Description
Taylor & Francis Ltd Introductory Finite Element Method 2001 Edition by Chandrakant S. Desai, Tribikram Kundu
Although there are many books on the finite element method (FEM) on the market, very few present its basic formulation in a simple, unified manner. Furthermore, many of the available texts address either only structure-related problems or only fluid or heat-flow problems, and those that explore both do so at an advanced level.Introductory Finite Element Method examines both structural analysis and flow (heat and fluid) applications in a presentation specifically designed for upper-level undergraduate and beginning graduate students, both within and outside of the engineering disciplines. It includes a chapter on variational calculus, clearly presented to show how the functionals for structural analysis and flow problems are formulated. The authors provide both one- and two-dimensional finite element codes and a wide range of examples and exercises. The exercises include some simpler ones to solve by hand calculation-this allows readers to understand the theory and assimilate the details of the steps in formulating computer implementations of the method.Anyone interested in learning to solve boundary value problems numerically deserves a straightforward and practical introduction to the powerful FEM. Its clear, simplified presentation and attention to both flow and structural problems make Introductory Finite Element Method the ideal gateway to using the FEM in a variety of applications. INTRODUCTIONBasic Concept Process of DiscretizationPrinciples and LawsCause and Effect Review AssignmentsSTEPS IN THE FINITE ELEMENT METHODIntroductionGeneral IdeaIntroduction to Variational CalculusSummaryONE-DIMENSIONAL STRESS DEFORMATIONIntroductionExplanation of Global and Local CoordinatesLocal and Global Coordinate System for the One-Dimensional ProblemInterpolation FunctionsRelation Between Local and Global CoordinatesRequirements for Approximation FunctionsStress-Strain RelationPrinciple of Minimum Potential EnergyExpansion of TermsIntegrationDirect Stiffness MethodBoundary ConditionsStrains and StressesFormulation by Galerkin's MethodComputer ImplementationOther Procedures for FormulationComplementary Energy ApproachMixed ApproachBoundsAdvantages of the Finite Element MethodONE-DIMENSIONAL FLOWTheory and FormulationProblemsBibliographyONE-DIMENSIONAL TIME-DEPENDENT FLOW: Introduction to Uncoupled and Coupled ProblemsUncoupled CaseTime-Dependent ProblemsOne-Dimensional ConsolidationComputer CodeFINITE ELEMENT CODES: ONE AND TWO-DIMENSIONAL PROBLEMSOne-Dimensional CodePhilosophy of CodesStagesExplanation of Major Symbols and ArraysUser's Guide for Code DFT/C1DFETwo-Dimensional CodeUser's Guide for Plane-2DSample Problems for Plane-2DUser's Guide for Field-2DSample Problems for Field-2DBEAM BENDING AND BEAM COLUMNIntroductionBeam-ColumnOther Procedures for FormulationONE-DIMENSIONAL MASS TRANSPORTIntroductionFinite Element FormulationReferencesBibliographyONE-DIMENSIONAL STRESS WAVE PROPAGATIONIntroductionFinite Element FormulationConvection Parameter uxBibliographyTWO AND THREE DIMENSIONAL FORMULATIONSIntroductionTwo-Dimensional FormulationThree-Dimensional FormulationONE-DIMENSIONAL STRESS WAVE PROPAGATIONIntroductionFinite Element FormulationBoundary and Initial ConditionsBoundary ConditionsTWO-AND THREE-DIMENSIONAL FORMULATIONSIntroductionTwo-Dimensional FormulationTriangular ElementQuadrilateral ElementThree-Dimensional FormulationTetrahedron ElementBrick ElementTORSIONIntroductionFinite Element Formulation (Displacement Approach)Comparison of Numerical Predictions and Closed Form SolutionsStress ApproachReview and CommentsHybrid ApproachMixed ApproachStatic CondensationOTHER FIELD PROBLEMS: POTENTIAL, THERMAL, FLUID, AND ELECTRICAL FLOWIntroductionPotential FlowFinite Element FormulationStream Function FormulationThermal or Heat Flow ProblemSeepageElectromagnetic ProblemsComputer Code TWO-DIMENSIONAL STRESS-DEFORMATION ANALYSISIntroductionPlane Deformations Finite Element FormulationComputer CodeMULTICOMPONENT SYSTEMS: BUILDING FRAME AND FOUNDATIONIntroductionVarious ComponentsComputer CodeTransformation of CoordinatesAPPENDIX 1: Various Numerical Procedures: Solution to Beam Bending ProblemAPPENDIX 2: Solution of Simultaneous EquationsAPPENDIX 3 Computer CodesEach chapter also contains sections of problems and references