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

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.