TOPOLOGY DESCRIPTION FUNCTION APPROACH USING NURBS INTERPOLATION FOR 3D STRUCTURES WITH SELF-WEIGHT LOADS

The self-weight of the structure is of great importance for large civil engineering structures like dams and bridges, and should be taken into account at the initial design stage. Three main methods to deal with the di culties arisen in optimization problems with self-weight loads are summarized. In this paper, a modified topology description function (TDF) approach using the non-uniform rational B-splines (NURBS) interpolation scheme is introduced for optimal design of 2D/3D continuum structures with design-dependent self-weight loads. In the present approach, the NURBS basis function is applied for the approximation of both the displacement field and the geometry, as well as the interpolation of the design variables. Based on this, the design model and analysis model can be combined closely to realize the computational analysis directly on exact geometry. The model of TDF approach using NURBS interpolation and its sensitivity analysis are detailed. And the method of moving asymptotes (MMA) algorithm is used to solve this optimization problem. Then several numerical examples are performed. It can be seen that the present TDF approach is a robust, fast convergence algorithm, and can effectively overcome the parasitic effect associated with low material density areas, and the nonmonotonous behavior of the compliance that often encountered in topology optimization problems with self-weight loads.