In the end, both of my models have survived the 18kg of weight on top. my lightest model 15.15g became the 13th place out of all 142 models from 70 other groups. Being the top 10% in of nearly 600 other students.

plywood support structure

MEC 209 module students were assigned to design a safe and risky structure capable of supporting an 18kg payload of the dimensions in fig.1 on the plywood bench, and its bottom space needs to be able to let the metal block pass through. 

The support structure needs to be made from birch and poplar plywood; only PVA wood glue can be used as adhesives. Students are not allowed any kind of infiltration into the material except water.

The test model can only be laser cut by module staff; any models which are produced elsewhere will be disqualified from the test.

On the testing day, the payload will be mounted to a pulley system, so students can slowly drop it down to reduce the risks of injury.

Assumptions

Materials during simulations are linear materials, and forces are applied slowly and keep their initial direction in respect of time.
All plywood sheets have the same material properties, the initial imperfect physical condition of the board is negligible (no defects)  
PVA glue has the same material properties (shear strength, density, UTS, young’s modulus) as the FEA material set.

The geometry of plywood components laser cut is ideally the same as the design.
At least one surface is fixed to the bench in the X, Y, Z direction.
Components contacts do not change in time; in other words, contact areas does not deform and move when a load is applied. 
The structure has small deformations, so the materials do not become stiffer due to kinetic hardening.

Material properties and selection

According to the graph, the 0.2 offset strength of birch is 0.6Mpa higher than poplar; however, the strength per mass (offset strength/density) is 13Mpa/0.1g/cm^3 higher than birch. Therefore, when weight and strength need to be considered, poplar is a more efficient material than birch.

Fusion 360 FEA

Machine tolerance

The tolerance of laser cutter is around 0.3mm in small hole geometries.

Therefore, the contact detection tolerances during the simulation were set to 0.3mm. This can increase the reliability of simulation and reduce the chance of getting phantom stress. Fig and fig show the difference between the real and designed model.

Mesh

To produce the most accurate results, both 1% and 10% model-based mesh was generated, with advanced setting set to default values.

Boundary constraints

In the yellow parts shown in picture, the grain direction is horizontal to the force applied direction. Therefore, the zig-zag parts should be extruded separately and set materials to poplar across the grain while other parts remain poplar along the grain.

Static stress analysis

When force is applied in the Z direction, the legs on one side may move to the X direction due to slight friction and buckling as another side remains in the same position. Therefore, the constraints on one side have been fixed in all directions, and another side has been fixed in Z(vertical to the testing bench) and Y directions.

ITERATIONS

ITERATION 1

Semi-circle and triangles are often used in structural engineering to transform bending forces into compression forces. Therefore, triangular beams were used in the first design; finger joints were used to increase the area of glueing the base and the structure. However, bucking was not considered; the structural buckling results show that it will buckle to the side with only 1.93 of 180N load.

ITERATION 2

In the second design, struts were added to every leg with 3x3mm finger joints to increase the resistance to buckling. In addition, although the semi-circle design on the side remained, triangular-shaped holes were added to decrease the total weight of the design.

According to Fusion FEA, buckling is predicted when 12.32x 180N is loaded.

ITERATION 3

To reduce the weight, various shaped holes were added, including triangles, x shaped beams, circles, ellipses. A plywood plug was used to connect top bars with T beams on the side to increase the tightness of the connection. The bucking factor is 6.6 x 180N. The total weight is 37g

ITERATION 4

To form the risky model from the safe model, weight needs to be reduced to below 20g; therefore, poplar was used instead of birch and reduced the number of legs and top bars. Drawback: the force is against the grain direction, exceeding UTS across the grain wood.

ITERATION 5

The Middle bridge was removed to reduce weight, which means the two bridges on the side need to carry 90N each; therefore, a top bar was added with finger joins to form a T beam. In addition, the zig-zag shaped beams were added to increase the resistance to buckling to the x-direction.

The triangle beams on the side’s length were reduced; however, holes were removed to increase their volume loss during laser cutting and give it more stability

ITERATION 6

The zig-zag beams have been designed to separate parts to let 2/3 of the beam be manufactured along the grain, to resist buckling in the Y direction.

T beams can resist buckling in both X and Y directions; however, if zig-zag beams can restrain the buckling in either direction, then a T beam is not needed. Therefore, component E was added to restrain the buckling in the X-direction.

FEA RESULTS

From the FEA results above, it can be said that both safe and risky structures can support 18kg of weight, with the highest safety factor of 15 and lowest safety factor of 2 concentrated on the bridge on top of both 1% 10% mesh. However, compared to the result from the two models, the safe model is relatively the model with a higher safety factor. It has a buckling factor of 6.4 compared to 2.0. From the result above, a smaller percentage of model-based mesh size will give a more accurate result; however, it also increases the chance of getting phantom stress which may lead to confusion about whether the stress will be concentrated on that point. Although the result generated from a smaller mesh size is more accurate, bigger mesh size can give a more vision of where the stress will be located. In the risky model, the highest stress is concentrated on the bridge with 17Mpa with a maximum displacement of 1.002mm; as the safe model used the same design for its bridge on top, it is also where the highest stress is, with 15Mpa and displacement of 0.81mm.

DISCUSSION

In conclusion, by looking at the 1 and 10 % mesh, these models have a high chance of supporting 18kg load in real life. High levels of compression or tension are unlikely to be the reason for these wood structures to fail. When designing these structures, buckling resistance should be the focus, which means students need to use beams with a high second moment of area or add struts to distribute bending force into compression. Grain direction and beam orientation are also the key factors to withstand more weight, as it improves stiffness by at least 400% (according to the second moment of area formula for rectangular beams) Using the Fusion linear material, FEA gives users a brief understanding of where the stress will be concentrated and which direction the structure will buckle; hence, users can use this information to improve their designs. However, from the assumption listed on page 3, many factors were to be ignored. These factors need to be a parameter during the simulation to produce more accurate results, which requires more advanced software

cOMPETITION RESULTS

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