Is there an aerodynamic reason why the concept of biplane or triplane has been completely abandoned? Practically all planes were biplanes in WW1, and in WW2 practically none were developed.
Firstly, there are:
But the main reason is that they're inefficient, and don't really do much that a monoplane can't.
They produce a lot of drag compared to the amount of lift they produce, meaning they use a lot of fuel to travel the same distance. They have fairly poor visibility, which is usually considered a bad thing!
They do have a few advantages - they have a good roll rate, making them quite maneuverable, and they have a very low stall speed and can fly on little power, meaning they can fly slowly very well (where their increased drag doesn't make much difference: drag increases with the square of airspeed)
Overall, though, the above makes them suited only to aerobatics, which can also be performed by monoplanes. Advances in wing design and composite materials take away most of the advantages of a biplane for any other use: ie actually travelling (the main purpose of an aeroplane) and carrying a load.
Overall, then, they're more complex than a monoplane, less efficient, and aren't much more manoeuverable. They have more disadvantages than advantages.
Biplanes were popular in WWI not because of any inherent advantage, but simply because technology hadn't advanced far enough to allow any other options. Once the monoplane was properly developed, it allowed much higher speeds (450mph for a late WWII fighter, 300mph for an Early WWII fighter, compared to around 120 mph for a late WWI fighter). High speed fighters beat low speed fighters (at least before stealth technology and guided missiles)
There were a few leftover biplanes in WWII - The Fairey Swordfish torpedo bomber was one of the most widely used, as the low speed and good lift from the biplane design allowed it to carry a heavy torpedo, while the drag issues didn't matter at the slow speeds they needed to fly to be able to release the torpedo properly and on target. Others were the Gloster Gladiator (UK), Fiat CR.42 (Italy) and Polikarpov I-15 (Soviet Union) which achieved varying levels of success in the early stages, but were well and truly outclassed when facing even early-war monoplanes.
This answer on a similar question gives some useful context about the direct advantages and disadvantages. It doesn't directly explain why biplanes fell out of favour, but it may help understand my own answer here.
Well there ARE still biplanes produced today, either for nostalgic, or recreational reasons; they're just cool and harken back to classic age in aviation. Biplanes are still popular with aerobatic pilots today for their agility as well.
The chief reasons the biplane largely went the way of the dinosaur have to do primarily with aerodynamics and structural mechanics. When the cantilevered wing was perfected as well as construction from lightweight, high strength aluminum alloys which facilitated the monoplane, aircraft designers could take advantage of the superior characteristics of a monoplane, specifically much lower drag, allowing for higher speed flight. World War II accelerated this transition, as the need for higher performance military fighters made the monoplane extremely attractive to designers on both sides.
But a Stearman or a Pitts are still a hell of a lot of fun to fly.