×

Advances in computational dynamics of particles, materials and structures. (English) Zbl 1248.74001

Hoboken, NJ: John Wiley & Sons (ISBN 978-0-470-74980-7/hbk; 978-1-119-96589-3/ebook). xxiv, 686 p. (2012).
This book is designed for mathematicians, physicists, and engineers who wish to understand the subject matter with rigor and in a contemporary setting. The book can also be used as a multi-semester course for graduate- or for upper-level undergraduate students.
An important advantage is that the authors treat the material from a unified viewpoint, thus providing a blend of various modern mechanical and numerical approaches.
Chapter 1 is an introduction and presents the overview of the book, whereas Chapter 2 provides the basic mathematical material necessary for studying classical mechanics, continuum mechanics, and finite element and time integration schemes for solving the equations of motion.
The remainder of the book is divided into three parts. Part 1 deals with particle systems. Chapter 3 covers classical mechanics including Newtonian, Lagrangian and Hamiltonian mechanics. In Chapter 4, after establishing a relation between Newton’s second law and the principle of virtual work, the authors develop subsequently theoretical and numerical methods starting from this principle. Chapter 5 describes both the Hamilton’s principle and the Hamilton’s law of varying action for \(N\)-body dynamical systems. In Chapter 6, the authors introduce the principle of balance of mechanical energy as a starting point for the total energy representation of the equations of motion for holonomic-scleronomic systems. Chapter 7 describes the equivalence among \(N\)-body dynamical systems with holonomic constraints within the Lagrangian, Hamiltonian and total energy frameworks.
Part 2 focuses on continuous-body systems and continuum mechanics examining the deformations, strains and stresses in solid/structural applications. Chapter 8 describes displacements, strains and stresses using the general tensors. This chapter also includes constitutive equations in elasticity, the principle of virtual work and variational principles, and direct variational methods for two-point boundary value problems (namely, the Rayleigh-Ritz method, the Bubnov-Galerkin weighted residual method, and the modified Bubnov-Galerkin weighted residual method). Chapter 9 deals with the principle of virtual work in dynamics, and consequently introduces the conventional finite element formulations and vector formalism for continuous body dynamical systems. Chapter 10 presents some special finite element formulations using descriptive scalar functions via Hamilton’s principle or Hamilton’s law of varying action. The related total energy representations and finite element formulations using various descriptive scalar functions are given in Chapter 11. Chapter 12 discusses the equivalences between strong weak forms of the principle of virtual work.
Part 3 is devoted to the time integration of equations of motion. Chapter 13 starts with a standard representation of linear semi-discretized equations of motion, and then develops various classical time integration schemes for linear dynamical systems, including historical perspectives. Here, the reader can also find variational integrators stemming from the so-called discrete Euler-Lagrange representations which are symplectic-momentum conserving. Finally, in Chapter 14, the authors present the more recent developments directly using the total energy framework in conjunction with a generalized time weighted residual approach.

MSC:

74-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to mechanics of deformable solids
70-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to mechanics of particles and systems
PDFBibTeX XMLCite
Full Text: DOI