| 000 | 04877cam a22003614a 4500 | ||
|---|---|---|---|
| 003 | CUTN | ||
| 005 | 20240906170715.0 | ||
| 008 | 110622s2011 enka b 001 0 eng | ||
| 020 | _a9780199609130 | ||
| 020 | _a0199609136 | ||
| 041 | _aEnglish | ||
| 042 | _apcc | ||
| 082 | 0 | 0 |
_a518.25 _223 _bDAV |
| 084 |
_aSK 910 _2rvk |
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| 100 | 1 | _aDavies, Alan J. | |
| 245 | 1 | 4 |
_aThe finite element method : _ban introduction with partial differential equations / _cA.J. Davies. |
| 250 | _a2nd ed. | ||
| 260 |
_aOxford ; _aNew York : _bOxford University Press, _c2011. |
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| 300 |
_aix, 297 p. : _bill. ; _c25 cm. |
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| 504 | _aIncludes bibliographical references and index. | ||
| 505 | _t Cover; Contents; 1 Historical introduction; 2 Weighted residual and variational methods; 2.1 Classification of differential operators; 2.2 Self-adjoint positive definite operators; 2.3 Weighted residual methods; 2.4 Extremum formulation: homogeneous boundary conditions; 2.5 Non-homogeneous boundary conditions; 2.6 Partial differential equations: natural boundary conditions; 2.7 The Rayleigh-Ritz method; 2.8 The 'elastic analogy' for Poisson's equation; 2.9 Variational methods for time-dependent problems; 2.10 Exercises and solutions; 3 The finite element method for elliptic problems. 3.1 Difficulties associated with the application of weighted residual methods3.2 Piecewise application of the Galerkin method; 3.3 Terminology; 3.4 Finite element idealization; 3.5 Illustrative problem involving one independent variable; 3.6 Finite element equations for Poisson's equation; 3.7 A rectangular element for Poisson's equation; 3.8 A triangular element for Poisson's equation; 3.9 Exercises and solutions; 4 Higher-order elements: the isoparametric concept; 4.1 A two-point boundary-value problem; 4.2 Higher-order rectangular elements; 4.3 Higher-order triangular elements. 4.4 Two degrees of freedom at each node4.5 Condensation of internal nodal freedoms; 4.6 Curved boundaries and higher-order elements: isoparametric elements; 4.7 Exercises and solutions; 5 Further topics in the finite element method; 5.1 The variational approach; 5.2 Collocation and least squares methods; 5.3 Use of Galerkin's method for time-dependent and non-linear problems; 5.4 Time-dependent problems using variational principles which are not extremal; 5.5 The Laplace transform; 5.6 Exercises and solutions; 6 Convergence of the finite element method; 6.1 A one-dimensional example. 6.2 Two-dimensional problems involving Poisson's equation6.3 Isoparametric elements: numerical integration; 6.4 Non-conforming elements: the patch test; 6.5 Comparison with the finite difference method: stability; 6.6 Exercises and solutions; 7 The boundary element method; 7.1 Integral formulation of boundary-value problems; 7.2 Boundary element idealization for Laplace's equation; 7.3 A constant boundary element for Laplace's equation; 7.4 A linear element for Laplace's equation; 7.5 Time-dependent problems; 7.6 Exercises and solutions; 8 Computational aspects; 8.1 Pre-processor. 8.2 Solution phase8.3 Post-processor; 8.4 Finite element method (FEM) or boundary element method (BEM)?; Appendix A: Partial differential equation models in the physical sciences; A.1 Parabolic problems; A.2 Elliptic problems; A.3 Hyperbolic problems; A.4 Initial and boundary conditions; Appendix B: Some integral theorems of the vector calculus; Appendix C: A formula for integrating products of area coordinates over a triangle; Appendix D: Numerical integration formulae; D.1 One-dimensional Gauss quadrature; D.2 Two-dimensional Gauss quadrature; D.3 Logarithmic Gauss quadrature | ||
| 520 | _aThe finite element method is a technique for solving problems in applied science and engineering. The essence of this book is the application of the finite element method to the solution of boundary and initial-value problems posed in terms of partial differential equations. The method is developed for the solution of Poisson's equation, in a weighted-residual context, and then proceeds to time-dependent and nonlinear problems. The relationship with the variational approach is also explained. This book is written at an introductory level, developing all the necessary concepts where required. | ||
| 650 | 0 | _aFinite element method. | |
| 856 | 4 | 2 | _uhttp://www.loc.gov/catdir/enhancements/fy1211/2011022386-b.html |
| 856 | 4 | 2 | _uhttp://www.loc.gov/catdir/enhancements/fy1211/2011022386-d.html |
| 856 | 4 | 1 | _uhttp://www.loc.gov/catdir/enhancements/fy1211/2011022386-t.html |
| 856 | 4 | 2 | _3Contributor biographical information |
| 856 | 4 | 2 | _3Publisher description |
| 856 | 4 | 1 | _3Table of contents only |
| 906 |
_a7 _bcbc _corignew _d1 _eecip _f20 _gy-gencatlg |
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| 942 |
_2ddc _cBOOKS |
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| 999 |
_c43481 _d43481 |
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