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Development and Application of the Finite Element Method based on MatLab
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Development and Application of the Finite Element Method based on MatLab
von: Herbert Baaser
Springer-Verlag, 2010
ISBN: 9783642131530
70 Seiten, Download: 1552 KB
 
Format:  PDF
geeignet für: Apple iPad, Android Tablet PC's Online-Lesen PC, MAC, Laptop

Typ: B (paralleler Zugriff)

 

 
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Inhaltsverzeichnis

  Title Page 2  
  Preface 6  
  Contents 8  
  A Quick Start into DAEdalon 10  
     Download and Installation 10  
     Elastomechanical Example 10  
     Principle of Virtual Displacements 11  
     Discretization of Basic Equations 12  
     Run DAEdalon 14  
  Fundamentals of Solid (Continuum) Mechanics 19  
     Vector–, Matrix– and Tensor–Notation 19  
     Kinematics and Deformation Gradient F 20  
        Definitions 20  
        Properties and Derivatives of F 21  
        Implementation 23  
     Strain– and Stress–Tensors 23  
        A Selection 23  
        Invariants and Derivatives of Strain Tensors 24  
        Stress Representation — Voigt Notation 24  
     Rate of Strain Energy — Stress Power, Internal Energy Turn Over 26  
     Variational Principle and Weak Form 26  
     Discretization in Space 27  
        Preparation and Rearrangement of Equations 27  
        Linear Shape Functions 28  
        Derivatives of the Shape Functions 29  
        Volume Integration 31  
     General Treatment of Nonlinearities — Solution by Newton–Procedure 33  
        Linearization 34  
        Iteration 34  
  Constitutive Behavior 35  
     The Materials Point of View 35  
        Stress Response 35  
        The Material Modulus ID 35  
     Selected Constitutive Models 36  
        Hyperelasticity 36  
        Parameter Calibration 39  
        Inelastic Behavior 40  
  FEM Implementation within {\sc Matlab} 45  
     {\sc Matlab} Basics 45  
     Structure of DAEdalon 46  
     Preprocessing 47  
        Structure of Input-Files and Processing 47  
     Numerical Solution 47  
        Assembly Procedure — The Global System 47  
        {\sc Newton}–Iteration 48  
     Postprocessing 49  
        Mesh Representation, Loads and Boundary Conditions 49  
        Contour-Plots 49  
        GUI — Realization of a Graphical Environment 49  
     Writing Extensions for DAEdalon 50  
        Continuum Element elem4.m with 4–Nodes in Plane Strain 50  
        Formulation for Rotational Symmetry of elem4.m 51  
        EAS Expansion of elem4.m 52  
        General Truss Element elem10.m with 2 Nodes 55  
     Material Models 56  
  Applications and Examples 58  
     Crane Modeled by 2D–Trusses 58  
     Axisymmetric Applications 60  
     Crack Tip Simulation 61  
        K_I–Field 61  
        Analysis of Plastic Zone within K_I–Field 64  
  What Does DAEdalon Mean ?— Background for Computational System — and Greek Mythology 65  
  References 67  
  Index 69  


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