I'm having difficulty turning an array of rectangular shapes into a circle. For simplicity's sake I've just used a rectangle in the below images.

1. I've tried sub-dividing the shape and applying the smooth modifier. Then tweaking various parameters in those modifiers. I also tried applying the array as well as moving the modifiers order in the stack.
2. I've tried using an addon called LoopTools, this either looked the same or the shape was vastly warped.

The basic rectangle shape.

The basic rectangle shape in an array.

The basic rectangle shape with lots of sub-divisions.

The sub-divided rectangle shape with the array applied and the smooth modifier added.

The sub-divided rectangle shape with the array applied and the smooth modifier added, but from above.

I'm having difficulty turning an array of rectangular shapes into a circle. For simplicity's sake I've just used a rectangle in the below images.

1. I've tried sub-dividing the shape and applying the smooth modifier. Then tweaking various parameters in those modifiers. I also tried applying the array as well as moving the modifiers order in the stack.
2. I've tried using an addon called LoopTools, this either looked the same or the shape was vastly warped.

The basic rectangle shape.

The basic rectangle shape in an array.

The basic rectangle shape with lots of sub-divisions.

The sub-divided rectangle shape with the array applied and the smooth modifier added.

The sub-divided rectangle shape with the array applied and the smooth modifier added, but from above.

=== UPDATE ===

Good suggestions. I've now tried just an array with the simple deform modifier but the result looks almost identical.

Bottom Circle is the original array with an empty. Top Circle is the array with the simple deform.

I need to make my rectangular array more circular like the below image. Which is just a squashed cylinder.