Family structure is defined as the form the family takes. One structure, or form, might be many generations living under one roof. One structure is the U.S. Census Bureau definition of two or more people related by marriage, birth or adoption who live together. Another structure is the prevalent single parent living with one or more children. I don't find any research on technology's influence on structure as here defined, though technology's affect on function has been much talked about. On this line, technology has made the family unit of co-functioning individuals into a unit of independently functioning individuals. This has been shown to have detrimental effects as youthful individuals make unwise, coerced and high risk decisions when functioning independently.
The makeup of the family itself has changed. Look at the popular program Modern Family. There are three kinds of families emphasized: the "normal" mom and dad and three children; the divorced couple (which is a variation in that the husband is a much older man); the gay couple adopting children. The point of the program is that if people love each other no matter who is involved it can be called a family. Technology has opened up the gate for the various forms of families to be accepted.
The idea of family in the past was the family doing everything together. Eating, playing, worshipping--that was the way a family worked. You sat down at the table, ate, and talked about your day. Of course, that is an idea long gone. Occasionally, something happens like the Olympics and people, i.e., families begin to have a topic to talk about together. That makes the media worth it.
I won't say that the family structure has been changed but I do believe that family activities and quality time spent together has changed. I have a lot of online work to do, and my husband has many things they he enjoys doing online. Most of the time we're both plucking away at our laptops, and it's not that we're ignoring each other or anything. Technology is just incorporated into our psyche, we're still able to be online a lot and feel like we're spending time together.
I believe that family structure has changed because of the number of people using technology in the home. Parents may use the computer and iPad/Kindle, etc., devices, but young people listen to music, text and surf the web (along with Facebook, etc.) for much longer periods. In general, technology pulls family members away from family interactions because so much time is being spent with technology. Conversation is stilted at home, while it is more highly engaged with others outside of the home. This creates a chasm within the family unit because of increased time spent with technology.
I cannot say that technology has changed the family structure (in a universal way). While some families may have been pulled apart for one reason or another, the family structure may not have been strong to begin with (and the use of technology is an excuse). On the other hand, families with close-knit bonds are not (normally) affected by the inclusion of technology in the home.
I don't really think it has changed family structure in any serious way. Ever since television became popular people have been saying that it was going to hurt the family, but it doesn't really seem to have done that. Yes, we have many things to do that don't involve sitting in the living room talking, but I haven't seen that it's really a damaging thing.
It's true that divorce rates and single parent households are higher than they used to be. But can that be blamed on technology? I haven't seen convincing evidence to support such a claim.
The one change that might have happened (if you call this an aspect of family structure) is that families may be less tightly knit today. Because we have so much technology, we have many ways for family members to avoid interacting with one another. You can argue that technology does this and, thereby, makes people feel less close to one another.