacle problems involve the navigation of a moving object or agent in a constrained environment. By employing variational techniques, researchers can develop efficient algorithms for navigating through complex obstacles, such as traffic jams or urban environments.

Quasi-Monotonicity: Quasi-monotonicity is a mathematical property that ensures the non-decreasing or non-increasing behavior of functions. It finds applications in optimization, control theory, and dynamical systems, where stability and controllability are critical.

Variational Views in Mechanics: This chapter provides an introduction to variational methods in mechanics, which aim to derive equations of motion or solutions to problems from first principles. It highlights the importance of variational techniques in understanding the behavior of mechanical systems.

This volume is of immense value to researchers in mathematics, solid-states physics, and mechanical, civil, and materials engineering. It offers a comprehensive and up-to-date understanding of the latest developments in the field, facilitating interdisciplinary research and collaboration. By leveraging the power of variational techniques, researchers can unlock new insights into complex mechanical systems and develop innovative solutions to real-world problems.

In conclusion, this comprehensive volume provides a valuable resource for researchers seeking to explore the intricate connections between the calculus of variations and theoretical and applied mechanics. With its expanded chapters, diverse topics, and potential research directions, it offers a comprehensive overview of the field and inspires further exploration into the exciting applications of variational techniques.

Weight: 658g
Dimension: 235 x 155 (mm)
ISBN-13: 9783030900502
Edition number: 1st ed. 2021