Using the input you've given I would simply take and divide the circular area into 4 triangular sections and map mesh those and sweep subsequently as Alex suggested. You can also map mesh spherical or ball shaped objects as well with hex elements although it's a little more complex.
A good way of meshing a sphere is to first split off a cylinder with domed ends by splitting straight through the centre of the sphere with a cylindrical face, the diameter should be between 1/3 and 1/2 that of the sphere. This part can be meshed as described above, then the remaining part can be swept if it is cut into 2 halves (cut in the direction of the cylinder axis, leaving c shaped parts) and sweeping around the circumferential direction.
Square in the middle. Four four-sided areas with 90deg arc on each side of the square. Largest angle will be 135deg, below limits for most 4node elements.
I am having trouble meshing a hollow sphere (2m diameter, thickness 35mm) that will form a hub for a turbine. There are 2 opposite flat faces that will form internal bolted flanges. There are also 3 equi spaced locations around the sphere where turbine blades will be attached on raised flat faces (modelled as a projected circle onto the external face of the sphere).
Does anyone have a good technique that will allow me to mesh this?