Belytschko T., Liu W.K., Moran B. Nonlinear Finite Elements for Continua and Structures

Chichester: John Wiley & Sons. – 2000. – 666 p. The objective of this book is to provide a comprehensive introduction to the methods and theory of nonlinear finite element analysis. We have focused on the formulation and solution of the discrete equations for various classes of problems that are of principal interest in applications of the finite element method to solid mechanics and structural mechanics. The topics include: the discretization by finite elements of continua in one dimension and in multi-dimensions; the formulation of constitutive equations for nonlinear materials and large deformations; procedures for the solution of the discrete equations, including considerations of both numerical and physical instabilities; and the treatment of structural and contact-impact problems. These are the topics which are of relevance to industrial and research applications and which are essential to those in the practice, research, and teaching of nonlinear finite elements. The book has a mechanics style rather than a mathematical style. Although it includes analyses of the stability of numerical methods and the relevant partial differential equations, the objective is to teach methods of finite element analysis and the properties of the solutions and the methods. Topics such as proofs of convergence and the mathematical properties of solutions are not considered.List of Boxes.Lagrangian and Eulerian finite elements in one dimension.
Continuum mechanics.
Lagrangian meshes.
Constitutive models.
Solution methods and stability.
Arbitrary Lagrangian Eulerian formulations.
Element technology.
Beams and shells.
Contact-impact.
Voigt notation.
Norms.
Element shape functions.