From the start, engineers noticed that the wings were not stiff enough to carry the outboard engines at cruising speed without warping and fluttering. To alleviate this, an underwing bulge called a plastron was developed to correct airflow problems around the engine pylons.
The reference used is not online, and having checked many high resolution images, I can't seem to spot that bulge/device.
It's also not mentioned as far as I checked in Scott E. Germain's Airbus A340. But I found the following paragraph on page 15, which may be of relation:
Attention also focused on drag reduction by achieving laminar flow across the wings, engine pylons, and structural intersections. This undisturbed flow requires perfectly smooth wings, aerodynamic surfaces, and fairings. Problems arise in the manufacturing process when surface irregularities lead to drag producing ridges and dimples in the surface of the aircraft. Airbus overcame these problems with automated component production, assembly line robots, and strict quality control measures.