Optimization of branching structures for free-form surfaces using force density method

Abstract

Branching structures are mechanically efficient in supporting large-span structures, such as free-form roofs. To support a roof with a specified geometry, we present a novel shape and topology optimization method to find the optimal branching structure in this paper. In the proposed method, the branching structure is modelled as a cable-net, while the reaction forces from the roof are taken as external loads. The force densities of the members are the design variables. The optimal branching structure can be obtained by minimizing one of the several proposed objective functions. The shape of the branching structure represented by the nodal coordinates is determined by solving the linear equilibrium equations. The topology is optimized by removing the members with small axial forces and incorporating the closely spaced nodes. The cross-sectional areas can be easily calculated, if the allowable stress is assigned. Hence, it is very convenient to simultaneously optimize the cross-section, shape, and topology of a branching structure. Numerical examples show that this method can be easily applied to a 2D problem. For a 3D problem, the constraints on the reaction forces should be relaxed. Considering the roof supports as variables is also an effective solution for 3D problems.

Keywords

• shape optimization
• topology optimization
• free-form surface
• force density method
• branching structure