Automation of finite element methods.

*(English)*Zbl 1367.74001
Cham: Springer (ISBN 978-3-319-39003-1/hbk; 978-3-319-39005-5/ebook). xxviii, 346 p. (2016).

Due to the power of symbolic computations it is possible to automatically generate efficient and highly compressed codes for linear and nonlinear problems. Based on the symbolic system AceGen, fast and reliable code can be created with a minimum of efforts and can be tested and verified by using the associated finite element program AceFEM. The symbolic system AceGen is a package within the symbolic-numeric system Mathematica and produces source code for different finite element environments. The use of AceGen is described within this book for applications in solid mechanics. So this book shows how an automated finite element method could be efficiently applied to problems of solid mechanics.

The book is subdivided into eight chapters. The foundation of nonlinear continuum mechanics is summarized in Chapter 1. The hybrid symbolic-numeric approaches to automation of the finite element method and the system for automatic code generation AceGen are described in Chapter 2. Chapter 3 discusses the automation process when problems are formulated in primal variables. Chapter 4 is related to the automation of discretization techniques and different possibilities how to discretize potentials and weak forms. Constitutive equations for elastic and inelastic response for small and finite strain primal analysis are provided in Chapter 5. Continuum elements for different two- and three-dimensional applications are developed in Chapter 6. Special two- and three-dimensional structural elements such as trusses, beams and shells are formulated in Chapter 7. The application of automation to sensitivity analysis is provided in the final Chapter 8.

The book is intended for students and engineers who want to develop new finite element formulations, especially for nonlinear problems of solid continuum mechanics.

The book is subdivided into eight chapters. The foundation of nonlinear continuum mechanics is summarized in Chapter 1. The hybrid symbolic-numeric approaches to automation of the finite element method and the system for automatic code generation AceGen are described in Chapter 2. Chapter 3 discusses the automation process when problems are formulated in primal variables. Chapter 4 is related to the automation of discretization techniques and different possibilities how to discretize potentials and weak forms. Constitutive equations for elastic and inelastic response for small and finite strain primal analysis are provided in Chapter 5. Continuum elements for different two- and three-dimensional applications are developed in Chapter 6. Special two- and three-dimensional structural elements such as trusses, beams and shells are formulated in Chapter 7. The application of automation to sensitivity analysis is provided in the final Chapter 8.

The book is intended for students and engineers who want to develop new finite element formulations, especially for nonlinear problems of solid continuum mechanics.

Reviewer: V. Leontiev (Ul’yanovsk)