  We prove partial regularity of stationary solutions and minimizers $u$ from a
set $\Omega\subset \mathbb R^n$ to a Riemannian manifold $N$, for the
functional $\int_\Omega F(x,u,|\nabla u|^2) dx$. The integrand $F$ is convex
and satisfies some ellipticity and boundedness assumptions. We also develop a
new monotonicity formula and an $\epsilon$-regularity theorem for such
stationary solutions with no restriction on their images. We then use the idea
of quantitative stratification to show that the k-th strata of the singular set
of such solutions are k-rectifiable.
