Browsing by Subject "Topology"

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    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.
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    Topology design of vehicle structures for crashworthiness using variable design time
    (2017-12) Tapkir, Prasad; Tovar, Andres; Chen, Jie; Nematollahi, Khosrow
    The passenger safety is one of the most important factors in the automotive industries. At the same time, in order to improve the overall efficiency of passenger cars, lightweight structures are preferred while designing the vehicle structures. Among various structural optimization techniques, topology optimization techniques are usually preferred to address the issue of crashworthiness. The hybrid cellular automaton (HCA) is a truly nonlinear explicit topology design method developed for obtaining conceptual designs of crashworthy vehicle components. In comparison to linear implicit methods, such as equivalent static loads, and partially nonlinear implicit methods, the HCA method fully captures all the relevant aspect of a fully nonlinear, transient dynamic crash simulation. Traditionally, the focus of the HCA method has been on designing load paths in the crash component that increase the uniform internal energy absorption ability; thus far, other relevant crashworthiness indicators such as peak crushing force and displacement have been less studied. The objective of this research is to extend the HCA method to synthesize load paths to obtain the different acceleration-displacement profiles, which allow reduced peak crushing force as well as reduced penetration during a crash event. To achieve this goal, this work introduces the concept of achieving uniform energy distribution at variable design simulation times. In the proposed work, the design time is used as a new design parameter in topology optimization. The desired volume fraction of the final design and the design time provided two dimensional design space for topology optimization, which is followed by the formulation of design of experiments (DOEs). The nonlinear analyses of the corresponding DOEs are performed using nonlinear explicit code LS-DYNA, which is followed by topology synthesis in HCA. The performance of the resulting structures showed that the short design times lead to design obtained by linear optimizers, while long simulation times lead to designs obtained by the traditional HCA method. To achieve the target crucial crash responses such as maximum acceleration and maximum displacement of the structure under the dynamic load, the geological predictor has been implemented. The concept of design time is further developed to improve structural performance of a vehicle component under the multiple loads using the method of multi-design time. Finally, the design time is implemented to generated merged designs by performing binary operations on topology-optimized designs. Numerical example of the simplified front frame is utilized to demonstrate the capabilities of the proposed approach.