Nonlinear structural dynamics using FE methods (Q2925447)

First, the author establishes principles of mechanics that are general enough to develop the finite element methods (FEM). Second, the book presents specific computer procedures to implement the FEM, so that the general problems can be solved -- that is, the responses can be produced given the loads, initial conditions, and so on. Finally, the book introduces methods to evaluate the finite element solutions. More precisely, the primary goals of this book are: {\parindent=6mm \begin{itemize}\item[-] to develop the solution methods, general and scalable enough to solve ``large dynamical problems''; \item[-] to develop the methods of analysis to ``make sense'' of the solutions obtained; \item[-] because the geometric nonlinearities are an intimate aspect of flexible structures, to make the solution and analysis methods general enough to effectively handle nonlinear problems. NEWLINENEWLINE\end{itemize}} The book is divided into two parts. Part 1 introduces the mechanics and computer models to handle general problems. Part 2 develops the analytical models. The nonlinear analyses are distributed throughout the chapters. Chapter 1 presents some basic ideas of the dynamics of elastic systems, such as resonance and damping. Chapter 2 develops the mechanics needed to handle large complex systems. Chapter 3 uses the Ritz method to convert continuous systems into discrete form, and then formalizes the process via the FEM. Chapter 4 is an attempt to classify the various types of dynamic problems based on the space-time variation of their loadings. Chapter 5 ends Part 1 with a review of computer methods used to implement the above models.NEWLINENEWLINEPart 2 contains a compilation of analytical models: modal analysis and eigenvalue problems in Chapter 6, spectral analysis and strong formulations in Chapter 7, flexible plates and shells in Chapter 8, and wave propagation and high-frequency analysis in Chapter 9. Chapter 10 ends Part 2 with an introduction to the stability of the motion. There are many example problems distributed throughout the chapters.