What are the forces acting on the doors of the main landing gear?
Aircraft have a maximum gear extension speed (V$_{LO}$, as in maximum landing gear operating speed), which is normally 1.6 times stall speed, so when the doors move, the dynamic pressure is rather low. Therefore, the forces during gear extension are not the only ones to check.

In cruise, suction on the gear doors might be the limiting factor for both stiffness and strength of the door itself, its latching mechanism or the hydraulic cylinder. I had the misfortune once to live through a flight test where part of one main door broke off in flight: It had no latch and was held shut by the hydraulic cylinder, which was mounted near the rear edge of the door. Suction and elasticity caused the forward edge to be pulled out into the airstream, so it soon became an air scoop, which only increased the pressure difference between the gear bay and the outside. Consequently, the door failed and needed to be redesigned, now with the actuation mechanism near the forward edge and an added latching mechanism.

If the door is aligned with the flight direction, make sure you look at the forces at maximum operating speed and maximum sideslip angle and treat the door like a regular fin. If the door opens into the airstream, use the proper drag coefficients for a flat plate and add some margin to account for oscillating flow separation. Make sure that the eigenfrequencies of the door or its operating mechanism are nowhere near the frequency of such flow patterns.

Here is a short note on the T-38 strut door loads which was written on occasion of the qualification of the T-38 as a chase plane for shuttle re-etries. The maximum gear extended speed had to be raised so the T-38 could follow the shuttle on the way down. Unfortunately, only measurements are given.