Browsing by Author "Liu, Kai"

Now showing 1 - 10 of 12
  • Thumbnail Image
    Item
    Cluster-Based Optimization of Cellular Materials and Structures for Crashworthiness
    (ASME, 2018-09) Liu, Kai; Detwiler, Duane; Tovar, Andres; Mechanical and Energy Engineering, School of Engineering and Technology
    The objective of this work is to establish a cluster-based optimization method for the optimal design of cellular materials and structures for crashworthiness, which involves the use of nonlinear, dynamic finite element models. The proposed method uses a cluster-based structural optimization approach consisting of four steps: conceptual design generation, clustering, metamodel-based global optimization, and cellular material design. The conceptual design is generated using structural optimization methods. K-means clustering is applied to the conceptual design to reduce the dimensional of the design space as well as define the internal architectures of the multimaterial structure. With reduced dimension space, global optimization aims to improve the crashworthiness of the structure can be performed efficiently. The cellular material design incorporates two homogenization methods, namely, energy-based homogenization for linear and nonlinear elastic material models and mean-field homogenization for (fully) nonlinear material models. The proposed methodology is demonstrated using three designs for crashworthiness that include linear, geometrically nonlinear, and nonlinear models.
  • Thumbnail Image
    Item
    Concurrent topology optimization of structures and materials
    (2013-12-11) Liu, Kai; Tovar, Andrés; Nematollahi, Khosrow; Koskie, Sarah; Anwar, Sohel
    Topology optimization allows designers to obtain lightweight structures considering the binary distribution of a solid material. The introduction of cellular material models in topology optimization allows designers to achieve significant weight reductions in structural applications. However, the traditional topology optimization method is challenged by the use of cellular materials. Furthermore, increased material savings and performance can be achieved if the material and the structure topologies are concurrently designed. Hence, multi-scale topology optimization methodologies are introduced to fulfill this goal. The objective of this investigation is to discuss and compare the design methodologies to obtaining optimal macro-scale structures and the corresponding optimal meso-scale material designs in continuum design domains. These approaches make use of homogenization theory to establish communication bridges between both material and structural scales. The periodicity constraint makes such cellular materials manufacturable while relaxing the periodicity constraint to achieve major improvements of structural performance. Penalization methods are used to obtain binary solutions in both scales. The proposed methodologies are demonstrated in the design of stiff structure and compliant mechanism synthesis. The multiscale results are compared with the traditional structural-level designs in the context of Pareto solutions, demonstrating benefits of ultra-lightweight configurations. Errors involved in the mult-scale topology optimization procedure are also discussed. Errors are mainly classified as mesh refinement errors and homogenization errors. Comparisons between the multi-level designs and uni-level designs of solid structures, structures using periodic cellular materials and non-periodic cellular materials are provided. Error quantifications also indicate the superiority of using non-periodic cellular materials rather than periodic cellular materials.
  • Thumbnail Image
    Item
    Design for Crashworthiness of Categorical Multimaterial Structures Using Cluster Analysis and Bayesian Optimization
    (ASME, 2019-12) Liu, Kai; Wu, Tong; Detwiler, Duane; Panchal, Jitesh; Tovar, Andres; Mechanical and Energy Engineering, School of Engineering and Technology
    This work introduces a cluster-based structural optimization (CBSO) method for the design of categorical multimaterial structures subjected to crushing, dynamic loading. The proposed method consists of three steps: conceptual design generation, design clustering, and Bayesian optimization. In the first step, a conceptual design is generated using the hybrid cellular automaton (HCA) algorithm. In the second step, threshold-based cluster analysis yields a lower-dimensional design. Here, a cluster validity index for structural optimization is introduced in order to qualitatively evaluate the clustered design. In the third step, the optimal design is obtained through Bayesian optimization, minimizing a constrained expected improvement function. This function allows to impose soft constraints by properly redefining the expected improvement based on the maximum constraint violation. The Bayesian optimization algorithm implemented in this work has the ability to search over (i) a real design space for sizing optimization, (ii) a categorical design space for material selection, or (iii) a mixed design space for concurrent sizing optimization and material selection. With the proposed method, materials are optimally selected based on multiple attributes and multiple objectives without the need for material ranking. The effectiveness of this approach is demonstrated with the design for crashworthiness of multimaterial plates and thin-walled structures.
  • Thumbnail Image
    Item
    An efficient 3D topology optimization code written in Matlab
    (Springer, 2015-06) Liu, Kai; Tovar, Andres; Department of Mechanical Engineering, School of Engineering
    This paper presents an efficient and compact Matlab code to solve three-dimensional topology optimization problems. The 169 lines comprising this code include finite element analysis, sensitivity analysis, density filter, optimality criterion optimizer, and display of results. The basic code solves minimum compliance problems. A systematic approach is presented to easily modify the definition of supports and external loads. The paper also includes instructions to define multiple load cases, active and passive elements, continuation strategy, synthesis of compliant mechanisms, and heat conduction problems, as well as the theoretical and numerical elements to implement general non-linear programming strategies such as SQP and MMA. The code is intended for students and newcomers in the topology optimization. The complete code is provided in Appendix C and it can be downloaded from http://​top3dapp.​com.
  • Thumbnail Image
    Item
    Machine Learning and Metamodel-Based Design Optimization of Nonlinear Multimaterial Structures
    (ASME, 2016-08) Liu, Kai; Detwiler, Duane; Tovar, Andres; Department of Mechanical Engineering, School of Engineering and Technology
    This study presents an efficient multimaterial design optimization algorithm that is suitable for nonlinear structures. The proposed algorithm consists of three steps: conceptual design generation, design characterization by machine learning, and metamodel-based multi-objective optimization. The conceptual design can be generated from extracting finite element analysis information or by using structure optimization. The conceptual design is then characterized by using machine learning techniques to dramatically reduce the dimension of the design space. Finally, metamodels are derived using Efficient Global Optimization (EGO) followed by multi-objective design optimization to find the optimal material distribution. The proposed methodology is demonstrated using examples from multiple physics and compared with traditional multimaterial topology optimization method.
  • Thumbnail Image
    Item
    Metamodel-Based Global Optimization of Vehicle Structures for Crashworthiness Supported by Clustering Methods
    (Springer, 2018) Liu, Kai; Detwiler, Duane; Tovar, Andres; Mechanical Engineering, School of Engineering and Technology
    This work introduces a metamodel-based global optimization method for crashworthiness with the ability to synthesize continuum structures with an optimal distribution of material phases or gauges. The proposed optimization method makes use of fully nonlinear, dynamic crash simulations and consists of three main elements: (1) the generation of a conceptual design from the structures crash response, (2) the optimal clustering of the conceptual design to define the location of the material phases or gauges, (3) the metamodel-based global optimization, which aims to find the optimal settings for each cluster. The conceptual design can be generated from extracting finite element analysis information or by using structural optimization. The conceptual design is then clustered using clustering analysis to reduce the dimension of the design space. The global optimization problem aims to find the optimal material distribution on the reduced design space using metamodels. The metamodels are built using sampling and cross-validation, and sequentially updated using an expected improvement function until convergence. The proposed methodology is demonstrated using examples from multi-objective crashworthiness design examples.
  • Thumbnail Image
    Item
    Multiphase Thermomechanical Topology Optimization of Functionally Graded Lattice Injection Molds
    (ASME, 2016-08) Wu, Tong; Liu, Kai; Tovar, Andres; Department of Mechanical Engineering, School of Engineering and Technology
    This work presents a design methodology of lightweight, thermally efficient injection molds with functionally graded lattice structure using multiphase thermomechanical topology optimization. The aim of this methodology is to increase or maintain thermal and mechanical performance as well as to lower the cost of thermomechanical components such as injection molds when these are fabricated using additive manufacturing technologies. The proposed design approach makes use of thermal and mechanical finite element analyses to evaluate the components stiffness and heat conduction in two length scales: mesoscale and macroscale. The mesoscale contains the structural features of the lattice unit cell. Mesoscale homogenized properties are implemented in the macroscale model, which contains the components boundary conditions including the external mechanical loads as well as the heat sources and heat sinks. The macroscale design problem addressed in this work is to find the optimal distribution of given number of lattice unit cell phases within the component so its mass is minimized, while satisfying stiffness and heat conduction constraints of the overall component and the specific regions. This problem is solved through two steps: conceptual design generation and multiphase material distribution. In the first step, the mass is minimized subject to constraints of mechanical compliance and thermal cost function. In the second step, a given number of lattice material are optimally distributed subjected to nonlinear thermal and mechanical constraints, e.g., maximum nodal temperature, maximum nodal displacement. The proposed design approach is demonstrated through 2D and 3D examples including the optimal design of the core of an injection mold. The results demonstrate that a small reduction in mechanical and thermal performance allows for significant mass savings: the second example shows that 3.5% heat conduction reduction and 8.7% stiffness reduction results in 30.3% mass reduction.
  • Thumbnail Image
    Item
    Multiphase topology optimization of lattice injection molds
    (Elsevier, 2017-11) Wu, Tong; Liu, Kai; Tovar, Andres; Mechanical Engineering, School of Engineering and Technology
    This work presents a topology optimization approach for lattice structures subjected to thermal and mechanical loads. The focus of this work is the design of injection molds. The proposed approach seeks to minimize the injection mold mass while satisfying constraints on mechanical and thermal performance. The optimal injection molds are characterized by a quasi-periodic distribution of lattice unit cells of variable relative density. The resulting lattice structures are suitable for additive manufacturing. The proposed structural optimization approach uses thermal and mechanical finite element analyses at two length scales: mesoscale and macroscale. At the mesoscale, lattice unit cells are utilized to obtain homogenized thermal and mechanical properties as a function of the lattice relative density. At the macroscale, the lattice unit cells are optimally distributed using the homogenized properties. The proposed design approach is demonstrated through 2D and 3D examples including the optimal design of an injection mold. The optimized injection mold is prototyped using additive manufacturing. The numerical model of the optimized mold shows that, with respect to a traditional solid mold design, a mass reduction of over 30% can be achieved with a small increase in nodal displacement (under 5 microns) and no difference in nodal temperature.
  • Thumbnail Image
    Item
    Optimal Design of Cellular Material Systems for Crashworthiness
    (SAE, 2016-04) Liu, Kai; Xu, ZongYing; Detwiler, Duane; Tovar, Andres; Mechanical and Energy Engineering, School of Engineering and Technology
    This work proposes a new method to design crashworthiness structures that made of functionally graded cellular (porous) material. The proposed method consists of three stages: The first stage is to generate a conceptual design using a topology optimization algorithm so that a variable density is distributed within the structure minimizing its compliance. The second stage is to cluster the variable density using a machine-learning algorithm to reduce the dimension of the design space. The third stage is to maximize structural crashworthiness indicators (e.g., internal energy absorption) and minimize mass using a metamodel-based multi-objective genetic algorithm. The final structure is synthesized by optimally selecting cellular material phases from a predefined material library. In this work, the Hashin-Shtrikman bounds are derived for the two-phase cellular material, and the structure performances are compared to the optimized structures derived by our proposed framework. In comparison to traditional structures that made of a single cellular phase, the results demonstrate the improved performance when multiple cellular phases are used.
  • Thumbnail Image
    Item
    Optimal Design of Nonlinear Multimaterial Structures for Crashworthiness Using Cluster Analysis
    (ASME, 2017-08) Liu, Kai; Detwiler, Duane; Tovar, Andres; Mechanical Engineering, School of Engineering and Technology
    This study presents an efficient multimaterial design optimization algorithm that is suitable for nonlinear structures. The proposed algorithm consists of three steps: conceptual design generation, clustering, and metamodel-based global optimization. The conceptual design is generated using a structural optimization algorithm for linear models or a heuristic design algorithm for nonlinear models. Then, the conceptual design is clustered into a predefined number of clusters (materials) using a machine learning algorithm. Finally, the global optimization problem aims to find the optimal material parameters of the clustered design using metamodels. The metamodels are built using sampling and cross-validation and sequentially updated using an expected improvement function until convergence. The proposed methodology is demonstrated using examples from multiple physics and compared with traditional multimaterial topology optimization (MTOP) method. The proposed approach is applied to a nonlinear, multi-objective design problems for crashworthiness.