(written from a Production point of view)
Responsible for the look of four new ship classes, introduced in Star Trek: First Contact and which included the Akira-class, was Alex Jaeger, who commented on the ships he designed for that movie, "The main reason they look really different is that from a distance, the producers wanted them to be completely new looks, because we introduced a new Enterprise in the film and didn't want it to get lost." An early favorite of creator and producers alike, it was decided that it was this design that would feature more prominently in the movie, "They initially planned to have at least one ship that we could get closer to camera. That was the Akira, so it got the most attention to detail. It wound up being almost as big as the Enterprise-E - the E is longer, but the saucer section is almost the same size." (Star Trek: The Magazine Volume 1, Issue 3, p. 48)
The Akira-class was one of those four new classes designed by Jaeger at Industrial Light & Magic (ILM) in 1996, and was inspired by the Miranda-class and the Klingon Bird-of-Prey designs, as was clarified by him, "I love the stance of the bird of Prey, so that was my main influence, to make a ship with an aggressive stance. I also wanted to make a carrier of sorts, more akin to the Galactica with fly-through shuttle hangers and I also loved the ‘roll bar’ weapons pod of the Excelsior [sic: what he meant was the Miranda]. Therefore the bay doors are both front and rear and the weapons pod on the boom. There was considerable thought put into the placement of elements. Since we were going to flesh out one of these background ships for a close up I knew it would be scrutinized….and it has :) For more than 13 years!" . It was named after the Japanese animated film Akira. (Star Trek Encyclopedia)
In parts of the July 1999 Larry Nemecek "Designing the Akira-class" interview that were published in Star Trek: The Magazine Volume 1, Issue 3, page 48, designer Alex Jaeger stated that he created the Akira as a sort of "carrier/gunship," armed with fifteen torpedo launchers, elaborating, "This was my gunship/battlecruiser/aircraft carrier. It has 15 torpedo launchers and two shuttlebays – one in front, with three doors, and one in the back. I really got into it with this one, with the whole idea that the front bay would be the launching bay, and then to return they'd come into the back, because they'd be protected by the rest of the ship.". Visual inspection of the hull and design drawings show all fifteen: ten on the ships weapons pod, one forward torpedo launcher over the deflector dish and also four flanking torpedo launchers on the saucer.
In June 2009 Jaeger commented in far more detail about the overall design of the Akira-class on the web blog of Doug Drexler,
"So the design started with the overall shape layout. Then in order to start the details I needed to set the scale, so I started with the bridge and worked out from there. Set nestled between the catamaran split secondary hulls the bridge is nicely protected. Just on either side of the bridge in a notch on top of the secondary hulls are the shield generators. This further protects the command unit of the ship since one of its duties is launching smaller craft, communication protection is a must. At the back of the bridge there are emissary docking hatches and just below that the circular hatch is the captain's lifeboat. The rear view at the back of the saucer is the main shuttle bay and shuttle control center. This area is also well protected tucked down between the hulls and below the weapons pod flanked by the Nacelles. This serves as a safe haven for the smaller craft in a fire fight and a calm entry point.
"Also in this protected center region are most of the sensor arrays for the transporters and communications with the remainder of the sensors atop the weapons pod. Moving forward the notch in the front of the saucer is the forward launch bay doors(3). This is for the fast exit of small craft into battle. There are extra shield generators on either side of this notch as this would be a target for enemy ships. Surrounding most of the saucer section is the phaser array strip. Also on the saucer there are flanking torpedo launchers. At the rear of the saucer are the impulse engines. Underneath is the deflector dish, 2 flanking phaser arrays and a forward facing torpedo launcher.
"You'll also notice that the Akira class utilizes the escape pods from the Sovereign-class, but the panel details more like the Galaxy-class. That's because I imagined this ship was commissioned right before the "E" and served as a testbed for the new escape pods. At the rear is the weapon's pod with spreads of both photon and quantum torpedo launchers. And of course the warp nacelles. This overall design makes for a much more narrow side profile and a more friendly crew environment as the engineering folks are no longer in "the bowels" of the ship :) Also the crew get a better view of their own ship as the split hull allows for more windows and a view of the bridge, something that's not very common in the previous ship designs. I’m sure there are flaws (like I've heard there are too many torpedo launchers etc…) as the time frame to do this plus all the other work I had to do was very short, so some of these details evolved during that process.
"The overall design didn’t change much during the approval process, in fact I believe the note was "excellent shape! must see detailed!". So here you go! The name Thunderchild was given to me by production and is named after the ship in H.G. Wells "[The] War of the Worlds". And Akira of course is for the awesome anime of the same name." 
As far as the heavy armament and overall "militaristic" look in general for the movie were concerned, Jaeger mused,
"As far as Torpedo launchers go, I believe it was 15 photon and 2 quantum for the total of 17, the Quantum ones would be the center 2 forward facing ones in the weapons pod. And to say a little something to the carrier aspect and "fighters". I hesitate to use the word "fighters" as I know that those are not only a thing of the past, but also a thing not Star Trek-ish. So the "small craft" would be more like runabouts and shuttles. But to be honest, when we were working on First Contact, there was a more military feel going on, especially with the design of the E and it's color scheme and panel details. The E is actually painted an almost sand color with dark brown-gray sections and harder angles.
"The movie it's self has a bit more military feel as well, so naturally when i was designing the Akira I was in military mode and since it was only going to show up in Earth's defense for the film I loaded it up with lots of defensive/offensive weapons. Also "Earth defense" was another task I had in mind with the carrier aspect. The "peace mission" wasn't on the forefront of my mind, but I can see how as a rescue ship the fly-through bays would work great for evacuation efforts in regions where transporters may not work. So having the ability to quick dock shuttles and get them back out asap would be a big plus. And the "weapons pod" could be converted into a science sensor array for "exploring strange new worlds". :) In design and in life it's always better to adaptable and perform multiple functions, that way you insure you'll be around a lot longer!" 
This design was further notable as an inspiration for Doug Drexler's later design of the Enterprise NX-01, the central ship of the fifth Star Trek series, of the same name. In defending the NX class, and contrasting the two designs, Star Trek scenic artist Geoffrey Mandel, stated that "while the Akira is a rather ugly, bowlegged vessel from some angles, the NX-01 is streamlined and elegant, and looks good from almost any angle. Having been around then, I also know that [the NX-class designers] Doug Drexler and John Eaves did exactly what the producers asked them to." 
Jaeger's design, being an early favorite of the producers, was quickly approved and Jaeger proceeded to produce blueprints for CGI modelers Larry Tan and Paul Theren at ILM, who had to build and map the CGI model. Jaeger has noted in regard to the software used that, "(...)ILM was using Electric Image for animation and Form-Z for the models of these ships back then."  Orthographic views and wire meshes of their model have been published in Star Trek: The Magazine Volume 1, Issue 3, page 49 and 51.
A year later ILM was requested by Paramount to hand over their models made for First Contact, amongst them the Akira, to Digital Muse in preparation for use in the upcoming Star Trek: Deep Space Nine episode "Sacrifice of Angels". Due to software differences, the model had to be largely rebuilt in LightWave 3D and was remapped at a higher resolution in the process, but was completed early enough to be already showcased in "Call to Arms".
In 2001 Digital Muse's model was refined by Adam Lebowitz and Robert Bonchune for representation as the USS Thunderchild in their reference book, Star Trek: Starship Spotter. Though a fan favorite, the model has, outside the movie references, hardly been featured in other licensed print publications, such as the Star Trek: Ships of the Line calendars or their book derivative.
While no physical studio models were constructed for on-screen use, a foam core camera test model used for First Contact or more likely the television shows, was sold as Lot 10184 in January 2009 in a It's A Wrap! sale and auction for US$86.85 and is one of the few physical representations of the class constructed by the production staff.