Hi.

On the right side transformer, the lines of flux by the 'E' of the word CORE,  repel themselves as split.    Does this repulsion at that point 'E' shows in any different (form of magnetostriction?) , or affects anything ?

-Image borrowed from the web-

The purpose of shell type construction is to reduce the leakage flux in a transformer.

Leakage flux outside the core does not link any windings and is therefore not 'useful' flux.

Other ways of achieving this are

Making the transformer 'window' long and narrow - obviusly limited by the required space for the windings.

Arranging the primary and secondary wiondings concentrically

Sandwiching the primary and secondary windings

Overwinding the primary and secondary on a ring or toroidal core.