Research

Research Interest
  • Multi-material topology optimization frameworks with material and geometric nonlinearities
  • Composite structures
  • Development of efficient optimization algorithms (that handle many materials and constraints/sources)
  • Stochastic approximation for structural optimization under many load cases
  • Randomization of structural dynamic optimization
  • Nonlinear topology optimization with discrete filtering and reduced-order modeling

  • Research Projects
  • Design multi-functional composite materials and structures via multi-material and multi-physics topology optimization
  • Topology optimization informed civil engineering structure innovation
  • Lattice design optimization for resilient and functional lightweight structures
  • Robust design optimization under uncertainty through stochastic programming

  • Design multi-functional composite materials and structures via multi-material and multi-physics topology optimization

    To discover multi-functional composites with distinct nonlinear materials, multi-physics interactions, and local geometric feature controls, we propose general multi-material topology optimization frameworks with many local constraints accounting for nonlinear elastic materials under large deformations. The proposed formulation handles a wide range of objective functions and constraints, and the material phases can possess distinct properties (e.g., hardening and softening [2, 3], isotropic, and anisotropic [1] behaviors). To effectively and efficiently solve the proposed formulations, we derive novel optimization update algorithms (e.g., ZPR [4]) and the Virtual Element Method in conjunction with mesh adaptivity strategies [3] to ensure the computational accuracy and efficiency. The proposed topology optimization frameworks can effectively design composites by simultaneously optimizing their topology as well as material phases, and offers a promising avenue toward the systematic design of composite meta-materials and innovative engineering structures. The potential applications include multi-functional devices, actuators, and adaptive systems in robotics and metamaterials.


    Design multi-functional composite materials and structures via multi-material and multi-physics topology optimization


    Related publications

    1. X. S. Zhang, H. Chi, and Z. Zhao. "Topology optimization of fiber-reinforced hyperelastic structures under large deformations." Computer Methods in Applied Mechanics and Engineering. Accepted.
    2. X. S. Zhang, H. Chi. "Efficient multi-material continuum topology optimization considering hyperelasticity: achieving local feature control through regional constraints. " Mechanics Research Communications. Vol. 105. pp. 103494. 2020. Link to Paper
    3. X. S. Zhang, H. Chi, and G. H. Paulino. "Adaptive multi-material topology optimization with hyperelastic materials under large deformations: A virtual element approach." Computer Methods in Applied Mechanics and Engineering. Vol. 370, pp. 112976. 2020. Link to Paper
    4. X. S. Zhang, G. H. Paulino, and A. S. Ramos Jr. "Multi-material topology optimization with multiple volume constraints: A general approach applied to ground structures with material nonlinearity. " Journal of Structural and Multidisciplinary Optimization. Vol. 57, pp. 161-182, 2018. Link to Paper

    Optimization-informed innovative, sustainable, and feasible civil structures

    Our group takes a unique approach that integrates topology optimization into civil structure designs to come up with novel solutions for innovative yet feasible civil applications. Designing civil structures using topology optimization not only improves structural performance but also leads to aesthetic design. However, real-world civil structures pose challenges, such as different construction materials and complex geometries, that require sophisticated modeling and optimization techniques. We propose theoretical and computational methods for innovative structural systems with improved performance and efficiency, incorporating both structural engineering principles and aesthetic values. Figure a shows our recent collaborations with Skidmore, Owings & Merrill (SOM) to employ topology optimization to design novel openings for lightweight beams for the Campus Instructional Facility project at UIUC. See here for details. Shown in Figure b is several optimized bridge designs using combinations of multiple linear/nonlinear materials. Different construction material combinations lead to distinct optimized designs that range from an arch bridge, cable-stayed bridge, to a hybrid composite bridge of both types [1-3]. Figure c shows the modeling and optimized design of the Lotte tower considering many load cases using an efficient stochastic sampling method [2, 4].


    Optimization-informed innovative, sustainable, and feasible civil structures


    Related publications

    1. X. S. Zhang. "Topology optimization with multiple materials, multiple constraints, and multiple load cases." PhD Dissertation, School of Civil and Environmental Engineering, Georgia Institute of Technology, 2018. Link to Paper
    2. X. S. Zhang, G. H. Paulino, and A. S. Ramos Jr. "Multi-material topology optimization with multiple volume constraints: A general approach applied to ground structures with material nonlinearity. " Journal of Structural and Multidisciplinary Optimization. Vol. 57, pp. 161-182, 2018. Link to Paper
    3. X. S. Zhang, A. S. Ramos Jr., and G. H. Paulino. "Material nonlinear topology optimization using the ground structure method with a discrete filtering scheme." Journal of Structural and Multidisciplinary Optimization. Vol. 55, No. 6, pp. 2045-2072. 2017. Link to Paper
    4. X. S. Zhang, E. de Sturler, and G. H. Paulino. "Stochastic sampling for deterministic structural topology optimization with many load cases: Density-based and ground structure approaches. " Computer Methods in Applied Mechanics and Engineering. Vol. 325, pp. 463-487. 2017. Link to Paper
    5. X. S. Zhang, S. Maheshwari, A. Ramos Jr., G. H. Paulino. “Macroelement and Macropatch Approaches for Structural Topology Optimization using a Ground Structure Method.” ASCE Journal of Structural Engineering. Vol. 142, No. 11, pp. 04016090-1 to 14. 2016. Link to Paper

    Lattice design optimization for resilient and functional lightweight structures

    Lattice materials and structures are characterized by superior properties, e.g., high stiffness-to-weight ratios, making them ideal for various applications. To design optimal structural- and material-scaled lattices that are resilient and lightweight, we create ground-structure-based optimization frameworks consider various nonlinear materials to optimize the functionality, e.g., to maximize stiffness and robustness or minimize weight. We propose the design update scheme that performs robust and efficient updates of the design variables associated with each constraint independently and in parallel [1, 2]. Optimized results including a crane, a bridge, and 3D cantilever can be seen in Figure a, b, and c, respectively.


    Lattice design optimization for resilient and functional lightweight structures


    Related publications

    1. X. S. Zhang, G. H. Paulino, and A. S. Ramos Jr. "Multi-material topology optimization with multiple volume constraints: A general approach applied to ground structures with material nonlinearity. " Journal of Structural and Multidisciplinary Optimization. Vol. 57, pp. 161-182, 2018. Link to Paper
    2. X. S. Zhang, G. H. Paulino, and A. S. Ramos Jr. "Multi-material topology optimization with multiple volume constraints: Combining the ZPR update with a ground structure algorithm to select a single material per overlapping set. " International Journal of Numerical Methods in Engineering. Vol. 114, pp. 1053–1073, 2018. Link to Paper

    Robust design optimization under uncertainty through stochastic programming

    Real-world structures are subjected to various types of random sources, ranging from loads, material properties to manufacturing errors. To effectively account for these uncertainties in the design optimization process, we derive stochastic programming algorithms, such as mirror descent stochastic approximation (MDSA), to our design problems with a challenging amount of random sources and various problem sizes. Shown in the figure are optimized designs accounting for various uncertainties. Figures (a) shows a disk structure with 200 load cases [1], (b) a bridge with 1764 load cases [1], and (c) a tower with 77 load cases [2], using a fraction of compute time of conventional methods. Generalizing the powerful stochastic programming methods to challenging problems such as robust topology optimization is our on-going research [3], as shown in Figure (d).


    Robust design optimization under uncertainty through stochastic programming


    Video demonstration of three dimensional high-rise building design with ground structure method


      Related publications

    1. X. S. Zhang, E. de Sturler, and A. Shapiro. "Topology optimization with many right-hand sides using mirror descent stochastic approximation—reduction from many to a single sample. " Journal of Applied Mechanics. Vol. 87, No. 5, pp. 051005. 2020. Link to Paper
    2. X. S. Zhang, E. de Sturler, and G. H. Paulino. "Stochastic sampling for deterministic structural topology optimization with many load cases: Density-based and ground structure approaches. " Computer Methods in Applied Mechanics and Engineering. Vol. 325, pp. 463-487. 2017. Link to Paper
    3. W. Li and X. S. Zhang. "Momentum-based accelerated mirror descent stochastic approximation for robust topology optimization under stochastic loads." Under Review. Link to Paper