As shown in your photograph, the iPad chassis has been physically bent. The illustrated damage is not typical of bowing that might occur due to a swelling of a malfunctioning or defective iPad battery.
iPad models do not spontaneously “bend” or otherwise deform - unless they are exposed to environmental conditions significantly beyond their design limits - or the device has experienced mechanical trauma, such as being sat upon or similar. Damage of this type is also atypical of a device being carried along with other items in an unsuitable bag or backpack - where the iPad may be unintentionally exposed to unexpected forces.
If you have benefit of an active AppleCare+ Plan, you should be able to make a damage claim - for which a small excess/deductible fee will be charged. Otherwise, an out-of-warranty repair is typically charged at c.60% of the “as new” cost of the device. Either way, you can explore your available options at the Genius Bar of your local Apple Store or Apple Authorised Service Provider (AASP):
Genius Bar Reservation and Apple Support Options - Apple
Alternatively, you might consider using Apple’s mail-in repair service:
iPad Service & Repair - Apple Support
For qualifying devices, for both AppleCare+ and iPad repairs, in lieu of repairing your own iPad, Apple will usually offer a permanent exchange for a refurbished/renewed iPad of the same model and specification. Where available, the cost is the same.