Topology Optimization with Multiple Materials, Multiple Constraints, and Multiple Load Cases 多种材料、多种约束和多个荷载工况的拓扑优化
Topology Optimization with Multiple Materials, Multiple Constraints, and Multiple Load Cases
Dr. Xiaojia Shelly Zhang
Department of Civil and Environ mental Engineering (CEE)
Department of Mechanical Science and Engineering (MechSE)
University of Illinois at Urbana-Champaign (UIUC)
Topology optimization is a computational design tool for finding optimal layouts of structures and material microstructures. However, most work in this field has been restricted to single material with linear material behavior, limited volume constraint settings, and a single load case. To address these issues, we propose an efficient multi-material topology optimization formulation considering material nonlinearity. The proposed formulation handles an arbitrary number of candidate materials with flexible material properties, features freely specified material layers, and includes a generalized volume constraint setting. To efficiently handle such arbitrary volume constraints, we derive a novel design update scheme that performs robust updates of the design variables associated with each volume constraint independently. We show that the update of design variables in each volume constraint only depends on the corresponding Lagrange multiplier. To obtain designs under many load cases, we also present a randomized approach that efficiently optimizes structures under hundreds of load cases. This approach only uses 5 or 6 stochastic sample load cases, instead of hundreds, to obtain similar optimized designs (for both continuum and truss topology optimization). Through examples using combinations of various materials, we demonstrate that the proposed topology optimization frameworks with the aforementioned update scheme and randomized algorithm lead to design tools that not only find the optimal topology but also select the proper type and local distribution, with drastically reduced computational cost.
Dr. Xiaojia Shelly Zhang is an Assistant Professor at the Department of Civil and Environmental Engineering and Department of Mechanical Science and Engineering in the University of Illinois at Urbana Champaign. Dr. Zhang holds a B.S. degree and a M.S. degree in Civil Engineering from University of Illinois at Urbana Champaign and a Ph.D. degree in Civil Engineering from Georgia Tech. She received the faculty fellowship from the National Center for Supercomputing Applications (NCSA), and the Best Ph.D. Thesis Awards from both the CEE school in 2018 and from the international scientific research honor society Sigma Xi in 2019. Her research explores topology optimization, stochastic programming, and additive manufacturing to develop resilient, smart, sustainable, and innovative engineering infrastructure and materials for applications at different scales, from as large as high-rise buildings to as small as material microstructures.