Nonlinear Dynamics of Structures
This book lays the foundation of knowledge that will allow a better understanding of nonlinear phenomena that occur in structural dynamics. Â This work is intended for graduate engineering students who want to expand their knowledge on the dynamic behavior of structures, specifically in the nonline...
Guardado en:
| Autor principal: | |
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| Formato: | Libro electrónico |
| Lenguaje: | Inglés |
| Publicado: |
Cham :
Springer International Publishing : Imprint: Springer,
2014.
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| Colección: | Lecture Notes on Numerical Methods in Engineering and Sciences,
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| Materias: | |
| Acceso en línea: | http://dx.doi.org/10.1007/978-3-319-05194-9 |
| Aporte de: | Registro referencial: Solicitar el recurso aquí |
Tabla de Contenidos:
- Introduction
- Thermodynamic Basis of the Motion Equation
- Introduction
- Kinematics of the Deformable Bodies
- Basic definitions of tensors describing the kinematics of a point in the space
- Strain Measurements
- Mechanical variables relations
- The Objective Derivative
- Velocity
- Stress Measurements
- Thermodynamics Basis
- First Law of Thermodynamics
- Second Law of Thermodynamics
- Lagrangian local form of Mechanical Dissipation
- Internal Variables
- Dynamic Equilibrium Equation for a Discrete Solid
- Different types of Nonlinear Dynamic Problems
- Materials.Nonlinearity
- Solution of the Motion Equation
- Introduction
- Explicit-implicit solution
- Implicit solution
- Equilibrium at time (t + Î"t)
- Equilibrium solution in time â_"implicit methods
- Newmark´s procedure
- Houbolt´s procedure
- Solution of the nonlinear-equilibrium equations system
- Newton-Raphson Method
- Modified Newton-Raphson Method
- Convergence accelerators
- Aitken accelerator or extrapolation algorithm
- B.F.G.S Algorithms
- Secant-Newton algorithms
- â_oLine-Searchâ__algorithms
- Solution control algorithms â_" â_oArc-Lengthâ__
- Ecuación de control de desplazamiento â_" Superficie esférica
- Convergence Analysis of the dynamic solution
- Introduction
- Reduction to the linear elastic problem
- Solution of second-order linear symmetric systems
- The dynamic equilibrium equation and its convergence-consistency and stability
- Solution stability of second â_"order linear symmetric systems
- Stability analysis procedure
- Determination of A and L for â_oNewmarkâ__
- Determination of A and L for central differences- Newmark´s explicit form
- Solution stability of second-order non-linear symmetric systems
- Stability of the linearized equation
- Energy conservation algorithms
- APPENDIX - 1
- APPENDIX - 2
- Time-independent models
- Introduction
- Elastic behavior
- Invariant of the tensors
- Non-linear Elasticity
- Introduction
- Non-linear hyper-elastic model
- Stress based hyper-elastic model
- Stability Postulates
- Plasticity in small deformations
- Introduction
- Discontinuity behavior or plastic yield criterion
- Elasto-Plastic behavior
- Levy-Mises theory
- Prandtl-Reus theory
- The classic plasticity theory
- Plastic unit or Specific work
- Plastic loading surface. Plastic hardening variable
- Isotropic hardening
- Kinematic hardening
- Stress-Strain relation. Plastic consistency and Tangent rigidity
- Drucker´s stability postulate and maximum plastic dissipation
- Stability condition
- Local stability
- Global stability
- Condition of Unicity of Solution
- Kuhn-Tucker. Loading-unloading condition
- Yield or plastic discontinuity classic criteria
- Rankine criterion of maximum tension stress
- Tresca criterion of maximum shear stress
- Von Mises criterion of octahedral shear stress
- Mohr-Coulomb criterion of octahedral shear stress
- Drucker-Prager criterion
- Geomaterials plasticity
- Basis of the plastic-damage model
- Mechanical behavior required for the constitutive model formulation
- Some characteristics of the plastic damage model
- Main variables of the plastic-damage model
- Definition of the plastic damage variable
- Definition of the law of evolution of cohesion c -κp
- Definition of the variable Ï+ internal friction angle
- Variable definition Ï dilatancy angle
- Generalization of the damage model with stiffness degradation
- Introduction
- Elasto-plastic constitutive equation with stiffness degradation
- Tangent constitutive equation for stiffness degradation processes
- Particular yield functions
- Mohr-Coulomb modified function
- Drucker-Prager Modified function
- Isotropic Continuous Damage â_" Introduction
- Isotropic damage model
- Helmholtz´s free energy and constitutive equation
- Damage threshold criterion
- Evolution law of the internal damage variable
- Constritutive tensor of tangent damage
- Particularization of the damage criterion
- General Softening
- Exponential softening
- Linear softening
- Particularization of the stress threshold function
- Simo -Ju. Model
- Setting of A parameter for Simo-Ju. Model
- Lemaitre and Mazars Model
- General model for different damage surfaces
- Setting of A parameter
- Time-dependent Models
- Introduction
- Constitutive equations based on spring-damping analogies
- Kelvin simplified model
- Maxwell simplified model
- Kelvin generalized model
- Kelvin multiple generalized model
- Maxwell generalized model
- Maxwell multiple generalized model
- Dissipation Evaluation
- Multiaxial generalization of the viscoelastic constitutive laws
- Multiaxial form of viscoelastic models
- Numerical solution of the integral and algorithms
- Kelvin model in dynamic problems
- Kelvin model dissipation
- Equation of the dynamic equilibrium for Kelvin model
- Stress considerations. Rayleigh vs. Kelvin model
- Dissipation considerations. Rayleigh vs. Kelvin model
- Cantilever beam
- Frame with rigid beam and lumped mass
- Viscoplasticity
- Limit states of viscoplasticity
- Over stress function
- Integration algorithm for the viscoplastic constitutive equation
- Particular case of the Duvaut-Lyon model a Von Mises viscoplastic material.