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" Nonlinear Dynamics of Structures "
by Sergio Oller.
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BL
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| Record Number
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734916
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b554751
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| Main Entry
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by Sergio Oller.
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| Title & Author
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Nonlinear Dynamics of Structures\ by Sergio Oller.
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| Publication Statement
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Cham: Springer International Publishing : Imprint : Springer, 2014
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| Series Statement
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Lecture Notes on Numerical Methods in Engineering and Sciences
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(XII, 192 p.)
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| ISBN
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3319051946
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: 9783319051949
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| Contents
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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 + t).- Equilibrium solution in time -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.- "Line-Search"algorithms.- Solution control algorithms - "Arc-Length".- Ecuacion de control de desplazamiento - Superficie esferica.- 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- 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 - p.- Definition of the variable internal friction angle.- Variable definition , 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.- 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.
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| Subject
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Engineering.
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Mechanics.
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Vibration.
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| LC Classification
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TA654.B974 2014
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| Added Entry
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Sergio Oller
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