Analysis And Optimal Design Of Beams Using Radial Basis Function

Abstract

The application of Multiquadric Radial Basis Function (MQ RBF) in the analysis and optimal design of beams are addressed in this dissertation. For static analysis, a new Least Square Collocation (LSC) method is introduced. For buckling and vibration analysis, Rayleigh-Ritz analysis procedures are presented using MQ RBF basis function. Numerical results show that LSC can provide better results than the classical collocation method when the same number of collocation points are used. In vibration analysis, MQ RBF-based Rayleigh-Ritz can be used to calculate natural frequency accurately for several hundred modes. The important question of choosing shift parameters is discussed and a guide line for choosing this parameter is developed. Finally, the MQ RBF is also used for beam cross-section shape parameterization. Minimum weight design of beam under buckling and natural frequency constraints are also presented in this dissertation.