How do I prepare for a postdoc position with requirements in working with the theoretical basis of the software, which I have never worked with? I am 5th year PhD, about to submit my thesis in few months and defend in around September this year. My computational materials science PhD thesis involved using a commercial software (ABAQUS) to model a machining problem. I had to come up with material models and write python codes to build new geometries and stuff. I did decent in my PhD with 3 publications in decent journals and few in preparation.

Now, I learnt the theory behind the working of the commercial software while beginning my work. I did it entirely through self study. However, my PhD thesis did not involve any manipulation or working with the actual theoretical formulation of the software. So, I don't have any working experience with the formulation of (Finite element method) FEA form of a problem and implementing it. 

Now, all the jobs or postdoc positions in FEA application requires one to be able to solve a problem by hand, compare with analytical solutions, be proficient in implementing FEA weak forms into the commercial software...and so on. I don't know if I would be able to do it when required as I have not worked with it till now.

I don't know if I am even eligible to call myself a PhD as I feel unconfident/ashamed in my abilities to be called an expert in the numerical analysis field. What do I do?
Three quick thoughts:


Discuss it with your advisor. They might know of more suitable positions, or have field-specific advice.
During your PhD (and before), you should have improved the skill of learning things on your own. This will be useful in a postdoc or maybe an industrial position. Just don't be afraid to use it.
It seems you have some time left before the defense. Use it to start learning the software and skills you need. Consider starting a new research project where you'd have to use these methods (nothing like learning by doing!), or just reimplementing an existing paper.


Good luck!