Element distortion is usually indicative of significant problems due to excessive loading or over-constaints.
Firstly, check that you have activated Large Deflection. Go to Analysis Settings->Solver Controls->Large Deflection->ON.
If convergence still isn’t achieved, I would suggest the following :
1. Check the Force Convergence Graph to see the behavior of the solution.
Go to Solution->Solution Information->Solution Output-> Force Convergence.
2. Insert a Result Tracker to monitor Deformation or Contact information. Go to Solution->Solution Information-> Solution Information tab (ribbon)->Result Trackers.
3. Request Newton-Raphson residuals. Then, you will be able to see which areas have the highest residuals, and prevent convergence. These areas are usually those where loads or supports are applied or contact exists. Go to Solution->Solution Information->Newton-Raphson Residuals.
4. Read carefully the warnings and errors you get while you run the solution.
5. Go to Solution->Solution Information->Solution Output->Solver Output, and review the contact information. Check the initial information (gap, penetration etc) of the contact regions.
6. Ensure that you specify a sufficient number of maximum substeps, to allow the solver to apply smaller load increments, and therefore achieve convergence.
7. If multiple nonlinear features are present (material, contact), remove all except one and solve the model. If the solution to this simplified model is successful and as-expected, begin adding the other nonlinear features back into the model one at a time, to find out which one is causing the problem. You may need to check the material model or the Normal Stiffness Factor for contacts.
Generally regarding convergence, and mesh best practices there are plenty of videos on Youtube which you can advise.
These will provide you all the tools that you need.