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| Introduction | |
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| Hooke's Law | |
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| Linear Solids with Memory | |
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| Sinusoidal Oscillations in Viscoelastic Material: Models of Viscoelasticity | |
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| Plasticity | |
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| Vibrations | |
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| Prototype of Wave Dynamics | |
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| Biomechanics | |
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| Historical Remarks | |
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| Tensor Analysis | |
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| Notation and Summation Convention | |
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| Coordinate Transformation | |
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| Euclidean Metric Tensor | |
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| Scalars, Contravariant Vectors, Covariant Vectors | |
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| Tensor Fields of Higher Rank | |
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| Some Important Special Tensors | |
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| The Significance of Tensor Characteristics | |
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| Rectangular Cartesian Tensors | |
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| Contraction | |
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| Quotient Rule | |
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| Partial Derivatives in Cartesian Coordinates | |
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| Covariant Differentiation of Vector Fields | |
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| Tensor Equations | |
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| Geometric Interpretation of Tensor Components | |
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| Geometric Interpretation of Covariant Derivatives | |
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| Physical Components of a Vector | |
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| Stress Tensor | |
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| Stresses | |
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| Laws of Motion | |
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| Cauchy's Formula | |
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| Equations of Equilibrium | |
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| Transformation of Coordinates | |
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| Plane State of Stress | |
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| Principal Stresses | |
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| Shearing Stresses | |
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| Mohr's Circles | |
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| Stress Deviations | |
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| Octahedral Shearing Stress | |
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| Stress Tensor in General Coordinates | |
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| Physical Components of a Stress Tensor in General Coordinates | |
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| Equations of Equilibrium in Curvilinear Coordinates | |
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| Analysis of Strain | |
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| Deformation | |
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| Strain Tensors in Rectangular Cartesian Coordinates | |
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| Geometric Interpretation of Infinitesimal Strain Components | |
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| Rotation | |
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| Finite Strain Components | |
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| Compatibility of Strain Components | |
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| Multiply Connected Regions | |
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| Multivalued Displacements | |
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| Properties of the Strain Tensor | |
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| Physical Components | |
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| Example--Spherical Coordinates | |
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| Example--Cylindrical Polar Coordinates | |
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| Conservation Laws | |
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| Gauss' Theorem | |
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| Material and Spatial Descriptions of Changing Configurations | |
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| Material Derivative of Volume Integral | |
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| The Equation of Continuity | |
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| Equations of Motion | |
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| Moment of Momentum | |
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| Other Field Equations | |
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| Elastic and Plastic Behavior of Materials | |
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| Generalized Hooke's Law | |
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| Stress-Strain Relationship for Isotropic Elastic Materials | |
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| Ideal Plastic Solids | |
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| Some Experimental Information | |
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| A Basic Assumption of the Mathematical Theory of Plasticity | |
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| Loading and Unloading Criteria | |
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| Isotropic Stress Theories of Yield Function | |
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| Further Examples of Yield Functions | |
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| Work Hardening--Drucker's Hypothesis and Definition | |
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| Ideal Plasticity | |
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| Flow Rule for Work-Hardening Materials | |
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| Subsequent Loading Surfaces--Isotropic and Kinematic Hardening Rules | |
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| Mroz's, Dafalias and Popov's, and Valanis' Plasticity Theories | |
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| Strain Space Formulations | |
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| Finite Deformation | |
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| Plastic Deformation of Crystals | |
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| Linearized Theory of Elasticity | |
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| Basic Equations of Elasticity for Homogeneous Isotropic Bodies | |
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| Equilibrium of an Elastic Body Under Zero Body Force | |
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| Boundary Value Problems | |
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| Equilibrium and Uniqueness of Solutions | |
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| Saint Venant's Theory of Torsion | |
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| Soap Film Analogy | |
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| Bending of Beams | |
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| Plane Elastic Waves | |
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| Rayleigh Surface Wave | |
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| Love Wave | |
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| Solutions of Problems in Linearized Theory of Elasticity by Potentials | |
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| Scalar and Vector Potentials for Displacement Vector Fields | |
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| Equations of Motion in Terms of Displacement Potentials | |
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| Strain Potential | |
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| Galerkin Vector | |
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| Equivalent Galerkin Vectors | |
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| Example--Vertical Load on the Horizontal Surface of a Semi-Infinite Solid | |
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| Love's Strain Function | |
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| Kelvin's Problem--A Single Force Acting in the Interior of an Infinite Solid | |
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| Perturbation of Elasticity Solutions by a Change of Poisson's Ratio | |
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| Boussinesq's Problem | |
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| On Biharmonic Functions | |
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| Neuber-Papkovich Representation | |
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| Other Methods of Solution of Elastostatic Problems | |
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| Reflection and Refraction of Plane P and S Waves | |
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| Lamb's Problem--Line Load Suddenly Applied on Elastic Half-Space | |
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| Two-Dimensional Problems in Linearized Theory of Elasticity | |
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| Plane State of Stress or Strain | |
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| Airy Stress Functions for Two-Dimensional Problems | |
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| Airy Stress Function in Polar Coordinates | |
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| General Case | |
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| Representation of Two-Dimensional Biharmonic Functions by Analytic Functions of a Complex Variable | |
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| Kolosoff-Muskhelishvili Method | |
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| Variational Calculus, Energy Theorems, Saint-Venant's Principle | |
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| Minimization of Functionals | |
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| Functional Involving Higher Derivatives of the Dependent Variable | |
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| Several Unknown Functions | |
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| Several Independent Variables | |
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| Subsidiary Conditions--Lagrangian Multipliers | |
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| Natural Boundary Conditions | |
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| Theorem of Minimum Potential Energy Under Small Variations of Displacements | |
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| Example of Application: Static Loading on a Beam--Natural and Rigid End Conditions | |
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| The Complementary Energy Theorem Under Small Variations of Stresses | |
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| Variational Functionals Frequently Used in Computational Mechanics | |
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| Saint-Venant's Principle | |
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| Saint-Venant's Principle-Boussinesq-Von Mises-Sternberg Formulation | |
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| Practical Applications of Saint-Venant's Principle | |
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| Extremum Principles for Plasticity | |
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| Limit Analysis | |
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| Hamilton's Principle, Wave Propagation, Applications of Generalized Coordinates | |
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| Hamilton's Principle | |
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| Example of Application--Equation of Vibration of a Beam | |
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| Group Velocity | |
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| Hopkinson's Experiment | |
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| Generalized Coordinates | |
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| Approximate Representation of Functions | |
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| Approximate Solution of Differential Equations | |
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| Direct Methods of Variational Calculus | |
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| Elasticity and Thermodynamics | |
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| The Laws of Thermodynamics | |
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| The Energy Equation | |
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| The Strain Energy Function | |
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| The Conditions of Thermodynamic Equilibrium | |
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| The Positive Definiteness of the Strain Energy Function | |
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| Thermodynamic Restrictions on the Stress-Strain Law of an Isotropic Elastic Material | |
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| Generalized Hooke's Law, Including the Effect of Thermal Expansion | |
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| Thermodynamic Functions for Isotropic Hookean Materials | |
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| Equations Connecting Thermal and Mechanical Properties of a Solid | |
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| Irreversible Thermodynamics and Viscoelasticity | |
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| Basic Assumptions | |
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| One-Dimensional Heat Conduction | |
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| Phenomenological Relations-Onsager Principle | |
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| Basic Equations of Thermomechanics | |
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| Equations of Evolution for a Linear Hereditary Material | |
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| Relaxation Modes | |
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| Normal Coordinates | |
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| Hidden Variables and the Force-Displacement Relationship | |
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| Anisotropic Linear Viscoelastic Materials | |
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| Thermoelasticity | |
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| Basic Equations | |
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| Thermal Effects Due to a Change of Strain; Kelvin's Formula | |
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| Ratio of Adiabatic to Isothermal Elastic Moduli | |
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| Uncoupled, Quasi-Static Thermoelastic Theory | |
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| Temperature Distribution | |
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| Thermal Stresses | |
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| Particular Integral: Goodier's Method | |
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| Plane Strain | |
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| An Example--Stresses in a Turbine Disk | |
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| Variational Principle for Uncoupled Thermoelasticity | |
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| Variational Principle for Heat Conduction | |
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| Coupled Thermoelasticity | |
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| Lagrangian Equations for Heat Conduction and Thermoelasticity | |
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| Viscoelasticity | |
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| Viscoelastic Material | |
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| Stress-Strain Relations in Differential Equation Form | |
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| Boundary-Value Problems and Integral Transformations | |
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| Waves in an Infinite Medium | |
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| Quasi-Static Problems | |
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| Reciprocity Relations | |
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| Large Deformation | |
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| Coordinate Systems and Tensor Notation | |
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| Deformation Gradient | |
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| Strains | |
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| Right and Left Stretch Strain and Rotation Tensors | |
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| Strain Rates | |
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| Material Derivatives of Line, Area, and Volume Elements | |
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| Stresses | |
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| Example: Combined Tension and Torsion Loads | |
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| Objectivity | |
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| Equations of Motion | |
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| Constitutive Equations of Thermoelastic Bodies | |
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| More Examples | |
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| Variational Principles for Finite Elasticity: Compressible Materials | |
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| Variational Principles for Finite Elasticity: Nearly Incompressible or Incompressible Materials | |
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| Small Deflection of Thin Plates | |
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| Large Deflection of Plates | |
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| Incremental Approach to Solving Some Nonlinear Problems | |
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| Updated Lagrangian Description | |
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| Linearized Rates of Deformation | |
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| Linearized Rates of Stress Measures | |
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| Incremental Equations of Motion | |
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| Constitutive Laws | |
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| Incremental Variational Principles in Terms of T | |
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| Incremental Variational Principles in Terms of r | |
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| Incompressible and Nearly Incompressible Materials | |
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| Updated Solution | |
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| Incremental Loads | |
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| Infinitesimal Strain Theory | |
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| Finite Element Methods | |
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| Basic Approach | |
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| One Dimensional Problems Governed by a Second Order Differential Equation | |
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| Shape Functions and Element Matrices for Higher Order Ordinary Differential Equations | |
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| Assembling and Constraining Global Matrices | |
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| Equation Solving | |
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| Two Dimensional Problems by One-Dimensional Elements | |
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| General Finite Element Formulation | |
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| Convergence | |
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| Two-Dimensional Shape Functions | |
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| Element Matrices for a Second-Order Elliptical Equation | |
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| Coordinate Transformation | |
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| Triangular Elements with Curved Sides | |
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| Quadrilateral Elements | |
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| Plane Elasticity | |
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| Three-Dimensional Shape Functions | |
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| Three Dimensional Elasticity | |
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| Dynamic Problems of Elastic Solids | |
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| Numerical Integration | |
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| Patch Tests | |
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| Locking-Free Elements | |
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| Spurious Modes in Reduced Integration | |
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| Perspective | |
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| Mixed and Hybrid Formulations | |
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| Mixed Formulations | |
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| Hybrid Formulations | |
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| Hybrid Singular Elements (Super-Elements) | |
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| Elements for Heterogeneous Materials | |
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| Elements for Infinite Domain | |
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| Incompressible or Nearly Incompressible Elasticity | |
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| Finite Element Methods for Plates and Shells | |
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| Linearized Bending Theory of Thin Plates | |
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| Reissner-Mindlin Plates | |
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| Mixed Functionals for Reissner Plate Theory | |
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| Hybrid Formulations for Plates | |
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| Shell as an Assembly of Plate Elements | |
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| General Shell Elements | |
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| Locking and Stabilization in Shell Applications | |
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| Finite Element Modeling of Nonlinear Elasticity, Viscoelasticity, Plasticity, Viscoplasticity and Creep | |
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| Updated Lagrangian Solution for Large Deformation | |
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| Incremental Solution | |
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| Dynamic Solution | |
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| Newton-Raphson Iteration Method | |
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| Viscoelasticity | |
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| Plasticity | |
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| Viscoplasticity | |
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| Creep | |
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| Bibliography | |
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| Author Index | |
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| Subject Index | |