Nonsmooth Mechanics and Convex Optimization

This book presents a comprehensive methodology for dealing with nonsmooth behaviors in mechanics, in accordance with contemporary theory and algorithms of optimization. Delving into both theoretical studies and numerical algorithms to provide a new perspective on the subject, this book addresses how linear, semidefinite, and second-order cone optimizations are applied to real-world problems in nonsmooth mechanics. It also covers complementarity problems, optimality conditions, Fenchel and Lagrangian dualities, and algorithms in optimization. The author also explores working with many practical applications in structural engineering, including cable networks, membranes, masonry structures, contact problems, and plasticity. This is an ideal guide to nonsmooth mechanics for graduate students and researchers in computational and applied mechanics, applied mathematics, and operations research.