University of chemical technology and metallurgy

1. University of chemical technology and metallurgy Department: Material science and engineering Discipline: Finite element materials Subject: Solid mechanical simulation By :Gergana Atanasova To: Prof. Iliev

2. Solid mechanics simulation

3. Its given: • The beam with dimensions 1200 x 40 x 100 mm • The beam material is homogeneous bilinear hardening • With yield strength 80 Mpa • And Poisson ratio 0.27 Determine the stress and strain state in varies tangent modulus.

4. There are 4 materials: Material 1: Ε = σ∕ε E =2500 Pa

5. Material 2: Ε = σ∕ε E =2ooo Pa

6. Material 3: Ε = σ∕ε E =1925 Pa

7. Material 4: Ε = σ∕ε E =2000Pa

8. Step 1 in working process • First build the beam from Ansys main menu-Modeling – Create – Areas – Rectangle – By dimensions We will work with meters and used dimensions for x= 0 to 1.2 and for y= 0 to o.1 m

9. Build Geometry

10. Step 2 in working process • Define the properties of materials from Ansys main menu – Preprocessor – Material Properties – Material Models Choose : Structural – Nonlinear – Inelastic – Rate independent – Isotropic hardening plasticity – Mises plasticity – Bilinear For PRXY we wrote Poisson’s ratio , for EX – Young’s modulus, for Yield Strr – Yield strength and for Tang Mod- the tangential model of elasticity.

11. Define material properties of material 1

12. Define material properties of material 2

13. Define material properties of materials 3

14. Define material properties of material 4

15. Define element type of materials

16. Sizing of the elements • Can mesh the element from Ansys main menu – Meshing – Mesh tool Choose Global and give Set to choose the distance between the nodes then give OK and Mesh.

17. Generate mesh

18. Apply constraints and Loads • Apply constraints from Ansys main menu- Solution- Define Loads- Apply- Structural- Displacement- On Nodes • Apply loads from Ansys main menu – Solution – Define Loads- Apply- Structural- Force/Moment – On Nodes Apply a vertical (FY) load of -2000N

20. Solve the system • Choose Ansys main menu – Solution – Solve – Current LS

21. Solution of material 1

22. Graphical representation • Choose Ansys main menu – General postproc – Plot Results – Contour Plot – Nodal Solution

24. Solution of material 2

25. Solution of material 3

27. Solution of material 4

29. Nodal solution • Choose Ansys main menu – General Postprocessor – Plot Results – Contour Plot – Nodal Solution

30. Von Mises state for material 2

32. Strain state for material 2

33. The strain state for material 3

34. Animation • Choose Menu – PlotCtrls – Animate- Deformed Shape

35. Animation Step 1

36. Animation Step 2

37. Animation Step 3

38. Questions • What is the mechanical behavior peculiarity of the material and where it is treated in the solution? • What element type was used? • What element options were used? • What real constant were used? • How many nodes and elements were created? • What is the % error for your solution?

39. Answers • Its uses the von Mises yield criteria coupled with an isotropic work hardening assumption. The material behavior is described by a bilinear stress-strain curve starting at the origin with positive stress and strain values. The initial slope of the curve is taken as the elastic modulus of the material. At the specified yield stress (C1), the curve continues along the second slope defined by the tangent modulus C2 (having the same units as the elastic modulus). The tangent modulus cannot be less than zero nor greater than the elastic . This material don’t have plastic deformation because the yield stress have very small value and the curve can’t continue to the second slope .

40. Answers 2. Solid 8 node 82 It provides more accurate results for mixed (quadrilateral-triangular) automatic meshes and can tolerate irregular shapes without as much loss of accuracy. The 8-node elements have compatible displacement shapes and are well suited to model curved boundaries. The 8-node element is defined by eight nodes having two degrees of freedom at each node: translations in the nodal x and y directions. The element may be used as a plane element or as an ax symmetric element. The element has plasticity, creep, swelling, stress stiffening, large deflection, and large strain capabilities. Various printout options are also available.

41. Answers 3. The element is meshed, supported on displacement stand and loaded. 4. For real constants are used only the area and the thickness. 5. There are 337 Nodes and 90 Elements