References:

When Non-Standard Missions Become Standard: Employing Field Artillery Brigades on the AirLand Battle – Future Battlefield
MAJ Donald C. McGraw, Jr. (December 1990) (2.2~ MB PDF)

He referenced:

Klein, Robert E. MAJ, "A Field Artillery Division," Field Artillery Journal, May-June 1974
(990~ kb PDF of Article)

Cathrae, William F. MAJ, "Artillery Divisions," Military Review, October 1946
(362~ kb PDF of Article)

Report of the General Board, US Forces, European Theater. "Organization and Equipment of Field Artillery Units." Study No. 59.
(2.4 MB PDF) (HTML Excerpt of Relevant Section)

The following books were consulted for information by me:

The Panzer Legions: A Guide to the German Army Tank Divisions of World War II and Their Commanders by Samuel W. Mitcham

Background of Artillery Divisions in World War II

The Soviets created their first Artillery Division in the Fall of 1942 out of eight Artillery Regiments. At first, they were used in a counterbattery role, but this later expanded to other missions such as long range fires, infantry support, destroying key enemy target areas or creating conditions vital for a breakthrough.

By 1944, the typical Soviet Artillery Division consisted of 6-7 Artillery Brigades, each one having up to four Artillery Regiments, for a total weapon count of between 248 and 356 guns/weapons. Despite their huge size, they were still very flexible – during the Artillery Preparation Fires of Operation Bagration, the Russians were able to change the fireplans of these divisions to respond to German counterbattery fire within five minutes of the Germans opening fire.

They were later in the war grouped into Breakthrough Artillery Corps, with a total weapon count of 1,000~ guns/weapons in the Corps.

On the German side, the 18^th Artillery Division was formed in October 1943 using the disbanded 18^th Panzer Division as a cadre, with the following units:

88^th Artillery Regiment (formerly 88^th Panzer Artillery Regiment of the 18^th Panzer Division)
288^th Artillery Regiment
388^th Artillery Regiment

It fought with 4^th Panzer Army and was ultimately disbanded in April 1944, with the HQ being used to form the HQ of the Grossdeutschland Panzer Corps, and the individual artillery regiments were used to form independent Army Artillery Brigades.

The Proposed Post-War US Army Artillery Division

In the Report of the General Board, US Forces, European Theater, "Organization and Equipment of Field Artillery Units," Study Number 59, the board recommended that for a corps consisting of three infantry divisions, an artillery division with the following composition should be organized:

1 x Divisional HQ
1 x Divisional HHC
1 x Divisional Band
1 x Ordnance Company, Medium Maintenance
1 x Quartermaster Detachment
1 x Signal Company
1 x Field Artillery Observation Battalion

4 x HHB, Artillery Group or Regiment

      3 x Field Artillery Battalions, 105mm Howitzer (Towed)
      3 x Field Artillery Battalions, 155mm Howitzer (Towed)
      2 x Field Artillery Battalions, 155mm Gun (Towed)
      1 x Field Artillery Battalion, 155mm Gun (Self-Propelled)
      3 x Field Artillery Battalions, 203mm Howitzer (Towed)
      1 x Field Artillery Battalion, 240mm Howitzer (Towed)

This was only a baseline. If the Corps had a different composition (number/type of divisions) than the baseline Corps, then the type of Artillery Battalions would change to meet the new composition.

The General Board then recommended that each Corps should be authorized an Artillery Division. Despite many senior artillery commanders advocating for this, the recommendation was never approved, due to the peacetime army being too small to support this level of organization, along with a feeling that with smaller units such as Regiments, the tactical and administrative problems encountered in WWII would be solved.

Artillery-75 – A 1968 Study by US Army Combat Developments Command (CDC)

In “A Field Artillery Division”, Field Artillery Journal (May-June 1974), Major Robert E. Klein went into some specifics on the Artillery-75 study by CDC, which looked into Field Artillery support in the 1970-1980 timeframe.

The study apparently posited an Artillery Division composed of around 20 FA Battalions commanded by four subordinate control HQs (Field Artillery Groups), organized like such: