Computational Mechanics: Continuous and Discrete Models for Solids, Fluids and Structures offers a unified presentation of continuum mechanical models and their discrete counterparts, giving a deeper understanding of the relationship that exists between the main numerical methods, finite element methods, and finite volume methods, also presenting the advantages and shortcomings of each.
This book shows, with the use of Matlab code snippets, how to implement the methods described for all types of different problems, including linear and nonlinear, stationary and time dependent, and solids and fluids, all presented for the typical common finite element, finite volume, and time stepping methods.
- Contains derivation of continuous models and discrete models in a unified, mixed engineering/mathematical manner
- Presents numerical methods and their implementation in Matlab
- Explores finite element methods, discontinuous finite element methods, and finite volume methods within the same framework
Muu info
This unified presentation of continuum mechanical models and their discrete counterparts covers the basic principles underlying the main continuum mechanical partial differential equation models used in practice, together with their numerical methods
Part I. Elementary mathematical models in continuum mechanics
1.
Mathematical modeling with ordinary differential equations
2. Boundary value
problems in several dimensions
3. Time dependent problems
4. Mixed
problems
Part II. Introduction to numerical modeling
5. The basics
6. Adaptive
finite element methods
7. Time-dependent problems
8. Mixed methods
Part III. Advanced and nonlinear models in continuum mechanics
9. Material
Models in Small Deformation Solid Mechanics
10. General Principles in
Continuum Mechanics
11. Large Deformation Solid Mechanics
12. Thermodynamics
13. Fluids
14. Stability problems
15. Contact problems
Part IV. Advanced numerical modeling
16. Solution algorithms for linear
systems of equations
17. Non-linear problems
18. Adaptive finite element
methods
19. Practical Adaptivity and Mesh Generation
20. Finite Elements in
Fluids
21. Non-conforming finite element methods
Peter Hansbo's research is aimed at developing improved (i.e., faster, more accurate, simpler) numerical models for the solution of problems related to classical field theories, i.e., systems of partial differential equations that describe phenomena such as convection, strength of materials, and wave propagation. In particular he focuses on multiphysics problems, e.g., the connection between various physical systems such as fluid-structure interaction.Peter Hansbo is known mainly for his work on adaptive Finite Element Methods (FEM), stabilised FEM for convection dominated flow, discontinuous FEM, and for methods for connecting models via interfaces
