Truss design and optimization using stress analysis and NURBS curves

This paper presents a novel design methodology, which combines topology and shape optimization to define material distribution in the structural design of a truss. Firstly, in order to identify the best layout, the topology optimization process in the design domain is carried out by applying the BESO (Bidirectional Evolutionary Structural Optimization) method. In this approach, the low energy elements are eliminated from an initial mesh, and a new geometry is constructed. This new geometry consists of a set of elements with a higher elastic energy. This results in a new division of material providing different zones, some subjected to higher stress and others containing less elastic energy. Moreover, the elements of the final mesh are re-arranged and modified, considering the distribution of tension. This new arrangement is constructed by aligning and rotating the original mesh elements coherently to the principal directions. In the Shape Optimization stage, the resulting TO (Topology Optimization) geometry is refined. A process of replacing the tabular mesh is performed by rearranging the remaining elements. The vertices of the mesh are set as control polygon vertices and used as reference to define the NURBS (Non-Uniform Rational B-Spline) curves. This provides a parametric representation of the boundaries, outlining the high elastic energy zones. The final stage is the optimization of the continuous and analytically defined NURBS curve outlining the solid material domain. The Shape Optimization is carried out applying a gradient-based optimization method.