can I use object style designer in structured document (DITA)

We will need a little more information about how the Object Style Designer isn't working. I'll start with a guess...

Do the changes that you apply work as you apply them in the Object Style Designer, but then you save and close the DITA document. When the document is opened again your object style changes have been lost?

If this is what you are experiencing, that is to be expected. DITA is an XML format with its own set of rules. As with most XML document types very little formatting information is stored in the XML. You will find sizes or scaling for graphics and some text alignment features in tables, but that's all you get. Everything else is supplied by style sheets applied to the DITA XML. In FrameMaker the style sheet is the Element Definition Document (EDD) which, in conjunction with the Read/Write rules is what provides the formatting that you see in your DITA topics. In short, to make the changes you require may entail editing the EDD, Read/Write rules and the structured template.

If my guess was wrong, then we may still be able to help, but need a more detailed description of what isn't working as you expect.

~Ian