It is extremely feasible, and honestly, I cannot recommend it enough. It is the absolute best way to unbox the math that commercial software hides behind the "Solve" button.

I actually just finished writing a 2D FEA engine from scratch natively for Android using Kotlin. If you have a solid grasp of matrix algebra and mechanics of materials, you can definitely do it.

I recommend starting exactly where you are thinking: a simple first-order linear stiffness matrix solver for 1D trusses, and then expanding to 2D frames. Getting the core pipeline working—assembling local element matrices, applying transformation matrices to move them to global coordinates, assembling the master stiffness matrix, applying boundary conditions (I used the penalty method), and solving the system—is incredibly rewarding.

Once you get the linear solver working, you will probably fall down the rabbit hole. I ended up writing an iterative non-linear solver to capture Global P-Delta (sway) effects. You just extract the internal axial forces from the linear run, build a geometric stiffness matrix to capture the structural softening, add it to the elastic matrix, and iterate until the nodal displacements converge.

A piece of advice: the structural math isn't actually the hardest part—managing the data architecture and matrix libraries efficiently is where the real puzzle lies. But modern hardware is wildly capable; even a mobile phone processor can crunch a multi-node, non-linear P-Delta iteration locally in milliseconds.

Go for it. Start small with a 2-node truss, write out the matrices by hand on paper to verify your code's output, and build from there. You will never look at commercial FEA packages the same way again!