9404380 Chen/Zhou This research will focus on (1) the formulation of boundary integral equations and development of boundary element schemes and software for dynamic shell equations; (2) the analysis of vibration eigenfrequencies and damping rates of dynamic shell equations; (3) the study of qualitative stability properties of shells when damping is present; (4) structural shape control and optimization, for several thin or shallow circular cylindrical, conical, and spherical shell models. Shells are known to have advantageous structural properties. Under suitable design, even very thin shells can support large loads. They are therefore widely used in aircraft and ship structures where light weight is essential. In other cases, such as pressure-vessels, roofs and domes, the combined strength and enclosing properties of shells are utilized. Mathematically, shells are described by coupled systems of partial differential equations of higher order. This research is directed towards (1) computing the deformation and stress distribution of shells in aerospace, civil and maritime structures (in particular, with efficiency greatly surpassing the traditional finite element method); (2) providing feedback designs of control systems that can stabilize dynamic shell motion; (3) analyzing and simulating ``smart structure control'' of shells such as the automatic tuning of the radius of curvature of a spherical shell in a deformable mirror.
