Topology optimization with beam features of variable cross-sections

Beam features of variable cross-sections are developed in this paper for topology optimization based on feature-driven method. As beam structures are extensively used and mostly hold standard cross-sections in engineering practice, this work is aimed at the simultaneous design of beam layout and beam cross-section. The H-shaped cross-section is taken as general design primitive owing to its flexible evolution into T-shaped, C-shaped, and L-shaped cross-sections. Meanwhile, it is represented by means of the level-set functions (LSFs) with design variables consisting of the beam position, rotation angles, cross-section sizes, and cross-section configurations. Through the continuous change of defined cross-section configuration variables, different specifications of standard cross-sections with normed size values can be obtained and selected from the parts library. Fixed-mesh technique is also implemented for structural analysis and sensitivity analysis. Several numerical examples are presented to demonstrate the effectiveness and merits of the proposed method.