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Finite elements : computational engineering sciences / A.J. Baker

By: Baker, A. J [author]Contributor(s): Baker, A. J [author]Material type: Text

TextPublication details: West Sussex : John Wiley & Sons, c2012Description: xx, 267 pages : illustrations ; 25 cmISBN: 9781119940500Subject(s): FINITE ELEMENT METHODLOC classification: TA 347.F5 .B35 2012

Contents:

Machine generated contents note: 1.1. Engineering Simulation -- 1.2. A Problem-Solving Environment -- 1.3. Weak Formulation Essence -- 1.4. Decisions on Forming WSN -- 1.5. Discrete WSh Implementations -- 1.6. Chapter Summary -- References -- 2.1. Engineering Simulation -- 2.2. Continuum Mechanics Viewpoint -- 2.3. Continuum Conservation Principle Forms -- 2.4. Constitutive Closure for Conservation Principle PDEs -- 2.5. Engineering Science Continuum Mechanics -- References -- 3.1. Example Linear Heat Conduction Solutions -- 3.2. Multidimensional PDEs, Separation of Variables -- 3.3. Mathematical Foundation Essence for GWSN -- 3.4. A Legacy FD Construction -- 3.5. An FD Approximate Solution -- 3.6. Lagrange Interpolation Polynomials -- 3.7. Chapter Summary -- Exercises -- References -- 4.1. A Steady Heat Conduction Example -- 4.2. Weak Form Approximation, Error Extremization -- 4.3. GWSw Discrete Implementation, FE Trial Space Basis -- 4.4. Finite Element Matrix Statements -- 4.5. Assembly of {WS}e to form Algebraic GWSh -- 4.6. Solution Accuracy, Error Distribution -- 4.7. Convergence, Boundary Heat Flux -- 4.8. Chapter Summary -- Exercises -- Reference -- 5.1. Introduction -- 5.2. Steady Heat Transfer, n = 1 -- 5.3. FE k = 1 Trial Space Basis Matrix Library -- 5.4. Object-Oriented GWSh Programming -- 5.5. Higher Completeness Degree Trial Space Bases -- 5.6. Global Theory, Asymptotic Error Estimate -- 5.7. Nonsmooth Data, Theory Generalization -- 5.8. Temperature-Dependent Conductivity, Nonlinearity -- 5.9. Static Condensation, p-Elements -- 5.10. Chapter Summary -- Exercises -- Computer Labs -- References -- 6.1. Introduction -- 6.2. The Euler-Bernoulli Beam Equation -- 6.3. Euler-Bernoulli Beam Theory GWSh Reformulation -- 6.4. Timoshenko Beam Theory -- 6.5. Mechanical Vibrations of a Beam -- 6.6. Fluid Mechanics, Potential Flow -- 6.7. Electromagnetic Plane Wave Propagation -- 6.8. Convection-Radiation Finned Cylinder Heat Transfer -- 6.9. Chapter Summary -- Exercises -- Computer Labs -- References -- 7.1. Introduction -- 7.2. Multidimensional FE Bases and DOF -- 7.3. Multidimensional FE Operations for {Nk([zeta][alpha])} -- 7.4. The NC k = 1,2 Basis FE Matrix Library -- 7.5. NC Basis {WS}e Template, Accuracy, Convergence -- 7.6. The Tensor Product Basis Element Family -- 7.7. Gauss Numerical Quadrature, k = 1 TP Basis Library -- 7.8. Convection-Radiation BC GWS Implementation -- 7.9. Linear Basis GWSh Template Unification -- 7.10. Accuracy, Convergence Revisited -- 7.11. Chapter Summary -- Exercises -- Computer Labs -- References -- 8.1. The FD-FE Correlation -- 8.2. The FV-FE Correlation -- 8.3. Chapter Summary -- Exercises -- 9.1. Introduction -- 9.2. The Galerkin Weak Statement -- 9.3. GWSh Completion for Time Dependence -- 9.4. GWSh + [theta]TS Algorithm Templates -- 9.5. GWSh + [theta]TS Algorithm Asymptotic Error Estimates -- 9.6. Performance Verification Test Cases -- 9.7. Dispersive Error Characterization -- 9.8. A Modified Galerkin Weak Statement -- 9.9. Verification Problem Statements Revisited -- 9.10. Unsteady Heat Conduction -- 9.11. Chapter Summary -- Exercises -- Computer Labs -- References -- 10.1. The Problem Statement -- 10.2. GWSh + [theta]TS Formulation Reprise -- 10.3. Matrix Library Additions, Templates -- 10.4. mPDE Galerkin Weak Forms, Theoretical Analyses -- 10.5. Verification, Benchmarking, and Validation -- 10.6. Mass Transport, the Rotating Cone Verification -- 10.7. The Gaussian Plume Benchmark -- 10.8. Steady n-D Peclet Problem Verification -- 10.9. Mass Transport, a Validated n = 3 Experiment -- 10.10. Numerical Linear Algebra, Matrix Iteration -- 10.11. Newton and AF TP Jacobian Templates -- 10.12. Chapter Summary -- Exercises -- Computer Labs -- References -- 11.1. Introduction -- 11.2. Structural Mechanics -- 11.3. Structural Mechanics, Virtual Work FE Implementation -- 11.4. Plane Stress/Strain GWSh Implementation -- 11.5. Plane Elasticity Computer Lab -- 11.6. Fluid Mechanics, Incompressible-Thermal Flow -- 11.7. Vorticity-Streamfunction GWSh + [theta]TS Algorithm -- 11.8. An Isothermal INS Validation Experiment -- 11.9. Multimode Convection Heat Transfer -- 11.10. Mechanical Vibrations, Normal Mode GWSh -- 11.11. Normal Modes of a Vibrating Membrane -- 11.12. Multiphysics Solid-Fluid Mass Transport -- 11.13. Chapter Summary -- Exercises -- Computer Labs -- References.

Summary: Uniting theory with hands-on computer practice, this book gives readers a firm appreciation of the error mechanisms and control that underlie discrete approximation implementations in the engineering sciences. Key features : illustrative examples include heat conduction, structural mechanics, mechanical vibrations, heat transfer with convection and radiation, fluid mechanics and heat and mass transport ; takes a cross-discipline continuum mechanics viewpoint ; includes Matlab toolbox and .m data files on a companion website, immediately enabling hands-on computing in all covered disciplines. It provides a holistic view of the topic from covering the different engineering problems that can be solved using finite element to how each particular method can be implemented on a computer. Computational aspects of the method are provided on a companion website facilitating engineering implementation in an easy way.

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Item type	Current library	Home library	Collection	Shelving location	Call number	Copy number	Status	Date due	Barcode
Books	LRC - Main	National University - Manila	Gen. Ed. - COE	General Circulation	GC TA 347.F5 .B35 2012 (Browse shelf (Opens below))	c.1	Available		NULIB000008312

Includes index.

Machine generated contents note: 1.1. Engineering Simulation --
1.2. A Problem-Solving Environment --
1.3. Weak Formulation Essence --
1.4. Decisions on Forming WSN --
1.5. Discrete WSh Implementations --
1.6. Chapter Summary --
References --
2.1. Engineering Simulation --
2.2. Continuum Mechanics Viewpoint --
2.3. Continuum Conservation Principle Forms --
2.4. Constitutive Closure for Conservation Principle PDEs --
2.5. Engineering Science Continuum Mechanics --
References --
3.1. Example Linear Heat Conduction Solutions --
3.2. Multidimensional PDEs, Separation of Variables --
3.3. Mathematical Foundation Essence for GWSN --
3.4. A Legacy FD Construction --
3.5. An FD Approximate Solution --
3.6. Lagrange Interpolation Polynomials --
3.7. Chapter Summary --
Exercises --
References --
4.1. A Steady Heat Conduction Example --
4.2. Weak Form Approximation, Error Extremization --
4.3. GWSw Discrete Implementation, FE Trial Space Basis --
4.4. Finite Element Matrix Statements --
4.5. Assembly of {WS}e to form Algebraic GWSh --
4.6. Solution Accuracy, Error Distribution --
4.7. Convergence, Boundary Heat Flux --
4.8. Chapter Summary --
Exercises --
Reference --
5.1. Introduction --
5.2. Steady Heat Transfer, n = 1 --
5.3. FE k = 1 Trial Space Basis Matrix Library --
5.4. Object-Oriented GWSh Programming --
5.5. Higher Completeness Degree Trial Space Bases --
5.6. Global Theory, Asymptotic Error Estimate --
5.7. Nonsmooth Data, Theory Generalization --
5.8. Temperature-Dependent Conductivity, Nonlinearity --
5.9. Static Condensation, p-Elements --
5.10. Chapter Summary --
Exercises --
Computer Labs --
References --
6.1. Introduction --
6.2. The Euler-Bernoulli Beam Equation --
6.3. Euler-Bernoulli Beam Theory GWSh Reformulation --
6.4. Timoshenko Beam Theory --
6.5. Mechanical Vibrations of a Beam --
6.6. Fluid Mechanics, Potential Flow --
6.7. Electromagnetic Plane Wave Propagation --
6.8. Convection-Radiation Finned Cylinder Heat Transfer --
6.9. Chapter Summary --
Exercises --
Computer Labs --
References --
7.1. Introduction --
7.2. Multidimensional FE Bases and DOF --
7.3. Multidimensional FE Operations for {Nk([zeta][alpha])} --
7.4. The NC k = 1,2 Basis FE Matrix Library --
7.5. NC Basis {WS}e Template, Accuracy, Convergence --
7.6. The Tensor Product Basis Element Family --
7.7. Gauss Numerical Quadrature, k = 1 TP Basis Library --
7.8. Convection-Radiation BC GWS Implementation --
7.9. Linear Basis GWSh Template Unification --
7.10. Accuracy, Convergence Revisited --
7.11. Chapter Summary --
Exercises --
Computer Labs --
References --
8.1. The FD-FE Correlation --
8.2. The FV-FE Correlation --
8.3. Chapter Summary --
Exercises --
9.1. Introduction --
9.2. The Galerkin Weak Statement --
9.3. GWSh Completion for Time Dependence --
9.4. GWSh + [theta]TS Algorithm Templates --
9.5. GWSh + [theta]TS Algorithm Asymptotic Error Estimates --
9.6. Performance Verification Test Cases --
9.7. Dispersive Error Characterization --
9.8. A Modified Galerkin Weak Statement --
9.9. Verification Problem Statements Revisited --
9.10. Unsteady Heat Conduction --
9.11. Chapter Summary --
Exercises --
Computer Labs --
References --
10.1. The Problem Statement --
10.2. GWSh + [theta]TS Formulation Reprise --
10.3. Matrix Library Additions, Templates --
10.4. mPDE Galerkin Weak Forms, Theoretical Analyses --
10.5. Verification, Benchmarking, and Validation --
10.6. Mass Transport, the Rotating Cone Verification --
10.7. The Gaussian Plume Benchmark --
10.8. Steady n-D Peclet Problem Verification --
10.9. Mass Transport, a Validated n = 3 Experiment --
10.10. Numerical Linear Algebra, Matrix Iteration --
10.11. Newton and AF TP Jacobian Templates --
10.12. Chapter Summary --
Exercises --
Computer Labs --
References --
11.1. Introduction --
11.2. Structural Mechanics --
11.3. Structural Mechanics, Virtual Work FE Implementation --
11.4. Plane Stress/Strain GWSh Implementation --
11.5. Plane Elasticity Computer Lab --
11.6. Fluid Mechanics, Incompressible-Thermal Flow --
11.7. Vorticity-Streamfunction GWSh + [theta]TS Algorithm --
11.8. An Isothermal INS Validation Experiment --
11.9. Multimode Convection Heat Transfer --
11.10. Mechanical Vibrations, Normal Mode GWSh --
11.11. Normal Modes of a Vibrating Membrane --
11.12. Multiphysics Solid-Fluid Mass Transport --
11.13. Chapter Summary --
Exercises --
Computer Labs --
References.

Uniting theory with hands-on computer practice, this book gives readers a firm appreciation of the error mechanisms and control that underlie discrete approximation implementations in the engineering sciences. Key features : illustrative examples include heat conduction, structural mechanics, mechanical vibrations, heat transfer with convection and radiation, fluid mechanics and heat and mass transport ; takes a cross-discipline continuum mechanics viewpoint ; includes Matlab toolbox and .m data files on a companion website, immediately enabling hands-on computing in all covered disciplines. It provides a holistic view of the topic from covering the different engineering problems that can be solved using finite element to how each particular method can be implemented on a computer. Computational aspects of the method are provided on a companion website facilitating engineering implementation in an easy way.

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