Modelling And Programming Assignment

Rules

The last part of the ModPro course will finish with a case. You must receive a pass in order tofinish the ’Mechanics of Materials and Modelling and Programming 4’ course.

The case must be done individually.

The solution of the case must be submitted via Canvas 

The submission must include a pdf print of the fully completed ModPro4Case.docx file, and all code that was used to complete the case in a zip file.

You are allowed to use the provided Finite Element code. Any other submitted code must be written by yourself, and may not be copied from other students.

A full bonus point for the ’MoM + ModPro 4’ grade can be obtained by either:

1. completing the main assignment with your own Finite Element code (which must contain the solutions of sessions 3 to 6) or
2. submitting the solution of the Bonus assignment (given below).

The fraction of the full bonus point that will be awarded will depend on the quality of the submitted work. The bonus point cannot be used to compensate for a Mechanics of Materials grade that is lower than a 5.5.

On Tuesday afternoon, Thursday morning and Friday morning, there will be TA’s available during support sessions at the UT to answer your questions. It is not mandatory to be present at the support sessions.

Assignment

Use the FEM code to create a 2D frame of a transmission tower as depicted in Figure 1.

The designed frame must meet the following requirements:

• The minimum number of used nodes is 20.
• All nodes must be placed within a rectangular area with 0 ? x ? 5 and 0 ? y ? 10 (in meters).
• No nodes or elements may be placed inside (or cross) the rectangular area defined by 0 ? x < 1>

Figure 1: Example of a transmission tower.

• The structure should be connected to the ground exclusively at two nodes: node 1 located at coordinates (x = 1.5, y = 0.0) and node 2 located at coordinates (x = 3.5, y = 0.0). Both x- and y-displacements at nodes 1 and 2 must be constrained.
• Node 3 must be defined at coordinates (x = 0.0, y = 5.0), node 4 must be defined at coordinates (x = 5.0, y = 5.0), node 5 must be defifined at coordinates (x = 4.75, y = 6.5) and node 6 must be defifined at coordinates (x = 4.5, y = 8.0).
• Two separate loadcases3 must be defifined. In the fifirst load case, a load of -100 kN in the y-direction should be applied at nodes 3, 4, 5 and 6. In the second load case, a load of 100 kN in the x-direction should be applied at nodes 4, 5 and 6.
• The following requirements must be met:
  • In the first loadcase, the magnitude of the total displacement 4 of the nodes where the loads are applied (nodes 3, 4, 5 and 6) must not exceed 2 mm.
  • In the second loadcase, the magnitude of the total displacement4 of the nodes where the loads are applied (nodes 4, 5 and 6) must not exceed 8 mm.
  • In both loadcases, the maximum stress must not exceed the maximum allowable stress, using a safety factor of 2. Buckling does not have to be taken into account.
• The weight of the frame and gravity force (in negative y-direction) must be included in the calculation using the applyWeights() function.
• Only bar elements should be used in the model.
• The following material properties must be used:

  yield stress = 100 MPa
  density = 7800 kg/m3
  elasticity modulus = 210 GPa

• The cross sectional area of the elements can be freely chosen. At least two different material definitions with different cross-sectional areas must be used in the model. The ratio between the smallest and largest cross-sectional area must be at least 2.
• The total weight of the frame may not exceed 10 tonnes.

Ranking by weight

Challenge yourself to make the frame as light as you can. The best solutions will be published on Canvas and ranked by weight, such that you can see how your solution compares to others’ solutions, and have a look at what type of solutions others’ have created.

Bonus assignment <!--;p-->

Minimize the weight of the frame using the fmincon function, using at least 5 optimization variables (e.g. cross-section geometry or nodal coordinates).

Create inequality constraints for the stress levels and for the displacements of the loaded nodes. The constraint function should include both load cases.

Store the optimal values by copying them to your code or storing them in a .mat file using the save command.

Plot the deformations and the maximum shear stresses in the elements for both loadcases.

Fill in all questions in the assignment form.

Available code

The 2D Finite Element code and the checkModel2D function5 that have been distributed during the course can be used for this assignment. Furthermore, a create Frame script has been made for this assignment, see Figure 2. It is not mandatory to use the createFrame function, but it can be helpful for creating a frame definition.

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