Yu's areas of research include structural mechanics (composite/smart/multifunctional structures), micromechanics (composite/smart/multifunctional materials), multi-physics modeling, flexible multi-body dynamics, and multi-scale modeling.

He also is the chief technology officer of AnalySwift, a company that markets and licenses the technologies developed in Yu’s group.

His expertise is in structural mechanics and micromechanics of composite/smart materials. He has authored over 140 refereed technical articles and developed several computer codes which are being extensively used in many government labs, universities, research institutes and companies. His research has been funded by both federal agencies and private industry.