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Computer Aided Engineering - Tandem Bike
The Module

"We will learn about the fundamentals of the FEM to enable you using industry-standard software for your design projects. Understanding the fundamentals will help you avoid many pitfalls that FE users face when using commercial FE software."

The Task

The given task was to design a lightweight unisex two-seat tandem bicycle frame with a resonant frequency larger than 30Hz in order to avoid discomfort from whole-body vibrations while supporting an effective life of at least 10 years.

The Solution

The final results of the Aluminium Alloy bike were 47.8Hz, had a mass of 5.38kg, and a life cycle of more than 40 million years. The frame made of magnesium had very similar results apart from its mass, where it weighed 3.57kg.

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Boundary Conditions

Boundary conditions were added to the frame to come up with an optimal final result.


Two loads to the seats and two oscillating loads in each of the cranks. For the resonant frequency, it was set to 30 Hz because vibrations from the bike on the body can lead to muscular pain. For the fatigue analysis, a study had to be made which estimated a ten-year effective life by simulating one million loading cycles.


Several iterations were made to make the optimal design. From the initial design, a bar was added to increase stiffness to the frame so that the Von Mises stress would decrease causing frequency to increase. The sizes of the pipes were made smaller so that the bike would weigh less and increase its frequency.



Mesh Convergence

The areas with the highest stress concentrators were the fillets which connected the two semi-vertical posts to both cranks and the back seat connecting to the wheel. After a convergence study, the mesh size of the fillets became 7.5 mm with a mesh control size of 0.5mm, resulting in the design having 161.7MPa for Aluminium Alloy and 104MPa for Magnesium Alloy.

Static Study

Two static studies had to be performed on the bike as the loads on either side of both cranks had to be considered separately. The Von Mises Stress resulted in an overall displacement of 5.053mm and an equivalent strain of 1.074 x 10-3.

Other studies were obtained to get the best possible result, such as a Frequency and a Fatigue study. 

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