Nonlinear computational solid mechanics
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| Main Authors: | , , |
|---|---|
| Format: | eBook |
| Language: | English |
| Published: |
Boca Raton, FL :
CRC Press, Taylor & Francis Group,
[2017]
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| Subjects: | |
| ISBN: | 9781498746137 1498746136 9781351682633 1351682636 9781523114221 1523114223 9781498746120 1498746128 9781315167329 1315167328 |
| Physical Description: | 1 online resource (xvi, 378 pages) |
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| LEADER | 14965cam a2200661 i 4500 | ||
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| 003 | OCoLC | ||
| 005 | 20240717213016.0 | ||
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| 007 | cr cn||||||||| | ||
| 008 | 170713s2017 flu ob 001 0 eng d | ||
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| 020 | |a 9781498746137 |q (electronic bk.) | ||
| 020 | |a 1498746136 |q (electronic bk.) | ||
| 020 | |a 9781351682633 |q (electronic bk.) | ||
| 020 | |a 1351682636 |q (electronic bk.) | ||
| 020 | |a 9781523114221 |q (electronic bk.) | ||
| 020 | |a 1523114223 |q (electronic bk.) | ||
| 020 | |z 9781498746120 |q (hardcover ; |q alkaline paper) | ||
| 020 | |z 1498746128 |q (hardcover ; |q alkaline paper) | ||
| 020 | |z 9781315167329 |q (print) | ||
| 020 | |z 1315167328 |q (print) | ||
| 024 | 7 | |a 10.1201/9781315167329 |2 doi | |
| 035 | |a (OCoLC)993587952 |z (OCoLC)994317766 |z (OCoLC)1202484002 |z (OCoLC)1303495346 | ||
| 100 | 1 | |a Ghaboussi, J., |e author. | |
| 245 | 1 | 0 | |a Nonlinear computational solid mechanics / |c Jamshid Ghaboussi, David A. Pecknold, Xiping Steven Wu. |
| 264 | 1 | |a Boca Raton, FL : |b CRC Press, Taylor & Francis Group, |c [2017] | |
| 264 | 4 | |c ©2017 | |
| 300 | |a 1 online resource (xvi, 378 pages) | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 504 | |a Includes bibliographical references and index. | ||
| 505 | 0 | |a 1.1. Linear computational mechanics -- 1.2. Nonlinear computational mechanics -- 1.3. Nonlinear behavior of simple structures -- 2.1. Motion and deformation of line elements -- 2.2. Deformation of volume and area elements -- 2.2.1. Volume elements -- 2.2.2. Area elements -- 2.3. Strains -- 2.3.1. Lagrangian (Green) strain -- 2.3.1.1. Interpretation of Green strain components -- 2.3.1.2. Diagonal components of Green strain -- 2.3.1.3. Off-diagonal components of Green strain -- 2.3.1.4. Simple shear -- 2.3.2. Eulerian (Almansi) strain -- 2.3.2.1. Uniaxial stretching -- 2.3.2.2. Uniaxial stretching and rigid body rotation -- 2.3.2.3. Relation between Green strain and Almansi strain -- 2.4. Objectivity and frame indifference -- 2.4.1. Objectivity of some deformation measures -- 2.4.1.1. Deformation gradient -- 2.4.1.2. Metric tensor -- 2.4.1.3. Strain tensors -- 2.5. Rates of deformation -- 2.5.1. Velocity and velocity gradient -- 2.5.2. Deformation and spin tensors. | |
| 505 | 0 | |a 2.5.3. Deformation gradient rates -- 2.5.4. Rate of deformation of a line element -- 2.5.5. Interpretation of deformation and spin tensors -- 2.5.6. Rate of change of a volume element -- 2.5.7. Rate of change of an area element -- 2.6. Strain rates -- 2.6.1. Lagrangian (Green) strain rate -- 2.6.2. Eulerian (Almansi) strain rate -- 2.7. Decomposition of motion -- 2.7.1. Polar decomposition -- 2.7.2. Polar decomposition of deformation gradient -- 2.7.3.Computation of polar decomposition -- 2.7.3.1. Right stretch tensor -- 2.7.3.2. Left stretch tensor -- 2.7.4. Strains -- 2.7.5. Strain and deformation rates -- 2.7.5.1. Green strain rate -- 2.7.5.2. Material rotation rate -- 2.7.6. Simple examples -- 2.7.6.1. Plate stretched and rotated -- 2.7.6.2. Simple shear -- 3.1. Traction vector on a surface -- 3.2. Cauchy stress principle -- 3.3. Cauchy stress tensor -- 3.4. Piola-Kirchhoff stress tensors -- 3.5. Stress rates -- 3.5.1. Material rates of stress. | |
| 505 | 0 | |a 3.5.2. Jaumann rate of Cauchy stress -- 3.5.3. Truesdell rate of Cauchy stress -- 3.S.4. Unrotated Cauchy stress and the Green-Naghdi rate -- 3.5.4.1. Unrotated Cauchy stress -- 3.5.4.2. Green-Naghdi rate -- 3.6. Examples of stress rates for simple stress conditions -- 3.6.1. Uniaxial extension of an initially stressed body -- 3.6.2. Rigid body rotation of an initially stressed body -- 3.6.3. Simple shear of an initially stressed body -- 3.6.3.1. Jaumann stress rate -- 3.6.3.2. Truesdell stress rate -- 4.1. Divergence theorem -- 4.2. Stress power -- 4.2.1.2PK stress power -- 4.2.2. Unrotated Cauchy stress power -- 4.3. Virtual work -- 4.4. Principle of virtual work -- 4.4.1. Internal virtual work -- 4.4.2. Lagrangian form of internal virtual work -- 4.5. Vector forms of stress and strain -- 5.1. Introduction -- 5.2. Linear elastic material models -- 5.3. Cauchy elastic material models -- 5.3.1. Characteristic polynomial of a matrix -- 5.3.2. Cayley-Hamilton theorem. | |
| 505 | 0 | |a 5.3.3. General polynomial form for isotropic Cauchy elastic materials -- 5.4. Hyperelastic material models -- 5.4.1. Strain energy density potential -- 5.4.2. Deformation invariants -- 5.4.3. Rubber and rubberlike materials -- 5.4.3.1. Ogden hyperelastic model -- 5.4.3.2. Balloon problem -- 5.4.4. Soft biological tissue -- 5.4.4.1. Fung exponential hyperelastic model -- 5.5. Hypoelastic material models -- 5.5.1. Hypoelastic grade zero -- 5.5.2. Hypoelastic grade one -- 5.5.3. Lagrangian versus hypoelastic material tangent stiffness -- 5.5.3.1. Truesdell stress rate -- 5.5.3.2. Jaumann stress rate -- 5.5.4.Comparison of linear isotropic hypoelastic models in simple shear -- 5.5.4.1. Truesdell rate hypoelastic model -- 5.5.4.2. Jaumann rate hypoelastic model -- 5.5.4.3. Green-Naghdi rate hypoelastic model -- 5.6. Numerical evaluation of a linear isotropic hypoelastic model -- 5.6.1. Natural coordinate system for triangle -- 5.6.2. Kinematics. | |
| 505 | 0 | |a 5.6.3. Nodal displacement patterns -- 5.6.4. Strain cycles -- 5.6.5. Calculation procedure -- 5.6.6. Numerical results -- 6.1. Introduction -- 6.2. Volumetric and deviatoric stresses and strains -- 6.3. Principal stresses and stress invariants -- 6.4. Alternative forms of stress invariants -- 6.5. Octahedral stresses -- 6.6. Principal stress space -- 6.7. Standard material tests and stress paths -- 6.7.1. Representations of stress paths -- 6.7.2. Uniaxial tests -- 6.7.2.1. Uniaxial tension -- 6.7.2.2. Uniaxial compression -- 6.7.3. Biaxial tests -- 6.7.4. Isotropic compression tests -- 6.7.5. Triaxial tests -- 6.7.6. True triaxial tests -- 6.7.6.1. Pure shear test -- 7.1. Introduction -- 7.2. Behavior of metals under uniaxial stress -- 7.2.1. Fundamental assumptions of classical plasticity theory -- 7.3. Inelastic behavior under multiaxial states of stress -- 7.3.1. Yield surface -- 7.4. Work and stability constraints -- 7.4.1. Work and energy -- 7.4.2. Stability in the small. | |
| 505 | 0 | |a 7.4.3.Complementary work -- 7.4.4.Net work -- 7.5. Associated plasticity models -- 7.5.1. Drucker's postulate -- 7.5.2. Convexity and normality -- 7.5.2.1. Normality of the plastic strain increment -- 7.5.2.2. Convexity of the yield surface -- 7.6. Incremental stress-Strain relations -- 7.6.1. Equivalent uniaxial stress and plastic strain -- 7.6.2. Loading and unloading criteria -- 7.6.3. Continuum tangent stiffness -- 7.6.4. Elastic-perfectly plastic behavior -- 7.6.5. Interpretation of incremental stresses -- 7.6.5.1. Elastic-perfectly plastic -- 7.6.5.2. Hardening plasticity -- 7.7. Yield surfaces in principal stress space -- 7.7.1. Material isotropy and symmetry requirements -- 7.7.2.von Mises yield surface -- 7.7.2.1. Biaxial (plane) stress -- 7.7.2.2. Tension-torsion test -- 7.7.3. Tresca yield surface -- 7.8. Hardening plasticity models -- 7.8.1. Determination of hardening parameter from uniaxial test -- 7.8.2. Isotropic hardening. | |
| 505 | 0 | |a 7.8.3. Kinematic hardening and back stress -- 7.8.4.Combined isotropic and kinematic hardening -- 7.9. Stress update -- 7.9.1.von Mises plasticity in simple shear problem -- 7.9.2. Stress update algorithm -- 7.9.2.1. Calculation of updated stress -- 7.9.2.2. Elastic trial stress at step (n + 1) -- 7.9.2.3. Stress correction -- 7.9.2.4. Elastoplastic response -- 7.10. Plasticity models for frictional and pressure-Sensitive materials -- 7.10.1. Mohr-Coulomb yield surface -- 7.10.2. Drucker-Prager yield surface -- 7.10.3. Model refinements -- 7.10.3.1. Cap models -- 7.10.3.2. Refined (q, theta) shape in octahedral plane -- 8.1. Introduction -- 8.2. Finite element discretization -- 8.2.1. Shape functions -- 8.2.1.1. Serendipity elements -- 8.2.1.2. Simplex elements -- 8.2.2. Isoparametric mapping -- 8.2.2.1. Numerical (Gaussian) quadrature -- 8.2.2.2. Shape function derivatives -- 8.3. Total Lagrangian formulation -- 8.3.1. Geometric nonlinearity -- 8.3.1.1. Green strain. | |
| 505 | 0 | |a 8.3.1.2. Green strain rate -- 8.3.1.3. Tangent stiffness matrix -- 8.3.2. Nonlinear material behavior -- 8.3.2.1. Elastoplastic material behavior -- 8.3.2.2. Consistent tangent stiffness -- 8.3.2.3.von Mises yield criterion -- 8.3.2.4. Discussion -- 8.3.2.5.2PK stress rate versus Green strain rate for TL formulation -- 8.3.3. Plane stress -- 8.3.3.1. Partial inversion and condensation of material stiffness -- 8.3.3.2. Nonlinear material properties -- 8.3.3.3. Expansion of strain increment and stress update -- 8.3.3.4. Condensed tangent stiffness and internal resisting force vector -- 8.3.4. Pressure loading -- 8.3.4.1. Load stiffness for 2D simplex element -- 8.3.4.2. Secant load stiffness -- 8.3.4.3. Tangent load stiffness -- 8.4. Updated Lagrangian methods -- 8.4.1. Basic UDL formulation -- 8.4.1.1. Virtual work in deformed configuration -- 8.4.1.2. Coordinate systems -- 8.4.1.3. Hughes-Winget incremental update -- 8.4.1.4. Element geometry updating -- 9.1. Introduction. | |
| 505 | 0 | |a 9.2. Finite rotations in three dimensions -- 9.2.1. Rotation matrix R -- 9.2.1.1. Euler's theorem -- 9.2.1.2. Rodrigues's formula -- 9.2.1.3. Extraction of the axial vector from R -- 9.2.1.4. Eigenstructure of the spin matrix -- 9.2.1.5. Matrix exponential -- 9.2.1.6. Exponential map -- 9.2.2. Cayley transform -- 9.2.3.Composition of finite rotations -- 9.2.3.1. Infinitesimal rotations -- 9.2.3.2. Two successive finite rotations -- 9.2.3.3. Update of finite nodal rotations -- 9.3. Element local coordinate systems -- 9.3.1. Euler angles -- 9.3.2. Orienting plate and shell elements in three dimensions -- 9.4. Corotational finite element formulation -- 9.4.1. Corotational coordinate systems -- 9.4.1.1. Notation -- 9.4.1.2. Element triads -- 9.4.1.3. Nodal triads -- 9.4.1.4. Nodal rotational freedoms -- 9.4.2. Incremental nodal degrees of freedom -- 9.4.2.1. Incremental nodal displacements -- 9.4.2.2. Incremental nodal rotations -- 9.4.3. Incremental variation of element frame. | |
| 505 | 0 | |a 9.4.4. Incremental variation of the nodal triad -- 9.4.4.1. Corotated incremental nodal rotations -- 9.4.5. Corotated incremental element freedoms combined -- 9.4.5.1. Geometric stiffness -- 9.4.5.2. Variation of LambdaTaui contracted with a nodal moment vector mi -- 9.4.5.3. Tangent stiffness summary -- 9.4.6. Discussion of a CR versus UDL formulation -- 10.1. Introduction -- 10.2. Modeling of shell structures -- 10.3.3D Structural element formulations -- 10.3.1. Kirchhoff beam, plate, and shell finite elements -- 10.3.1.1. Flat plate and shell elements -- 10.3.1.2. General form of geometric stiffness -- 10.3.1.3. Remarks -- 10.3.1.4. Synthesis of space frame stiffness matrices -- 10.3.1.5. Space frame geometric stiffness -- 10.3.1.6. Planar bending -- 10.3.1.7. Plane frame stiffness matrices -- 10.3.1.8. Remarks -- 10.3.1.9. Elastic tangent stiffness matrices -- 10.3.2. Mindlin plate theory -- 10.3.3. Degeneration of isoparametric solid elements. | |
| 505 | 0 | |a 10.3.4. Mindlin plate and flat shell finite elements -- 10.3.4.1. Bending stiffness -- 10.3.4.2. Shear stiffness -- 10.3.4.3. In-plane response -- 10.3.4.4. Geometric stiffness -- 10.3.4.5. Membrane stiffness -- 10.3.4.6. Performance of Mindlin elements -- 10.3.4.7. Shear locking, zero-energy modes, and hourglass control -- 10.3.4.8. Membrane locking -- 10.4. Isoparametric curved shell elements -- 10.4.1. Normal rotation in classic thin-shell theory -- 10.4.2. Isoparametric modeling of curved shell geometry -- 10.4.3. Nodal surface coordinate system -- 10.4.4. Jacobian matrix -- 10.4.5. Lamina Cartesian coordinate system -- 10.4.6. Summary of coordinate systems and transformations -- 10.4.7. Displacement interpolation -- 10.4.8. Approximations -- 10.4.9. Lamina kinematics -- 10.4.10. Lamina stresses -- 10.4.11. Virtual work density -- 10.4.12. Rotational freedoms -- 10.4.13.Comments on the UDL formulation -- 10.5. Nonlinear material behavior. | |
| 505 | 0 | |a 10.5.1. Through-thickness numerical integration -- 10.5.2. Layered models -- 11.1. Introduction -- 11.2. Pure incremental (Euler-Cauchy) method -- 11.3. Incremental method with equilibrium correction -- 11.4. Incremental-Iterative (Newton-Raphson) method -- 11.5. Modified Newton-Raphson method -- 11.6. Critical points on the equilibrium path -- 11.6.1. Characterization of critical points -- 11.6.2. Monitoring the incremental solution on the primary path -- 11.6.3. Determinant of the tangent stiffness -- 11.6.4. Current stiffness parameter -- 11.7. Arc-length solution methods -- 11.7.1. Crisfield's spherical method -- 11.7.2. Ramm's normal plane method -- 11.8. Lattice dome example -- 11.8.1. Load-deflection response of hexagonal dome -- 11.9. Secondary solution paths -- 11.10. Structural imperfections -- 11.10.1. Application to hexagonal dome example -- 12.1. Introduction -- 12.2. Multilayer neural networks -- 12.2.1. Training of neural networks. | |
| 505 | 0 | |a 12.3. Hard computing versus soft computing -- 12.4. Neural networks in material modeling -- 12.5. Nested adaptive neural networks -- 12.6. Neural network modeling of hysteretic behavior of materials -- 12.7. Acquisition of training data for neural network material models -- 12.8. Neural network material models in finite element analysis -- 12.9. Autoprogressive algorithm -- 12.9.1. Autoprogressive algorithm in modeling composite materials -- 12.9.2. Autoprogressive algorithm in structural mechanics and in geomechanics -- 12.9.3. Autoprogressive algorithm in biomedicine. | |
| 506 | |a Plný text je dostupný pouze z IP adres počítačů Univerzity Tomáše Bati ve Zlíně nebo vzdáleným přístupem pro zaměstnance a studenty | ||
| 590 | |a Knovel |b Knovel (All titles) | ||
| 650 | 0 | |a Mechanics, Applied |x Mathematics. | |
| 650 | 0 | |a Nonlinear mechanics |x Matematics. | |
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| 650 | 0 | |a Materials |x Mathematical models. | |
| 655 | 7 | |a elektronické knihy |7 fd186907 |2 czenas | |
| 655 | 9 | |a electronic books |2 eczenas | |
| 700 | 1 | |a Pecknold, D. A. W., |e author. | |
| 700 | 1 | |a Wu, Xiping, |d 1962- |e author. |1 https://id.oclc.org/worldcat/entity/E39PCjrmRQxprmqM6gk94vT9wC | |
| 776 | 0 | 8 | |i Print version: |a Ghaboussi, J. |t Nonlinear computational solid mechanics |z 9781498746120 |w (DLC) 2016059346 |w (OCoLC)967417700 |
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