The Finite Element Method Using MATLAB, Second Edition

Expanded to include a broader range of problems, this volume presents finite element approximation concepts, formulation, and programming in a format that streamlines the learning process by incorporating examples of computer programs for boundary value, initial value and structural controls.

Expanded to include a broader range of problems than the bestselling first edition, Finite Element Method Using MATLAB: Second Edition presents finite element approximation concepts, formulation, and programming in a format that effectively streamlines the learning process. It is written from a general engineering and mathematical perspective rather than that of a solid/structural mechanics basis.What's new in the Second Edition?Each chapter in the Second Edition now includes an overview that outlines the contents and purpose of each chapter. The authors have also added a new chapter of special topics in applications, including cracks, semi-infinite and infinite domains, buckling, and thermal stress. They discuss three different linearization techniques to solve nonlinear differential equations. Also included are new sections on shell formulations and MATLAB programs. These enhancements increase the book's already significant value both as a self-study text and a reference for practicing engineers and scientists.

INTRODUCTION TO MATLABFinite Element MethodOverview of the BookAbout MATLABVector and Matrix ManipulationsMatrix FunctionsData Analysis FunctionsTools for PolynomialsMaking Complex NumbersNonlinear Algebraic EquationsSolving Differential EquationsLoop and Logical StatementWriting Function SubroutinesFile ManipulationBasic Input-Output FunctionsPlotting ToolsAPPROXIMATION TECHNIQUESMethods of Weighted ResidualWeak FormulationPiecewise Continuous Trial FunctionGalerkin's Finite Element FormulationVariational MethodRayleigh-Ritz MethodRayleigh-Ritz Finite Element MethodFINITE ELEMENT PROGRAMMINGOverall Program StructureInput DataAssembly of Element Matrices and VectorsApplication of ConstraintsExample ProgramsDIRECT APPROACH WITH SPRING SYSTEMLinear SpringAxial MemberTorsional MemberOther SystemsLAPLACE'S AND POISSON'S EQUATIONSGoverning EquationLinear Triangular ElementBilinear Rectangular ElementBoundary IntegralTransient AnalysisTime Integration TechniqueAxisymmetric AnalysisThree-Dimensional AnalysisMATLAB Application to 2-D Steady State AnalysisMATLAB Application to Axisymmetric AnalysisMATLAB Application to Transient AnalysisMATLAB Application to 3-D Steady State AnalysisISOPARAMETRIC ELEMENTSOne-Dimensional ElementsQuadrilateral ElementsTriangular ElementsGauss QuadratureMATLAB Application to Gauss QuadratureMATLAB Application to Laplace EquationTRUSS STRUCTURESOne-Dimensional TrussPlane TrussSpace TrussMATLAB Application to Static AnalysisMATLAB Application to Eigenvalue AnalysisMATLAB Application to Transient AnalysisBEAM AND FRAME STRUCTURESEuler-Bernoulli BeamTimoshenko BeamBeam Elements with Only Displacement Degrees of FreedomMixed Beam ElementHybrid Beam ElementComposite BeamsTwo-Dimensional Frame ElementThree-Dimensional Frame ElementMATLAB Application to Static AnalysisMATLAB Application to Eigenvalue AnalysisMATLAB Application to Transient AnalysisMATLAB Application to Modal Analysis of Undamped SystemsMATLAB Applications to Modal Analysis of Damped SystemsMATLAB Applications to Frequency Response AnalysisELASTICITY PROBLEMPlane Stress and Plane StrainForce VectorEnergy MethodThree-Dimensional SolidAxisymmetric SolidDynamic AnalysisThermal StressMATLAB Application to 2-D Stress AnalysisMATLAB Application to Axisymmetric AnalysisMATLAB Application to 3-D Stress AnalysisPLATE AND SHELL STRUCTURESClassical Plate TheoryClassical Plate Bending ElementShear Deformable Plate ElementPlate Element with Displacement Degrees of FreedomMixed Plate ElementHybrid Plate ElementShell Made of Inplane and Bending ElementsShell Degenerated from 3-D SolidMATLAB Application to PlatesMATLAB Application to ShellsCONTROL OF FLEXIBLE STRUCTURESIntroductionStability TheoryStability of Multiple Degrees of Freedom SystemsAnalysis of a Second Order SystemState Space Form DescriptionTransfer Function AnalysisControl Law Design for State Space SystemsLinear Quadratic RegulatorModal Control for Second Order SystemsDynamic ObserverCompensator DesignOutput Feedback Design by Using Collocated Sensor/ActuatorSPECIAL TOPICSChapter OverviewStationary Singular ElementsQuarter-Point Singular ElementsMoving Singular ElementsSemi-Infinite ElementThermal Stress in Layered BeamsBuckling AnalysisNonlinear AnalysisMATLAB Application to Buckling ProblemMATLAB Application to Nonlinear ProblemREFERENCESAPPENDIX A: FEA MATLAB Function FilesAPPENDIX B: Examples of Pre- and Post-ProcessorINDEXNote: Each chapter also includes a Chapter Overview and Problems