Classical and Computational Solid MechanicsThis invaluable book has been written for engineers and engineering scientists in a style that is readable, precise, concise, and practical. It gives first priority to the formulation of problems, presenting the classical results as the gold standard, and the numerical approach as a tool for obtaining solutions. The classical part is a revision of the well-known text Foundations of Solid Mechanics, with a much-expanded discussion on the theories of plasticity and large elastic deformation with finite strains. The computational part is all new and is aimed at solving many major linear and nonlinear boundary-value problems. |
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Page viii
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Page xi
... Wave Dynamics 18 1.7 . Biomechanics 1.8 . Historical Remarks 22243 25 2 TENSOR ANALYSIS 2.1 . Notation and Summation Convention 2.2 . Coordinate Transformation 2.3 . Euclidean Metric Tensor 2.5 . Tensor Fields of Higher Rank 2.4 ...
... Wave Dynamics 18 1.7 . Biomechanics 1.8 . Historical Remarks 22243 25 2 TENSOR ANALYSIS 2.1 . Notation and Summation Convention 2.2 . Coordinate Transformation 2.3 . Euclidean Metric Tensor 2.5 . Tensor Fields of Higher Rank 2.4 ...
Page xiv
... Waves 7.9 . Rayleigh Surface Wave 7.10 . Love Wave 8 SOLUTIONS OF PROBLEMS IN LINEARIZED THEORY OF ELASTICITY BY POTENTIALS 222 224 229 231 235 238 8.1 . Scalar and Vector Potentials for Displacement Vector Fields 238 8.2 . Equations of ...
... Waves 7.9 . Rayleigh Surface Wave 7.10 . Love Wave 8 SOLUTIONS OF PROBLEMS IN LINEARIZED THEORY OF ELASTICITY BY POTENTIALS 222 224 229 231 235 238 8.1 . Scalar and Vector Potentials for Displacement Vector Fields 238 8.2 . Equations of ...
Page xv
... WAVE PROPAGATION , APPLICATIONS OF GENERALIZED COORDINATES 379 11.1 . Hamilton's Principle 379 11.2 . Example of Application - Equation of Vibration of a Beam 383 11.3 . Group Velocity 393 11.4 . Hopkinson's Experiment 11.5 ...
... WAVE PROPAGATION , APPLICATIONS OF GENERALIZED COORDINATES 379 11.1 . Hamilton's Principle 379 11.2 . Example of Application - Equation of Vibration of a Beam 383 11.3 . Group Velocity 393 11.4 . Hopkinson's Experiment 11.5 ...
Page xvii
... Waves in an Infinite Medium 500 15.5 . Quasi - Static Problems 15.6 . Reciprocity Relations 503 507 16 LARGE DEFORMATION 514 16.1 . Coordinate Systems and Tensor Notation 514 16.2 . Deformation Gradient 521 16.3 . Strains 525 16.4 ...
... Waves in an Infinite Medium 500 15.5 . Quasi - Static Problems 15.6 . Reciprocity Relations 503 507 16 LARGE DEFORMATION 514 16.1 . Coordinate Systems and Tensor Notation 514 16.2 . Deformation Gradient 521 16.3 . Strains 525 16.4 ...
Contents
INTRODUCTION | 1 |
FINITE ELEMENT MODELING OF NONLINEAR | 21 |
TENSOR ANALYSIS | 30 |
5 | 38 |
9 | 44 |
ANALYSIS OF STRAIN | 97 |
4 | 104 |
7 | 112 |
HAMILTONS PRINCIPLE WAVE PROPAGATION | 379 |
ELASTICITY AND THERMODYNAMICS | 407 |
IRREVERSIBLE THERMODYNAMICS | 428 |
THERMOELASTICITY | 456 |
VISCOELASTICITY | 487 |
LARGE DEFORMATION | 514 |
STRESS TENSOR | 534 |
INCREMENTAL APPROACH TO SOLVING | 587 |
9 | 118 |
CONSERVATION LAWS | 127 |
4 | 133 |
ELASTIC AND PLASTIC BEHAVIOR | 138 |
LINEARIZED THEORY OF ELASTICITY | 203 |
SOLUTIONS OF PROBLEMS IN LINEARIZED | 238 |
TWODIMENSIONAL PROBLEMS | 280 |
Functions by Analytic Functions | 299 |
VARIATIONAL CALCULUS ENERGY THEOREMS | 313 |
FINITE ELEMENT METHODS | 624 |
MIXED AND HYBRID FORMULATIONS | 756 |
FINITE ELEMENT METHODS FOR PLATES | 795 |
VISCOPLASTICITY AND CREEP | 848 |
873 | |
66 | 881 |
909 | |
919 | |
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Common terms and phrases
applied approximate assume base vectors beam body force boundary conditions Cartesian coordinates compatibility configuration consider constant constitutive equations coordinate system covariant curve defined in Eq degrees-of-freedom denote derived differential displacement elastic element matrices entropy equilibrium Əxi field variables finite element method flow rule formulation given in Eq Hence Hooke's law increment infinitesimal integration interpolation isotropic Lagrangian linear loading material matrix metric tensor modulus nodal nodes nonlinear normal obtain parameter plane strain plastic deformation plastic strain plate polynomial potential problem quadratic rectangular Cartesian coordinates respectively rotation satisfy shape functions shear shear stress shown in Fig solution strain energy strain tensor stress tensor stress-strain symmetric temperature theorem theory transformation values vanish variational velocity viscoelastic wave yield function yield surface zero მა მე მთ მი მუ მყ