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1 Dr. Faeq M. Shaikh Seattle, Washington, USA (Seattle is home of Boeing Jets) 1

2 Pre Requisites for Today s Seminar Basic understanding of Finite Element Analysis Working Knowledge of Laminate Plate Theory 2

3 NASTRAN & PATRAN are products of McNeal Schwendler Corporation (MSC) PATRAN = Pre & Post Processor NASTRAN (NASA Structural Analysis)= Solver 3

4 PATRAN 4

5 Summary of PATRAN Modeling Capabilities Line (Bar) Elements: 5

6 Summary of PATRAN Modeling Capabilities Line (Beam) Elements: 6

7 Summary of PATRAN Modeling Capabilities Surface (Shell) Elements: 7

8 Summary of PATRAN Modeling Capabilities Surface (Shell) Elements: 8

9 Summary of PATRAN Modeling Capabilities Solid Elements: 9

10 Summary of PATRAN Results Deformation Animate Deformation 10

11 Summary of PATRAN Results Deformation 11

12 Summary of PATRAN Results Stresses 12

13 Process of Finite Element Analysis: Set database units (British or Metric) Define or Import (from CAD tools) Geometry Create finite element mesh Define materials (isotropic, orthotropic, anisotropic) Define laminate / sandwich materials Apply materials to element properties Apply loads and boundary conditions Perform analysis (Linear, Non Linear, Buckling, etc) Access Results Create fringe and deformation plots 13

14 Shell (Plate) vs. Solid Elements Mesh Using Shell Elements: Can model bending. Usually much smaller model size Elements are created on a surface (area) Limited thruthickness results Mesh Using Solid Elements: Do not have bending capability Much larger model size Elements are created on a volume Thru thickness result capabilities 14

15 Examples of Models with Shell & Solid Elements: 15

16 Composites can be modeled using both shell and solid elements. Choice depends on: Computing power (large vs. small models) What kind of results are required (2D vs. 3D state of stress in plane vs. thru thickness) Importance of interfaces (fitting attachments, etc.) IF 16

17 2D vs. 3D State of Stress 17

18 Composites can also be modeled as a hybrid of shell and solid elements Model facesheet as shell elements Model core as solid elements Model facesheet as shell elements 18

19 Materials Isotropic: Composite Analysis 3D Constitutive Relationship Plane Stress Constitutive Relationship 19

20 Materials Orthotropic: Composite Analysis MAT3 Orthotropic material is defined for Solid elements. MAT8 orthotropic material is defined for shell elements. 20

21 Materials Anisotropic: Composite Analysis The MAT9 is used to define 3D orthotropic constitutive stress strain relation using the anisotropic material matrix. The MAT2 is used to define 2D anisotropic constitutive stress-strain relationship using the anisotropic material matrix. 21

22 Laminate Plate Theory Overview The laminate consists of perfectly bonded laminae. The bonds are infinitesimally thin and nonsheardeformable; i.e., displacements are continuous across laminae boundaries so that no lamina can slip relative to another. Each of the lamina is in a state of plane stress. 22

23 Modeling composites: Composite Analysis Laminated composites are a "stack" of laminae with different orientations 23

24 Modeling composites what do we need? Lamina properties (E, G, etc) Orientation Thickness Stacking sequence 24

25 Modeling composites what do we need? Data Recovery Displacements Forces Ply Stresses Ply Strains Margin of Safety / Failure Indices FI < 1, the lamina is assumed safe. FI > 1, the lamina is assumed to have failed. 25

26 Failure Indices: Composite Analysis Isotropic Materials: Strength is independent of orientation of body under load Laminated Composites (orthotropic ): Strength is a function of body orientation relative to load. Minimum Allowables Required: Tensile stress/strain in material 1 & 2 directions Compressive stress/strain in material 1 & 2 directions Shear stress/strain in principal material direction. 26

27 Failure Theories in NASTRAN / PATRAN: 27

28 Start a project: 28

29 PATRAN Modeling Window 29

30 PATRAN Application Form 30

31 Creating Geometry: 1 Composite Analysis

32 Creating Mesh:

33 Materials: 1 Creating Uni Directional Tape (for 2D Shell Elms)

34 Materials: 1 Creating Honeycomb Core (for 2D Shell Elms)

35 Materials: 1 2 Creating Honeycomb Core (for 2D Shell Elms)

36 Materials: Laminate Constants (for 2D Shell Elms)

37 Element vs. Material Coordinate System: For 2D shell elements, ECS from Node 1 to Node 2 Element Forces come out in Element Coordinate Sys MCS defines the 0 deg fiber direction Ply Strains & Stresses come out in ply fiber directions / Material Coordinate System 37

38 Properties:

39 Geometry: 1. Create Points 2. Create Surface 3. Create solid (for 3D analysis) 39

40 FEMs: 1. Create Nodes & Elements (2D) 2. Create solids (for 3D analysis) 40

41 Apply Loads:

42 Apply Boundary Conditions:

43 Analyze:

44 3D Modeling: 44

45 3D Modeling: Facesheets modeled with 2D Shell Elements Honeycomb Core modeled with 3D Solid Elements 45

46 3D Anisotropic Material: Composite Analysis 46

47 Results Deformation plot: Composite Analysis

48 Ply 1 (bottom) x direction strain fringe plot: 1 2 Compressive strain

49 Ply 13 (top) x direction strain fringe plot: Tensile strain 4 49

50 Printed Output File Displacements: 50

51 Printed Output File Element Forces (2D Shell): 51

52 Printed Output File Reactions at Support: 52

53 Printed Output File Ply Strains (2D Shell): 53

54 Printed Output File Stresses (3D Solid): 54

55 Word of Caution Use of Offsets: Composite Analysis Modeling with 2D shell elements Meshing surface is the bottom surface How do we model varying thicknesses? 55

56 Word of Caution Offsets: Composite Analysis 56

57 Thank You. For questions, please contact me at: 57

*Currently employed at UTAS, work for this paper was carried out while the author was formerly employed at MSC Software.

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