Nonlinear Dynamics of Structures by Sergio Oller.

This book lays the foundation of knowledge that will allow a better understanding of nonlinear phenomena that occur in structural dynamics. This work is intended for graduate engineering students who want to expand their knowledge on the dynamic behavior of structures, specifically in the nonlinea...

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Bibliographic Details
Main Author:	Oller, Sergio (Author)
Corporate Author:	SpringerLink (Online service)
Format:	eBook
Language:	English
Published:	Cham : Springer International Publishing : Imprint: Springer, 2014.
Edition:	1st ed. 2014.
Series:	Lecture Notes on Numerical Methods in Engineering and Sciences, Springer eBook Collection.
Subjects:	Vibration. Dynamical systems. Dynamics. Mechanics. Mechanical engineering. Electronic resources (E-books)
Online Access:	Click to view e-book
Holy Cross Note:	Loaded electronically. Electronic access restricted to members of the Holy Cross Community.

Table of Contents:

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 + Δt)
Equilibrium solution in time –implicit methods
Newmarḱs procedure
Houbolt́s 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
“Line-Search”algorithms
Solution control algorithms – “Arc-Length”
Ecuación de control de desplazamiento – 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 –order linear symmetric systems
Stability analysis procedure
Determination of A and L for “Newmark”
Determination of A and L for central differences- Newmarḱs 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
Druckeŕs 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 φ internal friction angle
Variable definition ψ, 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 – Introduction
Isotropic damage model
Helmholtźs 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.

Nonlinear Dynamics of Structures by Sergio Oller.

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