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Nonlinear dynamics of structures. Translated from the Spanish. (English) Zbl 1327.74002

Lecture Notes on Numerical Methods in Engineering and Sciences. Berlin: Springer; Barcelona: International Center for Numerical Methods in Engineering (CIMNE) (ISBN 978-3-319-05193-2/hbk; 978-3-319-05194-9/ebook). xii, 192 p. (2014).
The book is an elementary introduction into the fundamentals of continuum mechanics. In the first chapter, the author presents the basic problems and the mode in which various concepts are involved. In the second chapter, both implicit and explicit procedures are described in detail, and the advantages and drawbacks of each method are analyzed. The next chapter presents the stability concept for the solutions of conservative systems, and different methods are studied in order to solve the equations of motion. Then an approximation to nonlinear problems is made, and criteria for stability are provided. Energy is a crucial requirement. The formulation of conservative solution methods currently used in nonlinear dynamics is presented. This is shown for simple nonlinear problems. Then the author discusses the models of plasticity and damage in the context of structural nonlinearity. Some other models of time-dependent materials involved in delayed elasticity and relaxation are presented. Nonlinear damping is included in a natural way. The convergence conditions for nonlinear dynamic structure solutions are also studied, and the theoretical concepts and their solution algorithms are given. The literature mentioned is poor, because many important publications are missing.

MSC:

74-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to mechanics of deformable solids
74H45 Vibrations in dynamical problems in solid mechanics
74H55 Stability of dynamical problems in solid mechanics
74R20 Anelastic fracture and damage
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