Many non-ME’s seem to think that there is a job description written somewhere that says, “Mechanical Engineer.” No such job exists. What there are is thousands of different jobs, each requiring a different skill set. Some are very math intensive, and others are not. But mostly these days we find a computer application to do the math for us.
The product my company specializes in requires more analysis than any other mechanical system I’ve ever worked on since graduating in 1979. (Gas turbines and jet engines.) Part of the reason for this is that very hot and rapidly rotating precision mechanisms cannot be designed with large safety factors. Every airplane flying is operating critical components at yield or above on every flight.
I’m a mechanical design engineer. I’m expected to do quick hand calculations to get me into the ball park. In other jobs, I’d just throw a standard safety factor on top of that and whip out a drawing. But in this job, I’ll then generate a quick design and build an ANSYS model to help me optimize it. The design then goes to our analysis group where it gets a very detailed analysis on much larger computers than the designers have access to. Several engineers may spend weeks doing that analysis. They recommend changes to optimize the design, and we then begin several iterations of that.
Before I ever got the design parameters, another analysis group evaluated the customer’s requirements and gave me my design objectives.
From what you say in your postings, I have a hunch that you might enjoy a job in one of these analysis groups.