A while back I found a quick way of killing the wither. Between that time and a week ago I have been simplifying the design and eliminating what was not needed from the original design. What I ended up with was what I call the "Wither Trench". The name comes from the massive amount of iron that is required for the anvils. Additionally because one must dig all the way down the bedrock.
How this works is the wither is spawned with bedrock surrounding it and anvils occupying the same space as the wither. The ai first trys to break the anvils. At that point the player starts placing anvils from above that land on the wither's head. It is possible to place the blocks fast enough that the wither can't keep up. The reason bedrock is needed is because it is the only block that can not be broken by the Wither. This process takes about 30 seconds. However I will note that just becuase the wither's life span is 30 seconds does not mean that the whole process is under a minute. One must acumalate roughly 990 iron ingots per wither. In order to do that one must (perferably) build the Iron trench, or better yet the Iron Foundry (both designed by Tango Tek).
Why would anyone ever want to waste that much iron on killing the wither.. you can just dig a 25-50 block 1 wide tunnel underground and kill him as he makes his way to you
The title says with no weapons and armor. I kow for a fact that there are more convenient ways. Take Panda4994's way of killing a wither for . It takes even less resources and even less time. I didn't dub this "The Wither Trench" just to slap a name on it. I named it that because of its need for a ton of iron. Additionally anyone with an Iron Foundry (or Iron Trench) will have loads of extra Iron. I do agree this is not a first resort when killing a wither. But keep in mind no armor and weapons are needed.