Augmented Lagrangian and operator-splitting methods in nonlinear mechanics. (English) Zbl 0698.73001

SIAM Studies in Applied Mathematics, 9. Philadelphia, PA: Society for Industrial and Applied Mathematics. x, 295 p. $ 44.50 (1989).
This book deals with the numerical simulation of the behavior of continuous media by augmented Lagrangian and operator-splitting methods (coupled to finite element approximations). The book consists of two parts: The first three chapters present the method, starting with the mathematical modeling of different classes of continuous materials, the variational formulations of the mechanical problems associated with these and finally the augmented Lagrangian methods, their relation to operator- splitting methods and their application to linear and nonlinear eigenvalue problems.
The last five chapters are independent of each other and deal with different areas of application of the method, like flow of elastoviscoplastic materials, limit load analysis, equilibrium problems in finite elasticity or large displacement calculations of flexible rods.
Reviewer: K.Brod


74-02 Research exposition (monographs, survey articles) pertaining to mechanics of deformable solids
74S30 Other numerical methods in solid mechanics (MSC2010)
74S05 Finite element methods applied to problems in solid mechanics
65K10 Numerical optimization and variational techniques
74B20 Nonlinear elasticity
49M27 Decomposition methods