Linear Analysis of an Arch Dam

Transcription

1 Linear Analysis of an Arch Dam

2 Outline 1 Description 2 Finite Element Model 2.1 Coincidence Tolerance 2.2 Units 2.3 Import CAD File 2.4 Properties 2.5 Boundary Conditions 2.6 Loads 2.7 Meshing 3 Linear Static Analysis 3.1 Analysis Commands 3.2 Results Appendix A Additional information Linear Analysis of an Arch Dam 2/26

3 1 Description To prepare the model, we use the following procedure: Geometry and mesh Import geometry of the dam through a CAD file Make some adaptations to the geometry Introduce linear material properties for the concrete and the soil Define different mesh properties to the concrete part and bedrock foundation Loads and boundary conditions Define hydrostatic pressure Define self weight Define a structural interface in the contact face between the dam and the foundation Set rigid supports in the foundation Results Deformations Stresses Figure 1: Model of the dam Linear Analysis of an Arch Dam 3/26

4 The material properties assumed for the concrete and rock are listed in Table 1 Table 1: Material properties Linear elastic parameters Concrete Rock Elastic Modulus E Poisson s Ratio ν 2.5e e N/m 2 Mass Density ρ e-05 kg/m 3 No density will be assigned to the rock Linear Analysis of an Arch Dam 4/26

5 2 Finite Element Model 2.1 Coincidence Tolerance For the modelling session we start a new project [Fig. 2]. The default coincidence tolerance for the imported shapes/faces/edges is quite tight for this case. So, for the imported dam geometry we set this tolerance to 1e 04 [Fig. 3]. Main Menu File New [Fig. 2] Main menu Edit Project settings Advanced Coincidence tolerance [Fig. 3] Figure 2: New project dialog Figure 3: New project dialog Linear Analysis of an Arch Dam 5/26

6 2.2 Units We choose the default (SI) units: meter for the unit length and Newton for force [Fig. 5]. Geometry browser Reference system Units [Fig. 4] Property Panel [Fig. 5] Figure 4: Model windows Figure 5: Property panel - Units Linear Analysis of an Arch Dam 6/26

7 2.3 Import CAD File We import a CAD file *.step. The geometry consists of two bodies. We rename the shapes as Dam and Foundation. Main Menu File Import CAD file damstep.stp Main Menu Viewer Fit all [Fig. 6] Geometry browser Geometry Shapes Rename shape 1 Dam [Fig. 7] [Fig. 8] <Repeat to rename shape 2 as Foundation> <You can also press F2 to rename> Figure 6: Imported geometry Figure 7: Geometry browser Figure 8: Renamed shapes Linear Analysis of an Arch Dam 7/26

8 We will now edit the imported geometry to adapt it for the present case. We need to create a line to split the top surface of the foundation. This is done to be able to latter apply the hydrostatic pressure. Therefore, we start by adding two sheets at both sides of the concrete dam. Main Menu Geometry Create Add polygon sheet (2x) [Fig. 9] - [Fig. 11] Figure 9: Add sheet Figure 10: Add sheet Figure 11: Sheet 1 added to the geometry Linear Analysis of an Arch Dam 8/26

9 We imprint the two sheets on the foundation. Then we delete the shapes Sheet 1 and Sheet 2. We hide the Dam to see the imprint lines in the foundation [Fig. 13]. Main Menu Geometry Modify Imprint two bodies [Fig. 12] Model window Geometry Shapes Sheet 1 Right click < Repeat for shape Sheet 2> Remove Geometry browser Geometry Shapes Sheet 1 Right click Hide [Fig. 13] Figure 12: Imprint intersection Figure 13: Imprinted lines into foundation body Linear Analysis of an Arch Dam 9/26

10 We delete the unnecessary edges. The final view of the geometry of the rock body is shown in Figure 16. Model window Right click Remove [Fig. 14] [Fig. 15] Figure 14: Selected lines - Upper view Figure 15: Selected lines - Lower view Figure 16: Final geometry of the rock body Linear Analysis of an Arch Dam 10/26

11 2.4 Properties We assign properties to the foundation, the dam and the interface between the two. We start by assigning the properties to the foundation. We will use structural solid elements and the material properties are listed in Table 1. Main Menu Geometry Analysis Property assignments [Fig. 17] Property assignment Add new material [Fig. 18] [Fig. 19] Figure 17: Assign Foundation properties Figure 18: Add new material - Rock Figure 19: Edit material - Rock Linear Analysis of an Arch Dam 11/26

12 We continuing by assigning the properties to the dam. Main Menu Geometry Analysis Property assignments [Fig. 20] Property assignment Add new material [Fig. 21] [Fig. 22] Figure 20: Assign Dam properties Figure 21: Add new material - Concrete Figure 22: Edit material - Concrete Linear Analysis of an Arch Dam 12/26

13 We finally assign the properties of the interface to the bottom face of the dam in contact with the foundation [Fig. 24]. Main Menu Geometry Analysis Connection property assignments [Fig. 23] [Fig. 24] Figure 23: Assign Interface properties Figure 24: Interface Linear Analysis of an Arch Dam 13/26

14 We use a linear elastic surface interface. We add a new material [Fig. 25] - [Fig. 26] and a new geometry [Fig. 27] - [Fig. 28] for the interface and we fill in the properties. Property assignment Add new material [Fig. 25] [Fig. 26] Property assignment Add new geometry [Fig. 27] [Fig. 28] Figure 25: Add new material Figure 26: Material properties Figure 27: Add new geometry Figure 28: Edit geometry Linear Analysis of an Arch Dam 14/26

15 2.5 Boundary Conditions We attach supports to the foundation. The two YZ faces have fixed translations in the X-direction, the two XZ faces have fixed translations in the Y-direction and the bottom face XY face has fixed translations in the Z-direction. We start with the restraints in the X-direction to the lateral faces. Main Menu Geometry Modify Attach support [Fig. 29] [Fig. 30] Figure 29: Supports in X direction Figure 30: View of supported dam Linear Analysis of an Arch Dam 15/26

16 We apply the restraints in the Y-direction to the other lateral faces. Main Menu Geometry Modify Attach support [Fig. 31] [Fig. 32] Figure 31: Supports in Y direction Figure 32: View of supported dam Linear Analysis of an Arch Dam 16/26

17 Finally, we restraint the supports in the Z-direction to the bottom face of the foundation. Main Menu Geometry Modify Attach support [Fig. 33] [Fig. 34] Figure 33: Supports in Z direction Figure 34: View of supported dam Linear Analysis of an Arch Dam 17/26

18 2.6 Loads We define the self-weight [Fig. 35] and the hydrostatic pressure load [Fig. 36]. The variation of the hydrostatic pressure with the depth is automatically generated by the hydraulic head that, in this case, is 170 m. Main Menu Geometry Analysis Global load [Fig. 35] Main Menu Geometry Analysis Attach load [Fig. 36] [Fig. 37] Figure 35: Self-weight Figure 36: Hydrostatic pressure Figure 37: Representation hydrostatic pressure Linear Analysis of an Arch Dam 18/26

19 2.7 Meshing We set an element size of 50 m for the Foundation. Main Menu Geometry Analysis Set mesh properties [Fig. 38] [Fig. 39] Figure 38: Mesh properties Figure 39: Seeding preview Linear Analysis of an Arch Dam 19/26

20 We set an element size of 10 m for the Dam. Main Menu Geometry Analysis Set mesh properties [Fig. 40] [Fig. 41] Figure 40: Mesh properties Figure 41: Seeding preview Linear Analysis of an Arch Dam 20/26

21 We generate the mesh. Main Menu Geometry Analysis Generate mesh [Fig. 42] [Fig. 43] Figure 42: Mesh browser Figure 43: View of the mesh Linear Analysis of an Arch Dam 21/26

22 3 Linear Static Analysis 3.1 Analysis Commands We add a new analysis block and we choose to perform a Structural linear static analysis. Main Menu Analysis Add Analysis [Fig. 44] Analysis browser Analysis1 Add command Structural linear static [Fig. 45] [Fig. 46] Analysis browser Analysis1 Run analysis Figure 44: Analysis window Figure 45: Add command Figure 46: Analysis tree Linear Analysis of an Arch Dam 22/26

23 3.2 Results We display the deformed shape and the contour plot of total displacements for the self weight (SW) and for the hydrostatic pressure. Main menu Viewer View points Isometric view 1 Main menu Viewer Fit all Results browser SW Output linear static analysis Nodal results Total displacements DtXYZ [Fig. 47] [Fig. 48] <Repeat for the Case Hydrostatic pressure > [Fig. 49] Figure 47: Results browser Figure 48: Total displacement DtXYZ - SW Figure 49: Total displacement DtXYZ - Hydrostatic pressure Linear Analysis of an Arch Dam 23/26

24 We now display the contour plot of stresses SXX for the hydrostatic pressure. Results browser SW Output linear static analysis Element results Cauchy Total Stresses SXX [Fig. 50] [Fig. 51] Figure 50: Results browser Figure 51: Cauchy total stresses SXX - Hydrostatic pressure Linear Analysis of an Arch Dam 24/26

25 Appendix A Additional information Folder: Tutorials/LinearDam Number of elements Keywords: analys: linsta. constr: suppor. elemen: solid te12l tp18l py15l hx24l. load: weight hydro. materi: elasti isotro soil interf. option: direct units. post: binary ndiana. pre: dianai. result: displa green cauchy strain stress total. Linear Analysis of an Arch Dam 25/26

26 DIANA FEA BV Delftechpark 19a 2628 XJ Delft The Netherlands T +31 (0) F +31 (0) DIANA FEA BV Vlamoven TN Arnhem The Netherlands T +31 (0) F +31 (0)