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.

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

##### MSC:

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 |