Department of Mechanical Engineering

Mechanics and Materials (MCEN30017)

Part 3: Finite Element Analysis (FEA)

Semester 1, 2020

Created by: Reza Yosri

Assignment

Objective:

This assignment is intended to teach students an analytical approach to solve 1D/2D structural problems as well as using a commercial FEA package for 3D problems. It is not expected that students will gain a mastery of these or any specific package, but rather, it is hoped that students will gain a deeper insight into the issues which underlies computer based analysis, irrespective of the specific software being used. Students will use SolidWorks computer software to complete this assignment.

Assessment:

This assignment is worth 25% of your total mark. The report is to be completed by each student individually and submitted online by 5 pm on Friday, 05 Jun 2020. The report should not exceed 20 pages, including figures, tables, and appendices.

Section 1: FEA analytical approach

Q1: Determine the forces and displacements of point 2 of the structure shown in Fig. 1. (15 Marks).

Figure 1

Q2: Consider the system of linear elastic springs shown in Fig. 2. Assemble the element equations to obtain the force-displacement relations for the entire system. Use the boundary conditions to write the condensed equations for the unknown displacements and forces. (15 Marks).

Figure 2

Section 2: Computer-based stress and strain analysis

Introduction:

Bunnings Warehouse is considering a new design for a tools table (Figure.1) and has a good mechanical performance against holding tools up to 300 [kg]. The tools are placed on top the table (the region illustrated in Figure.3) which is connected to four leg-support frames angled at 45 degrees with respect to the floor/ground and one leg-support frames connecting the angle legs. Before analysis, some pre-assumptions are made as follows:

1) The weight of the table can be neglected and thereby excluded from the analysis.

2) The table is made of steel alloy.

3) The table is assumed to be fixed to the ground.

4) The load is evenly distributed on the top plane.

5) Assume g=10 m/s2

Figure 3. Schematic of a shooping table and applied loads

Part 1:

Format your report such that each numbered item below is repeated in the report, followed by your answer.

1- Construct a model for the table in SolidWorks, and provide a figure showing the final mesh, loads and constraints. Please present your model as a third angle projection with all relevant dimensions. (5 marks)

2- State and justify how you have modelled the loads and constraints, along with any assumptions you have made regarding this. (10 marks)

3- Perform a mesh sensitivity analysis to find an appropriate global and local mesh size. Justify the reason behind choosing the local mesh location. Present a figure showing average stress vs. mesh size, as well as a figure showing computation time vs. mesh size. (10 marks)

Hint: You can choose convergence of total average von_Mises stress for the global mesh size sensitivity analysis and average of von-Mises stress at the location of local mesh for the local mesh sensitivity analysis.

4- Provide a von-Mises stress contour plot of the table. Identify the location and magnitude of the region of highest stress. (5 marks)

5- Propose methods for checking and validation of your FEA results (Only propose). (10 marks)

Part 2:

A second design is required for the table to withstand a load which is 50% higher than the one used in the initial design. The goal is to minimize the mass, keeping the maximum von-Mises stress less than its yield stress, and the maximum resultant displacement (URES) less than 1 mm.

6- How does an independent increase in fillet radius or beam thickness change the maximum stress and displacement in the body? Which parameter has a greater effect? (10 marks)

7- Find the optimal geometry by changing both the beam thickness (for all beams) and the fillet radius (for all fillets) according to the information in the table below. Plot the results on a URES displacement vs. beam thickness graph, with separate lines for each fillet radius value. Present the optimal geometry in a table, including the maximum stress and displacement. (15 marks)

Table.1. Fillet and beam thickness sizes for optimal design.

Minimum Step Size Maximum

Beam Thickness 10 [mm] 5 [mm] 30 [mm]

Fillet Radius 5 [mm] 5 [mm] 25 [mm]

8- Provide a von-Mises stress contour plot of the optimized table. Identify the location and magnitude of the region of the highest stress. (5 marks)

Figure 4. The 3D Isometric view, third-angle projections, and geometrical dimensions of the proposed tools table

Mechanics and Materials (MCEN30017)

Part 3: Finite Element Analysis (FEA)

Semester 1, 2020

Created by: Reza Yosri

Assignment

Objective:

This assignment is intended to teach students an analytical approach to solve 1D/2D structural problems as well as using a commercial FEA package for 3D problems. It is not expected that students will gain a mastery of these or any specific package, but rather, it is hoped that students will gain a deeper insight into the issues which underlies computer based analysis, irrespective of the specific software being used. Students will use SolidWorks computer software to complete this assignment.

Assessment:

This assignment is worth 25% of your total mark. The report is to be completed by each student individually and submitted online by 5 pm on Friday, 05 Jun 2020. The report should not exceed 20 pages, including figures, tables, and appendices.

Section 1: FEA analytical approach

Q1: Determine the forces and displacements of point 2 of the structure shown in Fig. 1. (15 Marks).

Figure 1

Q2: Consider the system of linear elastic springs shown in Fig. 2. Assemble the element equations to obtain the force-displacement relations for the entire system. Use the boundary conditions to write the condensed equations for the unknown displacements and forces. (15 Marks).

Figure 2

Section 2: Computer-based stress and strain analysis

Introduction:

Bunnings Warehouse is considering a new design for a tools table (Figure.1) and has a good mechanical performance against holding tools up to 300 [kg]. The tools are placed on top the table (the region illustrated in Figure.3) which is connected to four leg-support frames angled at 45 degrees with respect to the floor/ground and one leg-support frames connecting the angle legs. Before analysis, some pre-assumptions are made as follows:

1) The weight of the table can be neglected and thereby excluded from the analysis.

2) The table is made of steel alloy.

3) The table is assumed to be fixed to the ground.

4) The load is evenly distributed on the top plane.

5) Assume g=10 m/s2

Figure 3. Schematic of a shooping table and applied loads

Part 1:

Format your report such that each numbered item below is repeated in the report, followed by your answer.

1- Construct a model for the table in SolidWorks, and provide a figure showing the final mesh, loads and constraints. Please present your model as a third angle projection with all relevant dimensions. (5 marks)

2- State and justify how you have modelled the loads and constraints, along with any assumptions you have made regarding this. (10 marks)

3- Perform a mesh sensitivity analysis to find an appropriate global and local mesh size. Justify the reason behind choosing the local mesh location. Present a figure showing average stress vs. mesh size, as well as a figure showing computation time vs. mesh size. (10 marks)

Hint: You can choose convergence of total average von_Mises stress for the global mesh size sensitivity analysis and average of von-Mises stress at the location of local mesh for the local mesh sensitivity analysis.

4- Provide a von-Mises stress contour plot of the table. Identify the location and magnitude of the region of highest stress. (5 marks)

5- Propose methods for checking and validation of your FEA results (Only propose). (10 marks)

Part 2:

A second design is required for the table to withstand a load which is 50% higher than the one used in the initial design. The goal is to minimize the mass, keeping the maximum von-Mises stress less than its yield stress, and the maximum resultant displacement (URES) less than 1 mm.

6- How does an independent increase in fillet radius or beam thickness change the maximum stress and displacement in the body? Which parameter has a greater effect? (10 marks)

7- Find the optimal geometry by changing both the beam thickness (for all beams) and the fillet radius (for all fillets) according to the information in the table below. Plot the results on a URES displacement vs. beam thickness graph, with separate lines for each fillet radius value. Present the optimal geometry in a table, including the maximum stress and displacement. (15 marks)

Table.1. Fillet and beam thickness sizes for optimal design.

Minimum Step Size Maximum

Beam Thickness 10 [mm] 5 [mm] 30 [mm]

Fillet Radius 5 [mm] 5 [mm] 25 [mm]

8- Provide a von-Mises stress contour plot of the optimized table. Identify the location and magnitude of the region of the highest stress. (5 marks)

Figure 4. The 3D Isometric view, third-angle projections, and geometrical dimensions of the proposed tools table

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