On a round drumhead the stress is spread evenly when you hit it.
On a square drumhead about 70% of the stress is distributed into the corners, leading to a much weaker drum.
Since the drumhead should be round it follows that the rest of the drum tends to be round. Percussion instruments where the striking point is made out of different materials (such as laminated wood) tend to have other shapes since the stress is distributed differently in materials with a strong direction (like wood).
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