On bicubic B-spline method and its applications to structural dynamics

Abstract

The thesis presents a powerful, efficient and versatile bicubic B-spline method for structural dynamic analysis. A new form of B-spline basis set is first developed to accurately approximate beam functions under any boundary conditions. Using the new form of B-spline basis set, three conventional edge conditions (clamped, simply supported, and free) and the fourth guided edge condition can be accurately accommodated. Vibration analysis of orthotropic rectangular plate is performed using bicubic B-spline approximation technique based on classical thin plate theory. The present method is capable of solving vibration of plates under any combinations of the three classical edges and guided edge. Versatility, fast convergence, high accuracy and computation efficiency have been demonstrated. The present method is also extended to transient response analysis of plates to exploit high efficiency of the present method.