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Part 3: FEM-Analysis of a IPE-Profile with MEANS V11____________________________ 34 Part 3: FEM-Analysis of a IPE-Profile with FEM-System MEANS V11 3.1 Exact Results For a cantilevered IPE Beam with a HE-B300 Profile according to DIN 1025, the greatest displacements as well as the greatest stresses are to be calculated. Input data: L = 5 600 mm F = 10 kN = 10 000 N E = 210 000 N / mm² I= we take the larger bending moment of inertia = 25 170 cm 4 Exact Displacments: Exact Stresses:

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Page 1: Part3:FEM-AnalysisofaIPE-Profilewith FEM-SystemMEANSV11 03 - FEM-Analysis with ME… · Part3:FEM-AnalysisofaIPE-ProfilewithMEANSV11_____36 3.2GenerateaTetrahedralMeshwithSTEP MeshGeneration

Part 3: FEM-Analysis of a IPE-Profile with MEANS V11____________________________34

Part 3: FEM-Analysis of a IPE-Profile withFEM-System MEANS V11

3.1 Exact ResultsFor a cantilevered IPE Beam with a HE-B300 Profile according to DIN 1025, thegreatest displacements as well as the greatest stresses are to be calculated.

Input data:L = 5 600 mmF = 10 kN = 10 000 NE = 210 000 N / mm²I = we take the larger bending moment of inertia = 25 170 cm4

Exact Displacments:

Exact Stresses:

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HE-B Profile according DIN 1025-2, Euronorm 53-62:

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3.2 Generate a Tetrahedral Mesh with STEP

Mesh Generation

Select the „Mesh Generation“ tab and „New“ to create a new FEM project.

Select "3D Tetrahedral Meshing with STL, STEP or IGES

A dialog box appears, showing the following CAD formats:

STL consists of a triangular outer shell for 3D mesh generationSTEP consists of solid elements and is the most suitable 3D formatIGES like STEP format but not so common anymore

Select the STEP file "300x300IPE.STP" from the FEM-Projects/New-Directory orwith "Browser" and click on the button "Start Mesh generator No. 2 with CAD File" todisplay it in the mesh generator.

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The STEP File can be seen in the mesh generator and can be rotated as required.

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Select the menu "Mesh" and "Meshing Options" and generate with the mesh density"moderate" and the menu "Generate Mesh" a FEM Model with tetrahedral elements.

The FEM Mesh now consists of 34 927 nodes and 122 329 tetrahedral elements.

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After Generation, the FEM Mesh named "test.fem" must be exported to MEANS V11.Select the "File" and "Export Mesh" menu and save the mesh "test.fem" into thedefault Debug / Mesh directory.

After exporting "test.fem", MEANS V11 will be started automatically and will firstcreate the surface model so that surfaces, edges and nodes for loads, boundaryconditions or element groups can be selected.

Set spatial rotation axis

Set the 3D Rotation with the View tab of XYZ Rotation to XZY Rotation so that theFEM model can be spatially rotated as in the CAD system.

This step is only done once unless you are working with different CAD systems.

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Load Case 1

Now rotate the model with the left and right mouse button (only for DX9) around theZ axis into the following view so that the front Surface 13 can be loaded in the Zdirection and the rear Surface 10 can be clamped.

Select the „Edit FEM Project“ tab and the drop-down menu "1. Point Load " to enterLoad Case 1.

In the next dialog box, enter Load Case 1 with the pro forma value "-1" because thenumber of nodes in area 13 is not yet known as well as the degree of freedom "in Z-direction" with the selection "Surface " and click on the button "Create load".

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Now create the Load with a Double-click on the Surface 13. This is displayed in the‘Select box and must be created there with "Create" as a Point Load with 86 nodes.

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Enter the load value

A point load with 86 node forces and the load value -1 has now been generated.Now multiply with menu "8. Editor " and „Load Factor" the loads with the value10 000 / 86 = 116.3.

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Create Boundary Conditions

Rotate to the rear view with the left and right mouse button (only for DX9) aroundthe Z axis to clamped Surface 10.

To clamp the model, select the "Edit FEM Project" tab and click on "Boundary-Conditions".

Select "Clamped fixed" and the Selection "Select Surfaces" and choose the "CreateRBs" button and double-click on the Surface 10 and confirm the entry in theSelectbox with "Create".

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Create Material Datas

Select the "Edit FEM Project" tab and the icon to enter the materialdata such as Young's modulus and Poisson Ratio where steel is always preset.

FEM Analysis

Following is a FEM Analysis, select the „FEM Analysis“ tab and "1. Statics" for eitherthe robust MEANS-Solver by Dr. Kühn or or the quick "Quick-Solver" to calculatethe deformations and stresses.

After the FEM Analysis you can start the Postprocessor for the result evaluation.

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Postprocessing

Select the tab "Postprocessing" and click on the Icon to start thePostprocessor for the result evaluation automatically.

The following Result Evaluations are available:

Contour of Displacments Nodal Stress Contour Element Stress Contour Reaction Forces Contour of Forces

With DirectX11 it is now possible to smoothly display a deformation or stressdistribution with over 50 million triangles, which was far from possible with theprevious DirectX9 version.

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max. Displacements in Z Direction = 11.258 mm

max. v.Mises Element Stresses = 33.479 N/mm²

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3.3 Generate Pentahedral Mesh with ExtrusionTo generate a pentahedral model of the IPE Profile, the Surface 13 of thetetrahedral surface model can be used as a template for a PEN6 extrusion.

Load the previous linear tetrahedral model "tet4.fem" with 34 927 nodes and122 329 TET4 elements and select the "Mesh generation" tab and menu "Meshfrom Surface“

Now carry out the following 3 steps:

Step 1:

Select "Step 1: Select Surface" and double-click on Surface 13. This is displayed inthe selectbox, where "Create" can be used to create the 2D mesh consisting ofTR3S triangles.

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Step 2+3:Now select again the menu "Mesh from Surface" as well as "Step 2: Create newMesh“ tol create a 2D mesh from Surface 13.Then start the node check and transform the mesh from the XZ plane to the XYplane with "Step 3: Transform XY Plane".

Refine

With the menu "Quad-Meshes, Refine, Delete.." and the Register "Refine" the 2Dmesh can be refined with menu "TRI3S -> 4x TRI3S".

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Extrude Pentahedron Model

The XY mesh can use as a template for Z Extrusion to a Pentahedron Model.Select menu „QUAD-Meshes, Refine, Delete“ and Register „Extrusion“ andgenerate a pentahedron mesh with Density in Z Direction= 40 andElevation in Z Direction = 5600.

Select menu „Create a 3D Mesh“ und create a Pentahedron Modell with 14352PEN6-Solids and 10520 Nodes.

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3.4 Create Hexahedral Mesh with ExtrusionTo create a hexahedron model with a 3D Extrusion, a 2D quad mesh in the XYplane is required as a template. For this purpose, the previous triangular mesh canbe converted into a quadrilateral mesh with the already known tetrahedral meshgenerator. To do this, select the "Mesh Generation" tab and "QUAD-Meshes, Refine,Delete" and the "Quadrangles" dialog box tab and click the "Generate QUAD meshwith NETGEN" button.

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The Steps are already known from tetrahedral meshing, one first sets with the menu"Mesh" and "Mesh Options" the mesh density "Very fine" and generates with"Generate Mesh" the quad mesh.

Finally, the quad mesh must be exported to the Debug/quadmesh directory insteadof the debug/mesh using the "File" and "Export Mesh" menus under the name"test.fem“.

Then, MEANS V11 is automatically started with the FEM Mesh of 1691 nodes and1450 QUA4S elements.

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Extrude Hexahedral Model

The „Mesh Generation“ tab and menu „QUAD-Mesh, Refine, Delete“ and Register„Extrusion“ now use the quad mesh as a template for hexahedral extrusion.

Enter the Density in Z direction = 40 and Elevation in Z direction = 5600and select menu "Create 3D Mesh" and generate a hexahedron model with 56 550HEX8 Solids and 67 640 nodes.

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max. Displacements in Z Direction = 11.199 mm

max. v.Mises-Stresses = 31.9 N/mm²