Underconstrained Structural Systems

This book is intended for the academic and technical community involved in research, development, design and manufacturing of modern lightweight, rapidly deployable structural systems for both terrestrial and space applications. It can serve as a graduate text for students specializing in structural, mechanical, aeronautical and shape control engineering, as well as in engineering science and mechanics. Underconstrained systems represent a rich and useful, yet often misunderstood class of structural systems. This book is the first treatise on the subject. It contains a concise and comprehensive theory of underconstrained systems with applications to their design, analysis and synthesis. The theory, a combination of advanced analytical statics and nonlinear structural mechanics, is developed in Part I (Chapters 1-4). Part II (Chapters 5-10) provides applications to particular types of systems. Most of the presented results and applications are new. They include: extended statical-kinematic duality, linking infinitesimal mobility and stability of self-stress; orthogonal load decomposition and the statical-kinematic stiffness matrix; a statical-geometric theory and analysis of nets; a resolution of an old paradox in the statics of toroidal membranes; theory and analysis of wrinkling membranes; numerous closed-form solutions; and some new mechanical analogies.