(written from a Production point of view)
The Akira-class is one of four ship classes that were created for the Battle of Sector 001 in Star Trek: First Contact. An early favorite of Alex Jaeger – who designed the class – and producers of the film alike, this design featured more prominently in the movie. "They initially planned to have at least one ship that we could get closer to camera," stated Jaeger. "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)
Along with the three other vessels of its ilk, the Akira-class was designed by Alex Jaeger at Industrial Light & Magic (ILM) in 1996. It was inspired by the Miranda-class and the Klingon Bird-of-Prey designs. Jaeger explained, "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: he meant the Miranda class]. 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!" The new class was named after the Japanese animated film Akira. (Star Trek Encyclopedia)
In a July 1999 partly published interview, conducted by Larry Nemecek, Alex Jaeger stated that he created the Akira as a sort of "carrier/gunship," 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.". (Star Trek: The Magazine Volume 1, Issue 3, p. 48) Visual inspection of the hull and design drawings show all fifteen, plus two more: twelve on the ship's weapons pod, one forward torpedo launcher under the deflector dish and four flanking torpedo launchers on the saucer, two on each side.
A decade later, in June 2009, Jaeger commented in far more detail about the overall design of the Akira-class on Doug Drexler's :
"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!"
As far as the heavy armament was 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."
Though Alex Jaeger was careful to make the Akira-class seem versatile, the process of designing the class was nonetheless influenced by First Contact featuring a heightened military "feel" to the Starfleet vessels. Jaeger continued,
"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'. :)"
Alex Jaeger's design of the Akira-class was quickly approved by the producers of First Contact. He proceeded to produce blueprints for CGI modelers Larry Tan and Paul Theren at ILM, who had to build and map the CGI model using Electric Image software for animation, and Form-Z software for the model. Orthographic views and wire meshes of their model have been published in Star Trek: The Magazine Volume 1, Issue 3 (pp. 49, 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 sixth season episode "Sacrifice of Angels". Due to software differences, the model had to be largely rebuilt in the LightWave 3D software, and was remapped at a higher, but still relatively low, resolution in the process. The model was completed early enough to be already showcased in the season five episode "Call to Arms".  Muse's model, as a variety of unnamed Akira-class starships, soldiered on to be featured in the Dominion War in nine more episodes of Deep Space Nine, including "Call to Arms" and the series' finale, "What You Leave Behind". Additionally, it made three appearances in Star Trek: Voyager, for the very last time featured in that series' finale, "Endgame".
In 2001, Digital Muse's model was refined by Adam Lebowitz and Robert Bonchune for representation as the USS Thunderchild (the same ship featured in First Contact) 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, conspicuously the Star Trek: Ships of the Line calendars or their book derivatives.
Nonetheless, the model received in 2014 its own entry in the Star Trek: The Official Starships Collection magazine partwork publication, followed in 2019 by an additional one in the "XL" (extra large) side collection of the publication. Despite its 2001 upgrade, the Collection project manager, Ben Robinson, decided that the Muse model needed an overhaul for that publication and had the model re-rendered (but not rebuilt) anew, a task he farmed out to outside contractor Fabio Passaro. 
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 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.
This design has been a notable source of inspiration for Doug Drexler's later design of Enterprise NX-01, the central ship of the fifth Star Trek series, of the same name.  In effect, the producers of the new show at first wanted to reuse the Akira-class without any changes, as a horrified Drexler recalled, "Believe it or not, the producers were of the mind to just use the Akira, lock stock and barrel." Production Designer Herman Zimmerman continued, "We did not use that ship, but we took ideas from it and from those ideas eventually – and this process took about four months, all week and weekend CGI work by [...] Doug Drexler – we finally came up with [the eventual] shape." (Behind the Scenes of Enterprise) In contrasting the two designs, Star Trek scenic artist Geoffrey Mandel observed, "The Akira is a rather ugly, bowlegged vessel from some angles, [but] the NX-01 is streamlined and elegant, and looks good from almost any angle."
Nevertheless, when fans were presented with the Enterprise NX-01 for the first time, they still were struck with the design resemblance of that ship with that of the Akira, and for a time the new ship was in certain fan circles endowed with the somewhat derogative sobriquet "Akiraprise". 
As a fan favorite, the design was slated for a 2009 release as the USS Thunderchild model kit release by Polar Lights, but was canceled later the following year without much further ado, despite being in an advanced state of development and having secured the input of Designer Alex Jaeger.  The company has later stated that they felt the ship was not the right choice as the debut outing in their new 1:1000 scaled product line, as it was not a "hero-ship", fearing it would not sell well enough to cover development costs; the sentiment was certainly not shared by fans. 
While several essentially illegal "garage kits" were released in the intervening years (including the 1:1400 scaled resin one from unlicensed "garage" model kit company Starcrafts Models, Jaeger is holding in the above featured picture ), the class had to wait for its "official" entrance into the physical realm until 2014 with the publication of the Official Starships Collection. Having been included in the very first batch of the collection as one of its very early releases, validated its status as a fan favorite.
- "Behind the Scenes: Designing the Akira Class", Larry Nemecek, Star Trek: The Magazine Volume 1, Issue 2, July 1999, pp. 48-51
- Star Trek: The Official Starships Collection
- Issue 12, January 2014
- Issue XL12, August 2019