An integrated approach to structural shape optimization of linearly elastic structures. Part II: Shape definition and adaptivity

In this paper we initially study how the number of design variables used affects the final optimum shape of the structure when employing two different types of curves to describe the boundary of the structure, i.e. quadratic Bezier and cubic B-spline curves. The advantage of using better shape definition is highlighted with several examples. An adaptive mesh refinement (AMR) procedure using six-node triangular elements is adopted in the structural shape optimization process. The procedure makes use of an h-version adaptive refinement technique based on error estimates determined from either best-guess stress values or residual terms in the governing equation. An example is presented to illustrate the performance of these error estimators with respect to their convergence, accuracy and cost of computation. Different strategies for the inclusion of AMR procedures in the shape optimization process are also proposed. Anomalies in predicting the optimum shape due to discretization errors are demonstrated using several examples.