From what I understand, to complete R&D projects you need enough materials, which you can get from sending people out to the valley, and enough tech and contract points accumulated. I might be wrong though.
there are a number of factors, some projects only become available to be completed after certain points in the story. make sure your team has plenty of tech and your exploration has surveying, as those are the most relevant stats for what this build has to offer. other than that, you may try the maths background, since it gives you the most explicit information. tech background will also give a passive buff to the tech stat.