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 xviii
... FINITE ELEMENT METHODS 624 18.1 . Basic Approach 626 18.2 . One Dimensional Problems Governed by a Second Order Differential Equation 629 18.3 . Shape Functions and Element Matrices for Higher Order Ordinary Differential Equations 638 ...
... FINITE ELEMENT METHODS 624 18.1 . Basic Approach 626 18.2 . One Dimensional Problems Governed by a Second Order Differential Equation 629 18.3 . Shape Functions and Element Matrices for Higher Order Ordinary Differential Equations 638 ...
Page xix
... Elements 18.7 . General Finite Element Formulation 18.8 . 18.9 . Convergence Two - Dimensional Shape Functions 18.10 . Element Matrices for a Second - Order 655 657 664 665 Elliptical Equation 672 18.11 . Coordinate Transformation 676 ...
... Elements 18.7 . General Finite Element Formulation 18.8 . 18.9 . Convergence Two - Dimensional Shape Functions 18.10 . Element Matrices for a Second - Order 655 657 664 665 Elliptical Equation 672 18.11 . Coordinate Transformation 676 ...
Page 346
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Page 624
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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