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Topology Optimization

Papers on Topology Optimization





  • LS-TaSC 4: Designing for the combination of impact, statics and NVH

    Katharina Witowski; DYNAmore GmbH, Stuttgart, Germany, Willem Roux, Guilian Yi, Imtiaz Gandikota; Livermore Software Technology Corporation, Livermore, CA, USA

  • Implementation of the Projected Subgradient Method in LS-TaSC™

    Willem Roux, Imtiaz Gandikota, Livermore Software Technology Corporation;, Guilian Yi, Dalian Fukun Technology Corporation

    The projected subgradient method is major new methodology development for the topology optimization of huge, multi-disziplinary structural problems; for example, the combined impact, statics and NVH design of a whole body in white. This paper accordingly discusses the projected subgradient method in LS-TaSC, with specific reference to the basic theory, the ability to combined impact and NVH load cases, and the performance for huge models. Also mentioned is how the method has been enhanced to handle generalized constraints using the multi-tensor numerical scheme.

  • Design Domain Dependent Preferences for Multi-disciplinary Body-in-White Concept Optimization

    Nikola Aulig,Honda Research Institute Europe GmbH, Offenbach/Main, Germany;, Satchit Ramnath, Emily Nutwell, The Ohio State University SIMCenter, Columbus, OH, USA;, Kurtis Horner, Honda R&D Americas, Inc., Raymond, OH, USA

    Recently methods for topology optimization are increasingly established in the virtual vehicle design process in the automobile industry. In particular a heuristic topology optimization process based on the assumption of uniform energy distribution throughout the structure combined with a scaled energy weighting approach was demonstrated to successfully to provide concepts for vehicle structures subject to static and crash loads concurrently.

  • Detail Design Evaluation of Extruded Sections on a Body-in-White Concept Model

    Satchit Ramnath, Emily Nutwell, SIMCenter, The Ohio State University, Columbus, OH, USA;, Nikola Aulig, Honda Research Institute Europe GmbH, Offenbach/Main, Germany;, Kurtis Horner, Honda R&D Americas Inc., Raymond, OH, USA

    Topology optimization allows for the design of structures with an optimum distribution of material for a given set of load cases. In the past, it has been shown that topology optimization can be implemented for a design space representing a body-in-white vehicle structure undergoing multiple load requirements. Using a Hybrid Cellular Automata algorithm along with a scaled energy weighting approach, both the objective of maximizing stiffness as ...

  • Topology Optimization of a Stamping Die Structure using LS-DYNA® and LS-TaSC™

    Jithesh Erancheri, Ramesh Venkatesan, Nanda Kumar, Kaizenat Technologies Pvt Ltd

    Cost of Stamping Dies accounts for about 45% of total cost of a vehicle program. The construction cost of these dies is used as benchmark by the automotive companies to evaluate the cost of any new vehicle program and also to determine where they stand compared to their competitions. The cascading effect goes down to the TIER-1 suppliers to optimize their die structure designs in order to stay afloat in the business. FE Simulation tools like ...

  • ACP-OpDesign: Optimal Design Gateway: Reveal the Path to Optimized Products

    A. Kaloudis, BETA CAE Systems International AG

    ACP OpDesign is an intuitive and process-guided optimization desktop environment. With its optimization oriented and highly specialized user interface, based on the process depicted as a diagram in the tool, it offers the user the capability to take advantage of an efficient, direct interaction to: - ANSA’s powerful morphing and parametrization functionality - custom-designed META Post-processor tools - Topology and parametric optimization ...


  • Topology optimization methods based on nonlinear and dynamic crash simulations

    Fabian Duddeck, Mariusz Bujny, Duo Zeng (Technische Universität München)

    Topology optimization for crashworthiness has been investigated during the last years, starting from methods based on linear elastic and static simulations [1] 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 [2, 3]. 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.

  • LS-TaSC Product Status

    Katharina Witowski (DYNAmore GmbH), Willem Roux (LSTC)

    The LS-TaSC Version 3.2 topology and shape design tool is presented, as well as the current development that will be available in the next version. The presentation introduces the multipoint numerical derivatives scheme that allows constrained optimization using the mass fractions and load case weights as variables. This allows constrained optimization using any response or mathematical expressions as constraints or objectives. Additionally, topology optimization of NVH load cases is presented. Application examples illustrate these capabilities.

  • A Systematic Study on Topology Optimization of Crash Loaded Structures using LS-TaSC

    Katrin Weider, André Marschner, Axel Schumacher (University of Wuppertal)

    Using topology optimization methods, new structural concepts can be generated. These methods are efficient in the field of structural design, taking into account linear structural properties and linear static loading conditions. Usually the mean compliance is considered, subject to a mass constraint. Therefore, the design space is divided into small volumetric elements (so-called voxels) and the algorithm decides based on an analytical sensitivity for every voxel, is there material or not. After this optimization, the engineer has a good proposal and the possibility for the interpretation and the generation of a CAD model.

  • Free-Form Shape Optimization using CAD Models

    D. Baumgärtner, M. Breitenberger, K.-U. Bletzinger (Technische Universität München)

    The current state of the art in shape optimization is dominated by approaches utilizing computer-aided design (CAD) to manipulate the shape under consideration. On the contrary, free-form shape optimization approaches have not reached the same industrial acceptance, although for example the Vertex Morphing Method showed with many practical problems promising characteristics like high optimization potential, minimum modeling effort or fast design space exploration (see e.g. [1], [2]). One major reason for this limited popularity of free-form shape optimization techniques is their missing link to CAD being the primary design tool in many industrial branches. More precisely, while it is common practice to discretize an initial CAD-model so that a numerical optimization may be performed, it is far from trivial to reconstruct a CAD-model once the discrete optimal design is found - unless the original CAD parametric is used to modify the shape in the first place. The latter, however, depending on the case, may limit the optimization significantly. In the following, we present a novel workflow which may close the existing gap between free-form shape optimization and CAD.


  • Preference-based Topology Optimization of Body-in-white Structures for Crash and Static Loads

    Nikola Aulig, Stefan Menzel (Honda Research Institute Europe GmbH), Emily Nutwell (Ohio State University SIMCenter), Duane Detwiler (Honda R&D Americas)

    Topology optimization methods are increasingly applied tools for the design of lightweight structural concepts in the automotive design process. Ideally, topology optimization provides the optimum distribution of material within a user-defined design space for a given objective function. In the vehicle design process, two important objectives are to maximize stiffness of components for regular working conditions and to maximize energy absorption in exceptional loading conditions, for instance in crash events. For these objective functions, the Hybrid Cellular Automata algorithm devises efficient structures in case of the separated disciplines, by heuristically aiming for a uniform distribution of energy densities. Recently, it was demonstrated that a concurrent optimization of crash and static load cases can be performed by a linear weighting, in which the user preference is separated from the scaling of the internal energies. In this paper, the approach is applied to the practical example of a vehicle body-in-white design, which is optimized for multiple crash and linear static load cases. By comparing resulting internal energies of different load case settings we demonstrate that the hybrid cellular automata algorithm with scaled energy weighting is capable to find a very good trade-off solution within a single concurrent optimization run.

  • The LS-TaSC(TM) Multipoint Method for Constrained Topology Optimization

    Willem Roux (LSTC)

    The new multi-point constrained optimization scheme is for the constrained topology design of highly nonlinear structures for which analytical design sensitivity information is hard to compute. These highly nonlinear structures are designed for multiple load cases and multiple constraints, which means that the final design should have load paths for each load case as well as satisfy the constraints. This is done here by using two sets of variables: the local variables describing the part topology on the element level and the global variables consisting of the load case weights and part masses. The two sets of variables are treated differently in the design algorithm: the local variables are computed using a suitable method such as fully stressed design, while the values of the global variables satisfying the constraints are computed using numerical derivatives and mathematical programming.

  • LS-TaSC Product Status

    Katharina Witowski (DYNAmore GmbH), Willem Roux (LSTC)


  • LS-TaSC Product Status

    Willem Roux, Imtiaz Gandikota (Livermore Software Technology Corporation), Katharina Witowski, Peter Schumacher (DYNAmore GmbH)

    The LS-TaSC Version 3.1 topology and shape design tool is presented, as well as the major new features in LS-TaSC Version 3.0. The presentation introduces the multi-point numerical derivatives scheme that allows constrained optimization using the mass fractions and load case weights as variables. This allows constrained optimization using any response or mathematical expressions as constraint or objectives. Additionally, the post-processing of the final design geometry by the creation of iso-surfaces is also reviewed.

  • A Weight Balanced Multi-Objective Topology Optimization for Automotive Development

    Nikola Aulig, Stefan Menzel (Honda Research Institute Europe GmbH, Offenbach/Main, Germany), Emily Nutwell (Ohio State University SIMCenter, Columbus, OH, USA), Duane Detwiler (Honda R&D Americas, Raymond, OH, USA)

    Recently, it was demonstrated that a multi-objective optimization can be performed by linearly weighting and careful scaling of the load case energy levels. In this paper the approach is applied to the practical example of a vehicle control arm structure which is subject to two compliance load cases and an energy maximization load case and compared to a sequential optimization approach of the disciplines. Results demonstrate the practical feasibility of the proposed methods. Particularly, the scaled weighting approach yields a set of non-dominated trade-off solutions, facilitating the selection of a suitable balance between energy absorption and stiffness requirements.

  • Topometry and Shape Optimization of a Hood

    Yong Ha Han (Hyundai Motor Group), Katharina Witowski, Nikolay Lazarov, Krassen Anakiev (DYNAmore GmbH)

    To comply with the regulations of pedestrian safety, particularly the head impact requirements, the geometry of the hood panel is significant. The objective of this research was to develop a standardized automated method to design a hood which meets the pedestrian headform impact safety regulations and additionally the stiffness and fatigue requirements. The developed method was performed in two steps. As a first step, a topometry optimization of the inner hood panel using Genesis from Vanderplaats R&D and the Equivalent Static Loads Method (ESL) has been executed. The dynamic simulations were performed with LS-DYNA® as the coupling module ESLDYNA of Genesis was used. From the result a preliminary CAD design of the inner hood panel was generated. This design is just one possibility to interpret the result of the topometry optimization. Furthermore, since the ESL method is an interaction of nonlinear dynamic simulations and linear static optimization, nonlinear dynamic quantities such as HIC values cannot be considered directly in the linear static topometry optimization. Hence a second step was necessary to refine the functional requirements. A parametric multi-disciplinary shape optimization with LS-OPT® was carried out using the preliminary CAD geometry as a baseline design. The parameters of the optimization with LS-OPT were gauge thicknesses and geometric changes of the inner panel structure. To apply the geometric parameters the ANSA Morphing Tool from BETA CAE Systems S.A. was used.

  • Meta-model based optimization of spot-welded crash box using differential evolution algorithm

    Ahmet Serdar Önal (Beycelik Gestamp Kalip ve Oto Yan San. Paz. ve Tic. A.S., Bursa, Turkey), Necmettin Kaya (Uludag University, Mechanical Engineering Department, Görükle, Bursa, Turkey)

    The objective of this study is to improve the energy absorption performance of spot-welded crash box using optimization techniques. The number of crush initiators and the number of spot welds were selected as design parameters for optimization study. Maximization of absorbed energy is selected as objective function and the upper bound of maximum initial peak force is defined as constraint. DOE study has been performed with full factorial sampling method, and then polynomial objective and constraint functions were defined to approximate the responses, such as absorbed energy and initial reaction force.

  • Topology optimization of transient nonlinear structures - A comparative assessment of methods

    E. J. Wehrle, F. Duddeck (Chair of Computational Mechanics, Technische Universität Münschen, Munich, Germany), Y. H. Han (Advanced Safety CAE Team, Hyundai Motor Group, Korea)

    The topology optimization methodologies are categorized by the abstraction of the loads, from fully transient nonlinear structural-mechanical analysis to multiple static replacement loads to a single static replacement load. Several methods are investigated for varying loading conditions and degrees of nonlinear behavior: 1) the use of the algorithms based on hybrid cellular automata with full transient nonlinear finite-element analyses; 2) multiple static replacement loads with updates via transient nonlinear finite-element analysis; 3) multiple static replacement loads without updates; 4) single static replacement load. These will be introduced in this paper.

  • Multidisciplinary Design Optimisation Strategies for Leightweight Vehicle Structures

    Amit Prem, Christophe Bastien (Coventry University, Faculty of Engineering and Computing), Mike Dickison

    The future of automobiles will be driven by lightweight structures and highly efficient powertrains. The TARF-LCV EPSRC funded project (Towards Affordable, Closed-Loop Recyclable Future-Low Carbon Vehicle Structures) 0 aims to provide a strong scientific and technological underpinning to future LCV development in areas of advanced materials, low carbon manufacturing technologies, holistic mass-optimised vehicle structure design and closed-loop recycling of end of life vehicles.The proposed model in this paper is the completion of the TARF vehicle architecture based on linear optimisation. The optimisation methodology investigated in this paper will address the very local structural changes which cannot be computed by a global topology and localised linear sizing 00000. The paper will focus on a multi-disciplinary optimisation which will solelly include size and material grades as the vehicle package is very well defined and no geometry modifications can be performed.

  • Optimization of turbine blade fir-tree root geometry utilizing LS-Prepost in pre- and post-processing

    Jiří Jankovec (Research and Testing Institute Plzen, Czech Republic)

    The turbine blade fir-tree root is a type of blade to disc connection, usually used for low pressure steam turbine blades. This part of turbine is exposed to extreme loading conditions caused by centrifugal loading during turbine operation and therefore there is a need to find a design that exhibits lower stresses, which determine low-cyclic fatigue life of the fir-tree root. This paper describes utilization of LS-Prepost [1] in optimization loop for design of new turbine blade fir-tree root geometry. The LS-Prepost pre- and post- processor offers a wide range of functionalities for geometry and mesh generation and is well suited for collaboration with the solver of LS-DYNA [2] commercial FE-code and with LS-OPT [3] optimization program. The other inconsiderable advantage of LS-Prepost is that it is delivered free with LS-DYNA and therefore it is not necessary to utilize any commercial Pre- and post-processor to parametrically control geometry of the analyzed problem.


  • Car Body Optimization Considering Crashworthiness, NVH and Static Responses

    Phani Adduri, Juan P. Leiva, Gary Quinn, Brian C. Watson (Vanderplaats Research and Development, Inc)

    This paper demonstrates a design system to efficiently perform optimization based on responses computed from multiple LS-DYNA® analyses while also taking into consideration the linear loading conditions such as the ones for NVH and Static responses. The proposed design system, ESLDYNA, is based on the Equivalent Static Load (ESL) method, which requires the iterative process of non-linear structural analysis (LS-DYNA) and linear structural analysis and optimization (GENESIS). Unlike general purpose optimization software packages, it does not require a large number of analysis calls even for problems with large numbers of design parameters. Therefore, large-scale optimization techniques, such as topology, topometry and topography, can be easily employed. Several examples using different optimization techniques will be presented. One of the examples will include optimizing the design for frontal crash, normal modes and static loading conditions simultaneously.

  • LS-TaSC® Product Status

    Willem Roux (LSTC)

    The LS-TaSC product status is presented. The current capabilities are discussed together with illustrative examples and release dates. In addition, the current development directions, such as new capabilities and CAE integration, are also revealed.

  • Topology and Topometry Optimization of Crash Applications with the Equivalent Static Load Method

    Katharina Witowski, Heiner Müllerschön, Andrea Erhart, Peter Schumacher, Krassen Anakiev (DYNAmore GmbH)

    This paper deals with topology and topometry optimization of structures under highly nonlinear dynamic loading such as crash using equivalent static loads (ESL). It reports about experiences in the application of the ESL methodology on industrial problems from the automotive industry. LS-DYNA® is used for the nonlinear dynamic, for topology and topometry optimization GENESIS from Vanderplaats R&D is applied. The methodical investigations have been performed within a research project, founded by the association BMBF, with several partners from German automotive companies. On the application of the method on large scale problems numerous problems are encountered. Setting up a fully automated and robust process on an HPC cluster with nested linear and nonlinear finite element analysis and optimization for multiple load cases turned out to be a challenging task. The general objective of the investigations was to evaluate the suitability of the method for different types of crash and impact problems. The appraisement is with respect to quality and usability of the results and with respect to the numerical costs.


  • Application of the equivalent static load method for impact problems with GENESIS and LS-DYNA

    Heiner Müllerschön, Andrea Erhart, Krassen Anakiev, Peter Schumacher (DYNAmore GmbH), Heribert Kassegger (MAGNA STEYR Engineering AG & Co KG)

  • Multi-disciplinary Topology Optimization for Vehicle Bonnet Design

    David Salway (GRM Consulting Ltd), Tayeb Zeguer (Jaguar Land Rover Ltd)

    Bonnet Pedestrian Head lmpact and Structural Stiffness and Strength targets have conflicting design requirements which currently result in design compromises, and the current CAE methods use different models and solvers. This paper highlights a new CAE capability to provide Multi-Disciplinary Optimization of bonnet geomety to achieve the conflicting Pedestrian Head Impact and structural stiffness/strength targets at lowest weight and cost. The aim has been to combine all bonnet load cases using one code "LS-DYNA" and cary out trade-oft and optimize weight using LS-OPT. A new developed topology process employing VR&D Genesis for HIC optimisation is presented and compared mih LS-TASC tools for a generic bonnet design.


  • LS-TaSC Version 2.1

    Willem Roux (LSTC, Livermore, CA, USA)

    This paper gives an overview of LS-TaSC version 2.1, a topology optimization tool using LS-DYNA® for the analysis of nonlinear structural behavior. The focus is on its capabilities, current development directions, and integration into an industrial design environment. Examples of using the new developments such as dynamic load scaling are given.

  • Topology Optimization for Crash

    Katharina Witowski, Andrea Erhart, Peter Schumacher, Heiner Müllerschön (DYNAmore GmbH)

    This paper is contributed to the topology optimization of structures under highly nonlinear dynamic loading, e.g. crash. We present our experiences with two software tools: LS-TaSCŒ (developed by LSTC, available since 2009, the first version was named LS-OPT/TopologyŒ) and Genesis-ESL® (developed by VR&D) and highlight the possible application areas, capabilities and limitations of the implementations. LS-TaSC nonlinear topology optimization with LS-DYNA can be applied to nonlinear static and dynamic problems. The underlying method is 3Hybrid Cellular Automata ́ (HCA) which is a heuristic, gradient-free approach. The objective is to obtain a structure with uniform internal energy density subject to a given mass fraction. The basic idea of the "Equivalent Static Load"- Method (ESL) is, to divide the original nonlinear dynamic optimization problem into an iterative "linear optimization <-> nonlinear analysis" process with linear static multiple loading cases for the optimization. The iterative optimization <-> analysis process is to capture the nonlinearities and the multiple loading cases reflect the nonlinear dynamic deformation progress of the structure within the optimization.

  • Benchmark of Topology Optimization Methods for Crashworthiness Design

    C. H. Chuang and R. J. Yang (Ford Motor Company)

    Linear structural topology optimization has been widely studied and implemented into various engineering applications. Few studies are found in the literature which deals with nonlinear structures during vehicle impact events. One of the major challenges for nonlinear structural topology optimization is the unavailability of design sensitivities in impact simulations, due to the highly nonlinear and computationally intensive nature of these problems. In this paper, three commercially available methods are reviewed and discussed: Equivalent Static Loads (ESL), Hybrid Cellular Automata (HCA), and Inertia Relief Method (IRM). A vehicle structure, subjected to a full frontal impact, is used to compare the topology optimization results generated using HCA and IRM.

  • A Topology Optimization Interface for LS-Dyna

    Dipl.-Ing. Nikola Aulig (Honda Research Institute Europe GmbH, Offenbach-Main, Germany), Dr.- Ing. Ingolf Lepenies (DYNAmore, Dresden, Germany)

  • Topology optimization with LS-TaSC and Genesis/ESL for crash-loading

    Dr. Andrea Erhart, Peter Schumacher, Nikolay Lazarov, Dr. Heiner Müllerschön (DYNAmore GmbH)

  • Topology optimization of crash structures – creativity versus computer-based algorithms

    Axel Schumacher (Bergische Universität Wuppertal, Wuppertal, Germany), Christopher Ortmann (Hochschule für Angewandte Wissenschaften Hamburg, Hamburg, Germany)

    The development of crash-loaded structures is still ambitious, especially if topology and shape variations have to be taken into account [1]. The research project CRASH-TOPO „Methodical and Software-Technical Implementation of Topology Optimization for Crash-loaded Vehicle Structures“ founded by the German Ministry of Education and Research (BMBF) work in this area. Research partners are the Automotive Simulation Center Stuttgart e.V. (asc(s), the DYNAmore GmbH, the SFE GmbH and the Hamburg University of Applied Sciences. Associated partners are Daimler, Opel, Porsche and the Goethe-University Frankfurt. The part of the Hamburg University of Applied Sciences is the development of the combined topology and shape optimization of profile structures (especially aluminium extrusion components) considering all relevant crash loads. We have an outer loop for the topology changes done by design rules and an inner loop for the shape variation done by mathematical optimization algorithms (using LS-OPT). The flexible description of the geometry is done by a mathematical graph together with the CAE software SFE CONCEPT. The crash simulation is done by LS-DYNA.


  • Topology Design Using LS-TASC Version 2 and LS-DYNA

    W. Roux (Livermore Software Technology Corporation, Livermore, California, USA)

    This paper gives an overview of LS-TaSC version 2, a topology optimization tool using LS-DYNA for the analysis of nonlinear structural behavior. The focus is on its capabilities, current development directions, and integration into an industrial design environment. Examples of using the new developments such as global constraints, geometric definitions such as symmetry and casting directions, and shells are given.


  • LSOPT/Topology Version 1

    Willem Roux, Tushar Goel (Livermore Software Technology Corporation), David Björkevik (Engineering Research AB)

    This paper presents LS-OPT/Topoloy, a new topology optimization tool. Topics such as its capabilities, current development directions, and integration into an industrial design environment are discussed.

  • Application of Topology Optimization for Crash with LS-OPT/Topology

    Heiner Müllerschön (DYNAmore GmbH), Nikolay Lazarov (University of Karlsruhe), Katharina Witowski (DYNAmore GmbH)

    Since end of 2009 a new software tool LS-OPT/Topology is available from LSTC. With LS-OPT/Topology nonlinear topology optimization with LS-DYNA can be applied for static and even for dynamic problems. ...

  • Preview of LS-OPT/Topology Version 2

    Willem Roux (Livermore Software Technology Corporation, Livermore, CA, USA)

    This paper gives a preview of LS-OPT/Topology version 2, a topology optimization tool. The focus is on its capabilities, current development directions, and integration into an industrial desgn environment. ...

  • Equivalent Static Loads Method for Non Linear Static Response Structural Optimization

    Gyung-Jin Park (Professor, Department of Mechanical Engineering, Hanyang University, Ansan City, Korea)

    Linear static response structural optimization using the finite element method for linear static analysis has been significantly developed. However, there is very little development of structural optimization where a non linear static analysis technique is required. To solve various structural optimization problems based on non linear analyses, ...


  • A Topology Optimization Tool for LS-DYNA Users: LS-OPT/Topology

    T.Goel, W. Roux, N. Stander (Livermore Software Technology Corporation)

    Topology optimization is a very powerful tool to develop new concepts an has widely used in engineering problems involving static loading conditions. However, there has been relatively little work for topology optimization of industrial size non-linear dynamic systems. The main issues are non-linear interactions among the material properties, contacts between parts, large strain-rates, transient behavior, etc. A hybrid cellular automata based method, combining cellular automata theory with the fully loaded...