Pursuing PhD with no relevant coursework. Is self study and publications sufficient to show competence? I am from metallurgical engineering background. I am doing PhD in mechanical engineering. I have an average of B+ in my undergrad advanced mathematics and programming courses. I have no past exposure to Non linear mechanics and Finite Element Analysis. 

I am in the first semester of my PhD and I don't have the courses on Nonlinear mechanics and Finite element analysis being offered in my university for the next two years.

If I manage to self study the material from books and publish 2-3 papers on the application of the subjects in the next 5 years, will that be enough to show competency in the topics on my future career applications?
Reading "stuff" doesn't demonstrate competency, but publishing papers certainly does. If you can "use" something, and demonstrate it, then no one will really question whether you are capable of using it. 

Don't worry about it, other than to worry about the difficulty of getting yourself to the point where publishers are willing to accept your papers. The rest will follow naturally. 

I'll point out that professionals do this as a matter of course. If they need competency in a subject to publish, then they just do it. They wouldn't normally take a course (for credit) and wouldn't require any certification. Academic life is, among other things, a continuous path of study.