The research in CRI Center aims at developing a unified analysis and design method called "Multiscale Isogeometric Optimal Design" through the integration of CAD, CAE, and design optimization in nano-continuum scales.

A finite element-based shape design optimization has been suffering difficulties in design parameterization. In the isogeometric approach, however, geometric properties are already embedded into NURBS basis and control points, whose perturbations provide smooth and continuous shape changes. Exact geometry can be used in both response and sensitivity analyses, where normal vector and curvature are continuous over the whole boundary so that enhanced shape sensitivity can be obtained. In the shape design optimization, design changes are implemented within the isogeometric framework, which maintains exact geometry without subsequent communication with CAD and is easily applicable for complicated multi-physics problems as well as the leading edge technologies such as MEMS, NT, and BT.

A multiscale optimal design method is developed considering both exact geometry in continuum scale and precise behavior in nano scale. Since the continuum shape function and the projection operator are mass or stiffness-weighted orthogonal, continuum and nano scale solutions can be obtained independently. The costly design sensitivity is efficiently obtained using a multiscale adjoint method. The reduced system in nano scale is efficiently solved using both generalized Langevin equation and lattice mechanics. Also, the reliability-based design optimization method can be utilized in considering the uncertainty of initial and boundary conditions in nano scale to enhance the quality of both response and design sensitivity in molecular dynamics.