You should first learn about breath control, since that's the most important part on keeping a consistent tone. The your singing will improve dramatically.
You may be confusing the abdominal muscles with the diaphragm, because from my experience you keep the abdomen open and consistent while pulling upwards with your diaphragm to push the air out.
The process goes something like this:
Breath in with the diaphragm; meaning you suck the air inwards with the diaphragm, not the upper chest. Your upper chest should remain relaxed while the diaphragm pulls the air inward. The bottom of your abdomen should expand for the most part.
Exhale by keeping the abdomen's shape consistent with step 1; while "pulling" (to me it feels that way) upwards with the diaphragm. While the air is let out your abdomen will slowly get smaller.
Doing breath control exercises is my best recommendation. A quick search on Breath Control yielded this page which has some good starting points:
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Something on that page really stood out to me:
Once you get it right, practice as often as possible, sitting, standing and whilst at work until you are breathing naturally from your abdomen.
After a while your natural breathing will even change for the better.