Application of Topology Size and Shape Optimization Methods in Polymer Metal Hybrid Structural.docx

1、Application of Topology Size and Shape Optimization Methods in Polymer Metal Hybrid StructuralApplication of Topology, Size and Shape Optimization Methods in Polymer Metal Hybrid Structural Lightweight EngineeringAbstractApplication of the engineering design optimization methods and tools to the des

2、ign of automotive body-in-white (BIW) structural components made of polymer metal hybrid (PMH) materials is considered. Specifically, the use of topology optimization in identifying the optimal initial designs and the use of size and shape optimization techniques in defining the final designs is dis

3、cussed. The optimization analyses employed were required to account for the fact that the BIW structural PMH component in question may be subjected to different in-service loads be designed for stiffness, strength or buckling resistance and that it must be manufacturable using conventional injection

4、 over-molding.The paper demonstrates the use of various engineering tools, i.e. a CAD program to create the solid model of the PMH component, a meshing program to ensure mesh matching across the polymer/metal interfaces, a linearstatic analysis based topology optimization tool to generate an initial

5、 design, a nonlinear statics-based size and shape optimization program to obtained the final design and a mold-filling simulation tool to validate manufacturability of the PMH component.KeywordsTopology, Optimization, Hybrid Structural, Lightweight Engineering1. IntroductionLightweight engineering f

6、or automobiles is progressively gaining in importance in view of rising environmental demands and ever-tougher emissions standards. Current efforts in the automotive lightweight engineering involve at least the following five distinct approaches 1: (a) Requirement lightweight engineering which inclu

7、des efforts to reduce the vehicle weight through reductions in component/subsystem requirements (e.g.a reduced required size of the fuel tank); (b) Conceptual lightweight engineering which includes the development and implementation of new concepts and strategies with potential weight savings such a

8、s the use of a self-supporting cockpit, a straight engine carrier, etc.; (c) Design lightweight engineering which focuses on design optimization of the existing components and sub-systems such as the use of ribs and complex crosssections for enhanced component stiffness at a reduced weight; (d) Manu

9、facturing lightweight engineering which utilizes novel manufacturing approaches to reduce the component weight while retaining its performance (e.g. a combined application of spot welding and adhesive bonding to maintain the stiffness of the joined sheet-metal components with reduced wall thickness)

10、; and (e) Material lightweight engineering which is based on the use of materials with a high specific stiffness and/or strength such as aluminum alloys and polymer-matrix composites or a synergistic use of metallic and polymeric materials in a hybrid architecture (referred to as polymer metal hybri

11、ds,PMHs, in the remainder of this manuscript). In the present work, the problem of integration of the engineering optimization methods and tools into the aforementioned lightweight engineering efforts, specifically into PMH technology for body-in-white(BIW) load-bearing automotive components process

12、ed by techniques such as injection over-molding 2 or metal over-molding 3. Such components are typically designed for stiffness and buckling resistance and their performance is greatly affected by the design of the plastic ribbing structure injection molded into a sheet-metal stamping.In conventiona

13、l automotive manufacturing practice, metals and plastics are fierce competitors. The PMH technologies, in contrast, aspire to take full advantage of the two classes of materials by combining them in a single component/sub-assembly. The first example of a successful implementation of this technologic

14、al innovation in practice was reported at the end of 1996, when the front end of the Audi A6 (made by Ecia, Audincourt/France) was produced as a hybrid structure, combining sheet steel with elastomer-modified poly-amide PA6 - GF30 (Durethan BKV 130 from Bayer). A key feature of hybrid structures is

15、that the materials employed complement each other so that the resulting hybrid material can offer an enhanced overall structural performance.Currently, PMHs are replacing all-metal structures in automotive front-end modules at an accelerated rate and are being used in instrument-panel and bumper cro

16、ss-beams, door modules, and tailgates applications. Moreover, new PMH technologies are beingintroduced.The main PMH technologies currently being employed in the automotive industry can be grouped into three major categories: (a) Injection over-molding technologies 2; (b)Metal-over-molding technologi

17、es combined with secondary joining operations 3; and(c) Adhesively-bonded PMHs 4. A detailed description for each of these groups of PMH manufacturing technologies can be found in our recent work 5. The objective of the present work is to extend the aforementioned two-step optimization approach to B

18、IW load bearing PMH components. A typical all-metal BIW load bearing component, Figure 1(a), consists of two flanged U-shape stampings joined along their matching flanges by spot-welding (often complemented by adhesive bonding). When such an all-metal component is replaced with a PMH component, Figu

19、re 1(b), one of its stampings is removed and the exterior of the remaining stamping reinforced using an injection-molded thermoplastic rib-like structure. Hence, the objective of the present work is to address the optimal architecture of the ribbing structure with respect to different loading requir

20、ements (axial compression, bending,twisting) and different design requirements (e.g. stiffness, strength, buckling resistance).The examples considered show how topology optimization may be used to suggest good initial designs, but also demonstrates how a topology optimization followed by a detailed

21、size and shape optimization may be used to provide efficient designs satisfying performance and manufacturing constraints.Fig.1 (a) A twin-shell all-metal rear cross-roof member and (b) its polymer metal hybrid counterpart consisting a single metal-shell stamping and injection-molded plastic ribbing

22、.The organization of the paper is as follows: An overview of the basics of topology,size and shape optimization methods is presented and a brief description of the main computational tools used in the present work is given in Section II. The results obtained in the present work are presented and dis

23、cussed in Section III. The main conclusions resulting from the present work are summarized in Section IV. 2. Computation Procedure2.1 The Basics of Structural Topology, Size and Shape OptimizationStructural optimization is a class of engineering optimization problems in which theevaluation of an obj

24、ective function(s) or constraints requires the use of structuralanalyses (typically a finite element analysis, FEA). In compact form, the optimizationproblem can be symbolically defined as:Minimize the objective function f (x)Subject to the non-equality constraints g( x) 0 and to the equality constr

25、aintsh( x) =0Where the design variables x belong to the domain Dwhere, in general, g( x) and h( x) are vector functions. The design variables x form a vector of parameters describing the geometry of a product. For example, x , f (x)g( x) and h( x) can be product dimensions, product weight, a stress

26、condition defining the onset of plastic yielding, and constraints on product dimensions,respectively.Topology OptimizationTopology optimization methods allow the changes in the way substructures are connected within a fixed design domain and can be classified as (a) discrete element(also known as th

27、e ground structure) approach; and (b) continuum approaches. In thediscrete element approach, the design domain is represented as a finite set of possiblelocations of discrete structural members such as truss, frame, and panels. By varying the width/thickness of each member in the design domain betwe

28、en zero (in this case the element becomes nonexistent) and a certain maximum value, structures with different sizes and topologies can be represented. In the continuum approach, the design domain is represented as the continuum mixture of a material and “void” and the optimal design is defined with

29、respect to the distributions of the material density within the design space. Since the discrete element approach utilizes a collection of primitive structural members, it allows easy interpretation of the conceptual design. However, potentially optimal topologies may not be attainable by the number

30、 and types of possible member locations defined in the design domain. The continuum approach, on the other hand, does not have this limitation, while it may be computationally more expensive. Over the last decades, major advances have been reported in the area of the discrete element structural opti

31、mization 6-10.Size OptimizationWithin size optimization approach, the dimensions that describe product geometry areused as design variables, x. The application of size optimization is, consequently, mostly used at the detailed design stage where only the fine tuning of product geometry is necessary.

32、 Size optimization is typically done in conjunction with feature-based variation geometry 11 which is available in many modern CAD programs. With present-day availability of fast personal computers, size optimization is relatively a straightforward task and it typically requires no re-meshing of the

33、 finite element models during optimization iterations. A difficulty may arise, however, when extremely large finite element models or highly nonlinear phenomena need to be analyzed, in which case surrogate (simplified) models are typically employed.Shape OptimizationShape optimization allows the cha