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Theoretical Manual

Vol. 1 Cellular Equations

    1. 1.1 Finite Equations (FE)

    2. 1.2 Thermal Eqs.

    3. 1.3 Solid Mechanics Eqs.

    4. 1.4 Thermo-Mechanics Eqs.

    5. 1.5 Energy Balance

    6. 1.6 Structural Eqs.

App. 1 Curvilinear Coordinates

Acronyms:

FE :Finite Eqs.

DE :Differential Eqs. CE :Cellular Eqs.

DOB :Data Object Base BC :Boundary Conditions

MBC :Mobile Boundary Conditions GE :Geometric Entities

OE :Output Entities

ZP :Tomographic Plane OP :Output Plane


Vol. 1 Cellular Equations


    1. 1.1 Finite Equations (FE)

      Differential Operators 1

      Numerical Stability 2

      Finite Operators 3

      FE Notation 4

      Continuity Eqs. 5

      Momentum Eqs. 6

      Summary of Eqs. 7

    2. 1.2 Thermal Eqs.

      Units SI 1

      Conversion Factors 2

      cases 3

      Differential Equations (DE) 4

      Cellular Equations (CE) 6

      CE Cartesian Axes 7

      Steady State 8

      Algo T Linear 9

      NonLin 11

      Critical time step 12

    3. 1.3 Solid Mechanics Eqs.

    4. Units SI 1

      Differential Equations 3

      Notation 4

      Variables 5

      DE Equilibrium Eqs. 6

      versus CE Eqs. 7

      Incompressibility 8

      Elasticity Eqs. 9

      CE Eqs. Linear 10

      Stress Signs 11

      Various Cases 12

      NonLinear 15

      displacements 16

      Algo M Linear 17

      Operations 18

      NonLinear 20

      Tensor Eqs. (TE) 21

      TE stress-strains 22

      Summary of finite strains 23

      Stress signs 24

      cases 25

      Plastic stress-strain curves, axial 26

      shear 27

    5. 1.4 Thermo-Mechanics Eqs.

      Overview1

      Thermal Strains2

      High Temperature Plasticity (HTP)3

      Algo H Strains4

      Balance5

    6. 1.5 Energy Balance

      Mechanical Linear1

      NonLin2

      Thermo-mechanical high Temp3

      cooling4

    7. 1.6 Structural Eqs. Bending

      Overview1

      Bending 1.5 Stiffness 2

      Loads3

      Integration4

      Solver5

      Algo B Notation XY6

      YZ7

      Rotations8

      Curvatures9

      Stresses, Linear10

      Bending NonLin11

      Material " 12

      Moment/curvature13

      Plastic hinges14

App. 1 Curvilinear Coordinates

  1. Input flag1

    SOlid Thermal

    Coordinate Systems4

    Cyl. Differential Eqs.5

    Geometry7

    Cellular Eqs.8

    Sph. Differential Eqs.12

    Geometry13

    Cellular Eqs.15

    SOlid Mechanical

    Cyl. Differential Eqs. 19

    Cellular Eqs.20

    STructures

    Fractal Geometry 22

    Conversion Factors25