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 xv
... VARIATIONAL CALCULUS , ENERGY THEOREMS , SAINT - VENANT'S PRINCIPLE 299 301 313 10.1 . 10.2 . Minimization of Functionals 313 Functional Involving Higher Derivatives of the Dependent Variable 319 10.3 . Several Unknown Functions 320 ...
... VARIATIONAL CALCULUS , ENERGY THEOREMS , SAINT - VENANT'S PRINCIPLE 299 301 313 10.1 . 10.2 . Minimization of Functionals 313 Functional Involving Higher Derivatives of the Dependent Variable 319 10.3 . Several Unknown Functions 320 ...
Page xvi
... Variational Calculus 402 402 12 ELASTICITY AND THERMODYNAMICS 12.1 . The Laws of Thermodynamics 407 407 12.2 . The Energy Equation 412 12.3 . The Strain Energy Function 414 12.4 . The Conditions of Thermodynamic Equilibrium 416 12.5 ...
... Variational Calculus 402 402 12 ELASTICITY AND THERMODYNAMICS 12.1 . The Laws of Thermodynamics 407 407 12.2 . The Energy Equation 412 12.3 . The Strain Energy Function 414 12.4 . The Conditions of Thermodynamic Equilibrium 416 12.5 ...
Page xvii
... Variational Principle for Uncoupled Thermoelasticity 473 14.11 . Variational Principle for Heat Conduction 474 14.12 . Coupled Thermoelasticity 478 14.13 . Lagrangian Equations for Heat Conduction and Thermoelasticity 481 15 ...
... Variational Principle for Uncoupled Thermoelasticity 473 14.11 . Variational Principle for Heat Conduction 474 14.12 . Coupled Thermoelasticity 478 14.13 . Lagrangian Equations for Heat Conduction and Thermoelasticity 481 15 ...
Page xviii
... Variational Principles in Terms of T 604 17.7 . Incremental Variational Principles in Terms of r * 610 17.8 . Incompressible and Nearly Incompressible Materials 612 17.9 . Updated Solution 617 17.10 . Incremental Loads 17.11 ...
... Variational Principles in Terms of T 604 17.7 . Incremental Variational Principles in Terms of r * 610 17.8 . Incompressible and Nearly Incompressible Materials 612 17.9 . Updated Solution 617 17.10 . Incremental Loads 17.11 ...
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