Pierre Ladeveze

Nonlinear Computational Structural Mechanics (eBook, PDF)

New Approaches and Non-Incremental Methods of Calculation
Übersetzer: Simmonds, J. G.

• Format: PDF

Produktbeschreibung

This book treats computational modeling of structures in which strong nonlinearities are present. It is therefore a work in mechanics and engineering, although the discussion centers on methods that are considered parts of applied mathematics. The task is to simulate numerically the behavior of a structure under various imposed excitations, forces, and displacements, and then to determine the resulting damage to the structure, and ultimately to optimize it so as to minimize the damage, subject to various constraints. The method used is iterative: at each stage an approximation to the displacements, strains, and stresses throughout the structure is computated and over all times in the interval of interest. This method leads to a general approach for understanding structural models and the necessary approximations.

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Produktdetails

• Verlag: Springer New York
• Seitenzahl: 222
• Erscheinungstermin: 6. Dezember 2012
• Englisch
• ISBN-13: 9781461214328
• Artikelnr.: 44179719

Inhaltsangabe

1 The Reference Problem for Small Disturbances.- 1.1. Notation.- 1.2. The reference problem.- 1.3. Sufficient conditions assuring uniqueness.- 1.4. Analogy with the basic problem of fluid mechanics.- 2 Material Models.- 2.1. Formulation with internal variables.- 2.2. Examples of material models.- 2.3. Formulation of the constitutive relation.- 2.4. Normal formulation of a constitutive model.- 2.5. Error as measured by the constitutive relation (error in CR).- 3 Solution Methods for Nonlinear Evolution Problems.- 3.1. The principle of incremental methods.- 3.2. Differential equation formulation of the reference problem.- 3.3. A general presentation of some classical methods for solving nonlinear problems.- 3.4. Other approaches to nonlinear evolution problems.- 4 Principles of the Method of Large Time Increments.- 4.1. Mechanics framework for the method of large time increments.- 4.2. Algorithms for two search directions.- 4.3. The local step.- 4.4. The global linear step.- 4.5. Convergence.- 4.6. A posteriori error estimates.- 4.7. Remarks.- 5 A Preliminary Example: A Beam in Traction.- 5.1. Quasi-static analysis for a viscoplastic material.- 5.2. Static analysis for a hyperelastic material.- 6 A "Mechanics Approximation" and Numerical Implementation.- 6.1. Discretization in time and space.- 6.2. Numerical treatment of the local step.- 6.3. Treatment of the linear global step in statics.- 6.4. Decomposition and approximation of the "radial loading" type for a function defined on ? × [0T].- 6.5. Applications and analysis of performance.- 7 Modeling and Calculation for Structures under Cyclic Loads.- 7.3. Treatment of the linear global step.- 7.4. A one-dimensional example.- 7.5. Example: viscoplastic disk with a loading of 1,000 cycles.- 8 Formulation and"Parallel" Strategies in Mechanics.- 8.1. Remarks on the degree of parallelism in the equations of reference.- 8.2. Partioning of the body into sub-structures and interfaces.- 8.3. Treatment of a static assemblage of elastic structures.- 8.4. Convergence for a static assemblage of elastic structures.- 8.5. Dynamic and static treatment of an assemblage of structures with nonlinear behavior.- 9 Modeling and Computation for Large Deformations.- 9.1. Material quantities and modeling of their behavior.- 9.2. Pure material formulation of large deformations-bases.- 9.3. Kinematic and other properties.- 9.4. Purely material formulation of the equilibrium of the body-properties and approximations.- 9.5. Two different representations of the modeling and computation of large deformations.- 9.6. Approaches to large time increments.- 9.7. Remarks and an example.