Mariano P. Variational Views in Mechanics 2022

Textbook in PDF format

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