Buch, Englisch, Band 29, 404 Seiten, HC runder Rücken kaschiert, Format (B × H): 160 mm x 241 mm, Gewicht: 1690 g
Buch, Englisch, Band 29, 404 Seiten, HC runder Rücken kaschiert, Format (B × H): 160 mm x 241 mm, Gewicht: 1690 g
Reihe: Solid Mechanics and Its Applications
ISBN: 978-0-7923-2761-5
Verlag: Springer Netherlands
Zielgruppe
Research
Autoren/Hrsg.
Fachgebiete
- Mathematik | Informatik EDV | Informatik Professionelle Anwendung Computer-Aided Design (CAD)
- Naturwissenschaften Physik Mechanik Klassische Mechanik, Newtonsche Mechanik
- Mathematik | Informatik EDV | Informatik Angewandte Informatik Computeranwendungen in Wissenschaft & Technologie
- Technische Wissenschaften Maschinenbau | Werkstoffkunde Maschinenbau
- Technische Wissenschaften Technik Allgemein Mathematik für Ingenieure
- Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
- Technische Wissenschaften Technik Allgemein Computeranwendungen in der Technik
Weitere Infos & Material
1 One-Dimensional Bar Model Problem (Principle of Virtual Work).- 1.1 Kinematics: material description.- 1.2 Dynamics: equilibrium of forces.- 1.3 Mechanics: principle of virtual work.- 1.4 Geometric and material non-linearities.- 1.5 Constitutive laws for solid materials.- 1.6 Discontinuities in space.- 1.7 Thermics: heat equation.- 1.8 Mathematics: functional analysis notions.- 1.9 Summary.- 2 Spatial Discretisation by the Finite Element Method.- 2.1 Global overview: Galerkin method.- 2.2 Nodal FEM: piecewise polynomial basis functions.- 2.3 Localisation of mesh nodal displacements.- 2.4 Interpolation of element nodal displacements.- 2.5 Integration of element nodal forces.- 2.6 Assembly of mesh nodal forces.- 2.7 Properties of force vectors.- 2.8 Automation: isoparametric maps and numerical integration.- 2.9 Boundary conditions condensation.- 2.10 Algorithm: element loop.- 2.11 Practice: heat equation discretisation.- 2.12 Accuracy: error norms and estimates.- 2.13 Summary.- 3 Solution of Non-Linearities by the Linear Iteration Method.- 3.1 Linearisation: classical and directional derivative.- 3.2 Nominal stress linearisation: nominal tangent modulus.- 3.3 Linearized equations of motion: mass and stiffness matrices.- 3.4 Finite element mass and stiffness matrices.- 3.5 Assembly of the mass and stiffness matrices.- 3.6 Properties of the mass and stiffness matrices.- 3.7 Linearized heat equation.- 3.8 Condensation of boundary conditions after linearisation.- 3.9 Linear iteration method: algorithm and variants.- 3.10 Standard and modified Newton methods.- 3.11 Secant or conjugate gradient methods.- 3.12 Gradient and Jacobi methods.- 3.13 Local and global convergence of iterative methods.- 3.14 Local convergence of the LIM: consistency and stability.- 3.15 Glocal convergence of the LIM: damping and continuation.- 3.16 Summary.- 4 Time Integration by the Finite Difference Method.- 4.1 Generalised trapezoidal rule or Euler scheme (applied to the linear heat equation).- 4.2 Modal analysis of the heat equation.- 4.3 General error analysis: summary and glossary.- 4.4 Stability of the heat-trapezoid algorithm.- 4.5 Consistency of the heat-trapezoid algorithm.- 4.6 Convergence of the heat-trapezoid algorithm.- 4.7 Generalized trapezoidal rale or Newmark scheme (applied to the linear wave equation).- 4.8 Modal analysis of the wave equation.- 4.9 Stability of the wave-trapezoid algorithm.- 4.10 Consistency of the wave-trapezoid algorithm.- 4.11 Convergence of the wave-trapezoid algorithm.- 4.12 Summary.- 5 Compact Combination of the Finite Element, Linear Iteration and Finite Difference Methods.- 5.1 Problem statement review.- 5.2 Galerkin-FE algorithm review.- 5.3 Newton-LI algorithm review.- 5.4 Newmark-FD algorithm review.- 5.5 Combining the FE, LI and FD algorithms.- 5.6 Nonlinear thermics algorithm.- 5.7 Nonlinear dynamics algorithm.- 5.8 Nonlinear thermodynamics synthesis.- 5.9 Convergence review.- 5.10 Programming guidelines (TACT example).- 5.11 FD and LI methods programming.- 5.12 FE and algebraic methods programming.- 5.13 Summary.- 6 Two- and Three-Dimensional Deformable Solids.- 6.1 Kinematics: material description.- 6.2 Dynamics: balance of forces.- 6.3 Mechanics: principle of virtual work.- 6.4 Objective constitutive laws.- 6.5 Nominal stress linearisation.- 6.6 Constitutive laws for solid materials.- 6.7 Spatial discretisation in three dimensions.- 6.8 Linearized discrete mechanics.- 6.9 Isoparametric solid finite elements.- 6.10 Finite difference time integration.- 6.11 Final algorithm.- 6.12 Summary.- Conclusion.- Appendix A: List of Symbols.- 1.- 2.- 3.- 4.- 5.- 6.- Appendix B: Exercises.- 1.- 2.- 3.- 4.- 5.- 6.
