Is there a design already that has honeycomb structure in a car door?

Yes, there are existing designs that incorporate honeycomb structures in car doors. While not extremely common in mass-produced vehicles, they are becoming increasingly popular, especially in high-end and performance cars, for the following reasons:

Lightweighting: Honeycomb structures offer a high strength-to-weight ratio, making them ideal for reducing the overall weight of the car door. This contributes to improved fuel efficiency and handling.

Crash Safety: The specific geometry of honeycomb structures allows them to absorb and distribute impact energy effectively during a collision, enhancing passenger safety.

Noise Reduction: Honeycomb cores can dampen vibrations and reduce noise transmission, leading to a quieter and more comfortable ride.

Examples:

Some high-end car manufacturers like Jaguar and Land Rover have utilized aluminum honeycomb cores in door panels and other structural components.
Motorsports vehicles, particularly in Formula 1 and other racing series, extensively use honeycomb composites in various parts of the car, including doors, due to their exceptional strength and lightweight properties.
Trend:

The use of honeycomb structures in car doors is likely to increase in the future as the automotive industry continues to pursue lightweighting and improved safety technologies. Advancements in materials and manufacturing techniques will further facilitate the integration of honeycomb structures into car designs.