Topology optimization methods based on nonlinear and dynamic crash simulations

Topology optimization for crashworthiness has been investigated during the last years, starting from methods based on linear elastic and static simulations or so-called equivalent static loads (ESL) obtained by a single nonlinear crash simulation with a subsequent optimization loop based on the linear stiffness matrix and the corresponding sensitivities. Both methods do not consider material nonlinearities in their optimization process, which are essential for structural components designed for energy absorption, although it is well-known that plasticity and failure play an important role. As alternative, optimization methods have been proposed, which use fully nonlinear and dynamic crash simulations. The first method, presented for example in Patel’s PhD thesis, is based on a hybrid cellular automata approach (HCA) and derives optimal structures using a homogenized energy density approach where each finite element (cell) is modified until the highest degree of homogeneity is achieved. Because this is not fully appropriate for thin-walled structures, Hunkeler modified the approach (HCA-TWS – Hybrid Cellular Automata for Thin-walled Structures) such that deformation energy is only homogenized between larger structural entities (i.e. thin ribs / walls). The most recent method, the EA-LSM, a combined level set method (LSM) and evolutionary approach, was then proposed by Bujny et al. where more appropriate objectives and constraints can be used with the drawback of higher computational costs. In this paper, the latest results for HCA-TWS and EA-LSM will be presented. Special focus is here the investigation of the influence of different material models for plasticity. Examples are inspired by recent material model developments for magnesium alloys with a characteristic anisotropy in the plasticity model. As a result, it is shown that the optimal topologies depend on the material model and that it is necessary to use nonlinear and dynamic finite elements for crash topology optimization.

[1]  Mathias Wallin,et al.  Topology optimization based on finite strain plasticity , 2016 .

[2]  Markus Olhofer,et al.  Identification of optimal topologies for crashworthiness with the evolutionary level set method , 2018 .

[3]  C B W Pedersen.  Topology optimization for crashworthiness of frame structures , 2003 .

[4]  Dipl. Ing. Karl Heinz Kellermayer.  NUMERISCHE OPTIMIERUNG VON COMPUTER-MODELLEN MITTELS DER EVOLUTIONSSTRATEGIE Hans-Paul Schwefel Birkhäuser, Basel and Stuttgart, 1977 370 pages Hardback SF/48 ISBN 3-7643-0876-1 , 1977 .

[5]  Ingo Rechenberg,et al.  Evolutionsstrategie : Optimierung technischer Systeme nach Prinzipien der biologischen Evolution , 1973 .

[6]  Andres Tovar,et al.  Bone Remodeling as a Hybrid Cellular Automaton Optimization Process , 2004 .

[7]  Xu Guo,et al.  Doing Topology Optimization Explicitly and Geometrically—A New Moving Morphable Components Based Framework , 2014 .

[8]  J. Kato,et al.  Analytical sensitivity in topology optimization for elastoplastic composites , 2015 .

[9]  E. Ramm,et al.  Adaptive topology optimization of elastoplastic structures , 1998 .

[10]  Fabian Duddeck,et al.  Multidisciplinary optimization of car bodies , 2008 .

[11]  Kapil Khandelwal,et al.  Topology optimization of structures with anisotropic plastic materials using enhanced assumed strain elements , 2017 .

[12]  Fabian Duddeck,et al.  Topology optimisation method for crashworthiness design using Hybrid Cellular Automata and thin-walled ground structures , 2013 .

[13]  Kurt Maute,et al.  Level-set methods for structural topology optimization: a review , 2013 .

[14]  D. Tortorelli,et al.  Topology optimization for effective energy propagation in rate-independent elastoplastic material systems , 2015 .

[15]  Markus Olhofer,et al.  Evolutionary Crashworthiness Topology Optimization of Thin-Walled Structures , 2016 .

[16]  Markus Olhofer,et al.  Hybrid evolutionary approach for level set topology optimization , 2016, 2016 IEEE Congress on Evolutionary Computation (CEC).

[17]  E. Ramm,et al.  Topology and shape optimization for elastoplastic structural response , 2001 .

[18]  Naoko Shimotai,et al.  Cellular automaton generating topological structures , 1994, Other Conferences.

[19]  John E. Renaud,et al.  Crashworthiness Design Using Topology Optimization , 2009 .

[20]  Fabian Duddeck,et al.  Improved hybrid cellular automata for crashworthiness optimization of thin-walled structures , 2017 .

[21]  O. Amir,et al.  Conceptual design of reinforced concrete structures using topology optimization with elastoplastic material modeling , 2012 .

[22]  Gyung-Jin Park,et al.  Technical overview of the equivalent static loads method for non-linear static response structural optimization , 2011 .

[23]  Markus Olhofer,et al.  Evolutionary Level Set Method for Crashworthiness Topology Optimization , 2016 .

[24]  Stephan Hunkeler,et al.  Topology Optimisation in Crashworthiness Design via Hybrid Cellular Automata for Thin Walled Structures. , 2014 .

[25]  Fabian Duddeck,et al.  Topology optimization for crashworthiness of thin-walled structures under axial impact using hybrid cellular automata , 2016 .

[26]  Fabian Duddeck,et al.  Topology optimization of transient nonlinear structures - A comparative assessment of methods , 2015 .

[27]  Fabian Duddeck,et al.  Material model dependency of optimal topologies for crashworthiness , 2017 .