Finite Element Modelling Techniques in MSC.NASTRAN and LSDYNA

PDF document. 171 pages.

ACKNOWLEDGEMENTS. 5

1    FINITE ELEMENT MODELLING TECHNIQUES AND MSC.NASTRAN CARDS COMMON TO ALL ANALYSES. 6

1.1    Input Deck .dat Format. 6

1.2    Grid Cards. 9

1.3    Finite Element Modelling Techniques. 10

1.3.1    Nature of the Finite Element Method. 10

1.3.2    Finite Element Displacement Interpolation Function, Output Stress Variation, and Corresponding Order of Error in Displacement and Stress. 11

1.3.2.1    One Dimensional Beam Finite Element 12

1.3.2.2    Two Dimensional Shell Elements (In-Plane Plane Stress or Plane Strain Membrane Stiffness) 14

1.3.2.3    Two Dimensional Shell Elements (Out of Plane Bending, Shear and Torsional Plate Stiffness) 17

1.3.3    Finite Element Modelling For Static Analyses. 21

1.3.3.1    Choice of Finite Element to Model the Load Path and Deformation. 21

1.3.3.2    Concepts of Stiffness. 21

1.3.4    Finite Element Modelling For Dynamic Analyses. 22

1.3.4.1    Mass and Stiffness Distribution. 22

1.3.4.2    Nonstructural Mass. 22

1.3.5    Modelling Mechanisms With Inertia Relief – Modelling Displacement Effects Due to Applied Loads On Systems in Conditionally Stable Equilibrium.. 24

1.3.6    Submodelling Techniques for Static Analysis 26

1.3.6.1    Submodelling by Substructuring – Static Condensation (Guyan Reduction) using Superelements. 26

1.3.6.2    Submodelling – Boundary Internal Force Method. 32

1.3.6.3    Submodelling – Boundary Internal Force Method of Substructure Isostatically Mounted Over Rest of Structure. 35

1.3.6.4    Boundary Enforced Displacement Method. 36

1.3.6.5    Numerical Example of Submodelling. 37

1.3.6.6    Static Submodelling Methods Summary. 42

1.3.7    Submodelling Techniques for Dynamic Analysis. 43

1.3.7.1    Submodelling by Substructuring - Static Condensation (Guyan Reduction) using Superelements. 43

1.3.7.2    Submodelling by Substructuring - Generalized Dynamic Reduction (GDR) using Superelements. 43

1.3.7.3    Submodelling by Substructuring - Component Mode Synthesis (CMS) using Superelements. 43

1.3.8    Modelling Flat Plates Using 2D Shells or 1D Grillages 44

1.3.9    Modelling Down-Stand Beams on Structural Floors, Pile Caps and Changes in Thickness of Plates. 44

1.3.10    Modelling Stiffened Plates. 44

1.3.11    Modelling Connections. 45

1.3.12    Modelling Spot Welds. 46

1.3.13    Modelling Bolts. 46

1.3.14    Modelling Applied Loads. 47

1.3.14.1    Applied Concentrated Loads on One Dimensional Elements. 47

1.3.14.2    Applied Face and Line Loads on Two and Three Dimensional Elements. 47

1.3.14.3    Applied Concentrated Loads on Two and Three Dimensional Elements  48

1.3.15    Modelling Support Conditions. 49

1.3.16    Primary and Secondary Component in Dynamic Analysis  50

1.3.17    Modelling Rigid Body Motion. 50

1.3.18    Meshing Strategies. 51

1.3.19    Mesh Transition Techniques. 52

1.3.19.1    Connecting 1D Elements to 2D Elements. 52

1.3.19.2    Connecting 2D Elements to 3D Elements. 53

Connecting a shell into solid by extending the shell one layer into the solid WILL introduce stress concentrations. The best method would thus be to use rigids or RSSCON to connect transverse to plane of shell. 54

1.3.19.3    Connecting 1D Elements to 3D Elements. 55

1.3.19.4    Fine to Coarse Mesh Transitions in Shell Meshes. 55

1.3.20    Stress Singularity (Artificial Stress Concentration) and St. Venant’s Principle in Linear and Nonlinear (Material) Analysis. 56

1.3.21    Modelling Preload (Prestress) 58

1.3.21.1    Temperature Load Method. 58

1.3.21.2    MPC Constraint Method. 58

1.3.21.3    GAP Element Method. 58

1.3.22    Modelling Symmetry. 59

1.3.23    Multi-Point Constraints (MPC) 60

1.3.24    Model Checkout 62

1.3.24.1    Grid Point Singularities (AUTOSPC, EPZERO, K6ROT, SNORM) 62

1.3.24.2    Mechanism Singularity of Stiffness Matrix (MAXRATIO, BAILOUT) 65

1.3.24.3    Grid Point Singularities (AUTOSPC, K6ROT) and Local and Global Mechanism Singularity (MAXRATIO, BAILOUT) for Linear, Nonlinear, Static and Dynamic Solutions. 67

1.3.24.4    Ill-Conditioning of Stiffness Matrix (EPSILON, Load and Reaction Discrepancy PRTRESLT) 68

1.3.24.5    Grid Point Weight Generator 70

1.3.24.6    Displacement Compatibility Check. 70

1.3.24.7    Element Quality Checks. 71

1.3.24.8    Maximum Values. 72

1.3.24.9    Element Orientation Check. 72

1.3.24.10    Duplicate Grid and Element Check. 72

1.3.24.11    Element Summary Table. 72

1.3.24.12    Unconstrained Equilibrium Check (Grounding Check) 73

1.3.24.13    Deformed Shape. 75

1.3.24.14    Massless Mechanisms. 75

1.3.25    Isoparametric Elements and Numerical Integration 76

1.3.26    Element and Nodal Stress Recovery 83

1.3.26.1    Stress Recovery at Gauss Points. 83

1.3.26.2    Extrapolation of Stress From Gauss Points to Element Grids. 84

1.3.26.3    (Transformation into Global Coordinates and) Averaging of the Elemental Grid Stresses to Yield the Grid Point Stresses. 85

1.3.26.4    Element Stress Recovery Procedures in MSC.NASTRAN.. 86

1.3.26.5    Grid Point Stresses in MSC.NASTRAN.. 90

1.3.27    Full Integration Quadrature, Reduced Integration Quadrature and Optimal Gauss Sampling Points. 92

1.3.28    Stress Interpretation. 94

1.3.28.1    State of Stress i.e. Global Coordinate Stress Tensors sxx , syy , szz , txy , tyz , tzx 95

1.3.28.2    Failure Criteria. 96

1.3.28.3    Deriving Forces (Moments, Shear, Torsion & Axial Force) from Stresses in Shells. 103

1.3.29    The Element Strain Energy Density. 104

1.3.30    Error Estimation. 106

1.3.30.1    GL, ML Analysis Error Estimation: h- or p- Refinement 106

1.3.30.2    GNL, MNL Analysis Error Estimation: h- or p- Refinement 106

1.3.30.3    Adaptive Analysis in MSC.NASTRAN with p-Elements. 107

1.3.30.4    Stress Discontinuity Error Estimator 110

1.3.30.5    Hand Verification: Deriving Stresses From Forces (Axial, Moments, Shear and Torsion) in Beam Elements and Stresses Due to External Loading of General Shell and Solid Continuum.. 113

1.4    Stiffness Element Cards. 116

1.4.1    Scalar CELAS Element 117

1.4.2    One-Dimensional Element Cards. 118

1.4.2.1    Axial and Torsional Stiffness CROD, CONROD, CTUBE Elements  118

1.4.2.2    CBAR Element 121

1.4.2.3    CBEAM Element 131

1.4.2.4    CBEND Element 132

1.4.3    Two-Dimensional Element Cards. 133

1.4.3.1    Transverse Bending, Transverse Shear and In-Plane Membrane (Plane Stress or Plane Strain) CQUAD4, CQUAD8, CTRIA3, CTRIA6 Elements. 133

1.4.3.2    In-Plane Shear and Extension CSHEAR Elements. 136

1.4.3.3    CRACK2D.. 136

1.4.4    Three-Dimensional Element Cards. 137

1.4.4.1    CHEXA8 or CHEXA20 Element 138

1.4.4.2    CPENTA6 or CPENTA15 Element 138

1.4.4.3    CTETRA4 or CTETRA10 Element 138

1.4.4.4    CRACK3D.. 138

1.5    Mass Element Cards. 139

1.6    Damping Element Cards. 141

1.6.1    Viscous Damping Elements CDAMP and CVISC.. 141

1.6.2    Structural Damping Elements. 141

1.7    General Nonlinear Excitation Frequency Dependent Spring And Linear Excitation Frequency Dependent Damper CBUSH (PBUSH and PBUSHT) Element. 142

1.8    One Dimensional Nonlinear Spring And Nonlinear Damper CBUSH1D (PBUSH1D) Element. 143

1.9    Material Cards. 144

1.9.1    Linear, Elastic, Isotropic Material Card for 1-D, 2-D and 3-D Elements MAT1. 144

1.9.2    Linear, Elastic, Anisotropic Elastic Material for Shell MAT2 and Solid Elements MAT9. 144

1.9.3    Linear, Elastic, Orthotropic Elastic Material for Shell Elements MAT8 and Solid Elements MAT9. 144

1.10    Rigid Element Cards. 145

1.11    Boundary Conditions. 148

1.11.1    Single Point Constraints (SPCs) 148

1.12    Linear Optimization SOL 200. 149

1.12.1    Objective Function and Constraints. 149

1.12.2    Design Variables and Constraints. 149

1.12.3    Optimization Control Parameters. 150

1.13    Computational Memory and Processing Power Demand. 150

2    LS-DYNA Cards. 151

2.1    Keyword Format of Input Deck.. 151

2.2    Output Cards. 151

2.2.1    ASCII Output Files. 151

2.2.2    BINARY Output Files. 152

2.3    Node Cards. 153

2.4    Stiffness Element Cards. 153

2.4.1    Spring Element Cards. 155

2.4.2    Beam Element Cards. 156

2.4.3    Shell (QUAD4, QUAD8, TRIA3, TRIA6) Element Cards  157

2.4.4    Solid (Brick, Wedge, Tetrahedral) Element Cards. 159

2.5    Mass and Inertia Element Cards. 162

2.6    Damping Cards. 163

2.7    Rigid Element Cards and Structural Internal Constraints. 164

2.7.1    Rigid Body. 164

2.7.1.1    Formulation of Rigid Body Joint 164

2.7.1.2    Rigid Body With Mass And Inertia Properties From A Set Of Nodes  164

2.7.1.3    Rigid Body With Mass And Inertia Properties From An Element 164

2.7.1.4    Extra Nodes on Rigid Bodies. 165

2.7.1.5    Merging Rigid Bodies. 165

2.7.2    Rigidwall 165

2.7.3    Constraints Between DOFs. 166

2.7.3.1    Interpolation Constraint 166

2.7.4    Global Restraints. 166

2.7.5    Welds and Rivets. 167

2.7.5.1    Generalized Spot Weld. 167

2.7.5.2    Generalized Fillet Weld. 167

2.7.5.3    Generalized Butt Weld. 167

2.7.5.4    Generalized Cross-Fillet Weld. 167

2.7.5.5    Generalized Combined Weld. 167

2.7.5.6    Mass-Less Spotweld. 167

2.7.5.7    Mass-Less Rivet 167

2.7.6    Concrete Rebars. 167

2.8    Boundary Conditions Cards. 168

2.8.1    Single Point Constraints SPCs. 168

2.8.2    Non-Reflecting Boundaries. 168

2.8.3    Contact Cards. 169

2.8.3.1    Rigidwall Contact 169

2.8.3.2    Surface To Surface Contact 169

2.8.3.3    Single Surface Contact 169

2.8.3.4    Nodes to Surface Contact 169

2.8.3.5    Eroding Contacts. 169

2.8.3.6    Tied Interface. 169

2.9    Restart Capabilities. 170

BIBLIOGRAPHY.. 171