Development of differential quadrature methods and their applications to plane elasticity

Abstract

Three differential quadrature (DQ)-based numerical methods have been developed for plane elasticity in this thesis. Firstly, direct multi-domain DQ method, based on DQ and domain decomposition technique, is applied to plane elastic multi-material problems which are assembly of regular sub-domains. The technique of treating material discontinuity is proposed. Secondly, multi-domain DQ method in conjunction with coordinate transformation is exploited for the analysis of plane elastic heterogeneous solids. The above approaches are characterized by being first-order accurate at the interfaces of two different materials, but high-order accurate elsewhere. Finally, as the extension of DQ to the complex plane, a complex variable boundary collocation method is proposed based on Lagrange interpolation and complex variable theory. The new method features high accuracy by use of a small number of nodes as well as dimensionality advantage. Its application to two-dimensional potential problems and plane elastic problems are successful.