marvel - When and why did the shape of Captain America's shield change?

In his first appearances, Captain America's shield is an elongated triangle with three peaks at the top:

_{Joe Simon's first sketch of Captain America}

_{Cover of Captain America issue #1, 1941}

Now, of course, his shield is round.

_{Late 60's issue of Captain America}

When did this change occur, and why?

Answer

I cannot find any in-universe reason as to why this occurred, but out-of-universe I can.

Apparently the original sketch of Captain America came to the attention of Archie Comics (then MLJ Magazines) - they noticed there was a similarity between Captain America's shield and the chest detail of their own character The Shield (below).

Consequently, Captain America's shield was changed to the Kite design.

(Source: Cronin, Brian (2009). Was Superman a Spy?: And Other Comic Book Legends Revealed. Plume. pp. 135–136. ISBN 978-0-452-29532-2.)

When

The Marvel Wikia site refers to President F D Roosevelt presenting Captain America with this. This puts it between 1933 and 1945

From Captain America Vol 1 255: 'The Living Legend' in which

It details the origin of Captain America and focuses on his early adventures in 1941-42.

Why

As correctly pointed out in the question:

Rogers was originally issued a traditionally "kite" shaped shield made of mundane steel, as well as a sidearm.

(Source)

This new disc-shaped shield, however, had two main advantages:

1: It was better as an offensive weapon

He discovered:

that its excellent aerodynamic properties made it an effective offensive weapon

(Source)

2: It was made of a nearly indestructible alloy

Originally, Dr. Myron MacLain was attempting to perfect an indestructible alloy as strong as the legendary 'Adamantine', which Hercules' Golden Mace was made from. Dr. MacLain was hoping the alloy would provide a distinct advantage in the armor of American war machines, during World War II. The Doctor worked tirelessly, using the exotic Vibranium metal and an unknown substance. While the Doctor was asleep, as a result of his exhaustion, an unknown factor caused the metals he was working with to bond.

(Source)

An almost indestructible shield has obvious advantages over one made from 'mundane steel'!

Not only is the shield nearly indestructible though, it also has other useful properties which are inherent to Wakandan Vibranium, namely the ability to absorb vibratory energies in the vicinity.

The Wiki page on his shield explains the following (however bear in mind that it does not reference the said sources):

Some sources say that Dr. MacLain chose the discus shape because of its versatility, while other say that he used an existing cast designed for tank hatches.