Getting rid of naked edges

ive been trying to make this structure thicker. when i offset the surface i get a lot of naked edges. is there an easier way to fix these edges rather than doing them on by one, as there are 500. if not,could i do this in another way?

It is difficult to diagnose problems without the geometry. You can upload a .3dm file using the vertical arrow icon above where you type a post.

It appears that you geometry has a very large number of individual surfaces even though it appears to be a relatively simple geometry. Did you create the geometry in Rhino or import it from elsewhere? Was it originally a mesh which you converted to NURBS using the MeshToNURB command? If so that command creates a separate surface for each mesh face which is usually not desirable.

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