Rigid Structures with Point-Flexibility

This book deals with kinematics and statics of rigid-body systems, lumped elasticity, variational principles, dynamics, stability and bifurcation, piece-wise linear (rigid-plastic or elasto-plastic) constitutive behavior, and geometrically nonlinear behavior. The presentation of the matter is strongly innovative: all the fundamental principles and methods, which are usually discussed for continuous media (namely, the displacement and force methods, the virtual work principle, the stationarity theorems of the total potential and complementary energies), are here illustrated for naturally discrete structures. Consequently, the fundamental problem of mechanics, which, for centenary worldwide tradition, is discussed in the context of the mathematical analysis, is here brought back to the algebra environment. Due to the strong simplifications of the calculus, the learner can focus his attention on the (complex) logical architecture of the linear and nonlinear elasticity theory (and later, of limit analysis), not being distracted by the mathematical difficulties inherent partial differential equations and boundary conditions. Moreover, he easily gains insight into the mechanical behavior of structures, which clearly emerges from the numerous examples presented. The book is mainly devoted to undergraduate students. However, it is also meant as a reading successive to classic texts on continuous systems, useful to graduate and Ph.D. students to deepen their knowledge of general principles and methods of structural mechanics.