This work is concerned with three topics: error estimation, data smoothing process and the structural shape optimization design and analysis. In particular, the superconvergent stress recovery technique, the dual kriging B-spline curve and surface fittings, the development and the implementation of a novel node-based numerical shape optimization package are addressed.

The new node-based shape optimization method is based on the consideration that the critical stress and displacement constraints are generally located along or near the structural boundary. The method puts the maximum weights on the selected boundary nodes, referred to as the design points, so that the time-consuming sensitivity analysis is related to the perturbation of only these nodes. The method also allows large shape changes to achieve the optimal shape. The design variables are specified as the moving magnitudes for the prescribed design points that are always located at the structural boundary.

Concept and new technique of accurate stress recovery are developed and applied in finding the lateral buckling parameters of plate structures. Some useful conclusions are made for the finite element Reissner-Mindlin plate solutions.

The powerful dual kriging B-spline fitting technique is reviewed and a set of new compact formulations are developed. This data smoothing method is then applied in accurately recovering curves and surfaces.

Theories, implementations and applications are presented for various modules by which the package is constructed. Especially, techniques involving finite element error estimation, adaptive mesh generation, design sensitivity analysis, and data smoothing are emphasized.