structural optimization in cad software

STRUCTURAL OPTIMIZATION IN CAD SOFTWARE Nenad MARJANOVIC Biserka ISAILOVIC Mirko BLAGOJEVIC

Abstract: In this paper one way of integrating structural optimization and CAD tools is presented. Structural optimization is an automated synthesis of a mechanical component based on structural properties. In the first part of this paper two methods of CAD based optimization are described. After that three types of structural optimization are elaborated. Integrated structural optimization as method proper for structural optimization in concrete CAD software is particularly described. As illustration of suggested approach optimization of bracket clamped on the left side and saddled on right side by the vertical force is performed. Modeling, FEM analysis and optimization is performed using different workbenches in PLM software CATIA V5. Optimization results indicate improvement of objective function value of over 60 percent. Proposed approach is designer oriented. The designer is fully involved in optimization process, as well as in design process. This approach assures practical implementation of optimization results. Key words: Optimization, CAD, FEM

1. INTRODUCTION Computer Aided Design (CAD) tools become very popular and common within engineering and design departments. They considerably facilitate the designer work and some of them even offers powerful calculation function using Finite Element Method (FEM). However, there is still a lack of CAD tools that give the opportunity to proceed to optimization calculations. This is a bit surprising that a major concern for most manufacturers is optimization of a product before its launching. New competitive products must meet the growing demands of the market. They must be light-weighted, resourceefficient, durable, stable, etc. At the same time, the product must be introduced quickly into the market. These demands can only be met if optimization tools are

used in addition to establish CAD, CAE, DMU and/or PLM systems. Calculation of different product variants and improvements can be carried out on digital prototype at a very early project stage. Then, the number of required prototypes can be reduced which results in probable time and cost savings. The functionality, the handling and especially the integration and combination with other tools of the virtual product development process are of decisive importance. So far, the optimization tools have not been completely integrated in the design process. Among the few existing products that offer optimization capabilities for design, some of them propose to optimize a structure by using FEM. This roughly means that FEM calculations are performed at each of iterations of the optimization process in order to optimize the static or dynamic behaviour of the studied system. Optimization of mechanical systems is very difficult task because of very complex mathematical model which have to describe operating of real system in real circumstances. CAD based optimization can be performed using stand alone optimization or CAD imbedded optimization. Typical examples of stand-alone optimization are given in [1, 2] on gear train optimization sample. Some other optimization examples of concrete mechanical systems are presented in [3, 4, 5 and 6]. In reference [7] parameter - based topology optimization is given. The basic of the optimization approach, which is presented in this paper, is bubble method. The strategy of this method is an alternation of shape optimization and positioning of additional holes (bubbles). Three –dimensional structural optimization is described in [8]. This paper presents an automated process for interpreting three-dimensional topology optimization result into a smooth CAD representation. A tuning process is employed before the interpretation process to improve the quality of the topology optimization result. Paper [9] considers isogeometric structural shape optimization as special case of shape optimization. Extensive mathematical optimization engine is applied on relatively simply practical problem. Paper [10] presents a new approach to topology optimization based on implicit functions. The implicit functions are approximated by the same mesh and shape functions that are used for the solution of equilibrium equation. A web based interface for topology optimization program is presented in [11]. The paper discusses implementation issues and educational aspects as well as statistics and experience with the program. Paper [12] presents advanced solution methods in topology optimization and shape sensitive analysis. Topology optimization is usually employed first, in order to avoid local optima due to a crude initial layout, followed by shape optimization in order to fine tune the optimum layout. Beside foregoing there is large number of references in area of structural optimization but mostly they consider special methods and software for stand-alone structural optimization. Number and actuality of published research indicates importance and contemporarity of structural optimization topics. 27

2. GENERAL APPROACH TO CAD BASED OPTIMIZATION Optimization is a mathematical technique for minimizing or maximizing a objective function while satisfying the constraints, or:

Optimize subject to and

Weaknesses of this approach are that (1) only few PLM commercial software has optimization module and (2) possibilities of their optimization modules are limited. Initial Design CAD model

f ( x) g ( x ) ≤ 0, i = 1, ..., m i h ( x ) = 0, j = 1, ..., l j

Optimization Model

(1)

Optimization requires definition of design variables (x), objective function f ( x ) , and constraints functions

Optimization Engine

g i ( x ) and/or h j ( x ) .

The functions in pervious mathematical model can be any property of a product. Designers are almost never capable of foreseeing all design options in a product. Optimization can often find surprising or interesting solution that designer would not have thought of. CAD based optimization can be performed using two methods. The first method is stand alone optimization and the second is CAD imbedded optimization.

2.1. Stand alone optimization Stand alone optimization considers CAD independent optimization engine (software). In this case it is necessary to create link between CAD model and optimization model. This link can be established by using design variables. Optimization can be done only once and any change in CAD model mean repetition of entire optimization process. This optimization approach is shown in Figure 1.

Initial Design CAD model Link Optimization Model Optimization Engine Link Optimal Design CAD model Fig.1. Stand alone optimization

2.2. Imbedded optimization Imbedded optimization has an optimization engine integrated in CAD (PLM) software. A link between CAD and optimization model exists. It is easy to perform optimization even when changes are made in CAD model. This approach is design oriented. This optimization approach is shown in Figure 2. 28

Re Design

Optimal Design CAD model

Fig.2. Imbedded optimization

3. STRUCTURAL OPTIMIZATION Structural optimization is defined as an automated synthesis of a mechanical component based on structural properties, or as a method that automatically generates a mechanical component design that exhibits optimal structural performance. Structural optimization always considers some kind of stress and/or deformation analysis, which is performed using CAE (Computer Aided Engineering) tools. There are two kinds of CAE. The first kind is Mechanical CAE (MCAE) which involves structures (linear and nonlinear), explicit FEA (forming, crash, simulation), and multi-body dynamics (simulation). Second kind is fluid CAE (FCAE) which involves heat transfer/ conduction, Newtonian and non-Newtonian fluid flow, and mold flow simulation. Three types of CAE software exists stand alone, CAD linked and CAD imbedded CAE. Characteristics of stand alone CAE are standard FEA based CAE codes, special analysts oriented high accuracy, and independent CAD and pre-processing. CAD linked CAE is present trend; it involves automatic mesh generation methods. CAD imbedded CAE is design oriented approach. Structural optimization is divided into size, shape and topology optimization.

3.1. Size optimization Size optimization involves a modification of the cross section or thickness of finite elements. The optimization is carried out by mathematical optimization algorithms with different objective functions e. g. maximum stiffness or minimum weight. Many programming approaches were tested and implemented in finite element programs or special optimization programs. Due to the easy sensitivity calculation of for size optimization even realistic problems can be handled. It is the simplest method and it is applied to the design of truss structures. Figure 3 illustrates this type of structural optimization.

optimized design proposal for a given space. Figure 5 illustrates this type of structural optimization.

Shape and topology are given. Optimize dimensions and cross sections.

Optimize topology.

Fig.3. Size optimization Fig.5. Topology optimization

3.2. Shape optimization Compared to size optimization, shape optimization is more complex. The coordinates of the surface are regarded as design variables which will be modified during the optimization. Surface modification is also used to reduce stress peaks found in a design proposal. The resulting component shape is optimally adjusted to the strains resulting from the specified loads and boundary conditions. Thus the reliability and life of a component can be increased. The main difficulty with shape optimization is to transfer the surface changes to the finite element mesh. Only a few programs are capable of such a transfer without destroying the element topology. In this case design variables control the shape. There are various approaches to represent the shape. Figure 4 illustrates this type of structural optimization.

Topology is given. Optimize boundary shape.

Fig.4. Shape optimization

3.3. Topology optimization Before using a size or shape optimization, an initial design proposal has to be available. In the planning phase, a fundamental structure of the object can be found using topology optimization. Starting from known loads and boundary conditions and the maximum available design space, a design concept can be found which is as light as possible while meeting all requirements on, e.g., stiffness and durability. Areas that are not needed are removed from the design space. The new structure indicates the optimal energy flow. The result of the topology optimization serves as a design draft for the creation of a new FE model for the subsequent simulation calculation and shape optimization. This method provides the designer and the development engineer, even in the early planning stage, a tool capable of creating a weight-

3.4. Integrated structural optimization Shape optimization is characterized by small number of design variables, smooth definite results and unchanged topology remains (cannot make holes in design domain). On the other hand, topology optimization is characterized by extremely large number of design variables, non smooth indefinite results, and intermediate “densities” between void and full material, so optimization results, in this case, may be unrealistic. Because of these properties of two different types of optimization and characteristics of optimization modules in CAD software, it is rationally to integrate shape optimization and topology optimization. In this approach the designer decides the initial shape for shape optimization interactively with results on the topology optimization. Integrated structural optimization can be done throughout three-phase design process: (1) generate information about the optimal topology, (2) process and interpret the topology information, and (3) create a parametric model and apply standard optimization. Characteristics of the integrated approach are the following: (1) communications between shape and topology optimization are not easy, (2) the designer must provide many control parameters for optimization because the optimal solutions highly depend on the user defined parameters and (3) computation is very expensive. The main benefit of this approach is that designer is fully involved in optimization process, so optimal solutions can be practical.

4. INTEGRATED OPTIMIZATION OF TRUSS STRUCTURES IN PLM SOFTWARE CATIA CATIA is a 3D Product Lifecycle Management software suite, which supports multiple stages of product development (CAx), from conceptualization, design (CAD), manufacturing (CAM), and analysis (CAE). Catia V5 features a parametric solid/surface-based package which uses NURBS as the core surface representation and has several workbenches that provide KBE (Knowledgebased engineering) support. The bracket which is clamped on the left side and saddled on right side by the vertical force of 7000 N was used as example for truss structure optimization. CAD model of 29

the bracket was made in the Part and Sketcher workbenches in CATIA and it is shown in Figure 6.

objective function in this case was 114584,458 mm3 . Apperance of Von Mises stresses is shown in Figure 10.

Fig.6. CAD model of bracket The Optimization was performed in Product Function Optimization workbench. The aim of optimization was minimization of volume of bracket. In the first case design variable was height of bracket. Constraints were maximum value of Von Mises stress (250 MPa), as well as implicit constraint of design variable. Values of Von Mises stresses were obtained using Generative Structural Analysis workbench and are shown in Figure 7.

Fig.9. Shape of the bracket defined by B-Spline

Fig.10. Von Mises stresses – Shape optimization From Figure 10. it is obviously that the inner part of the bracket is at low stress, so materail can be removed from that area. In the next step, integrated optimization was performed combining topology and shape optimization. In the first case the inner hole was defined by B-Spline with nine control points (Figure 11). Fig.7. Von Mises stresses – Size optimization – Case I Optimal value of objective function in this case was 164486,962 mm3 . In the second case, the similar optimization model was used, with two design variables. Optimal value of objective function in this case was 126532,280 mm3 . Apperance of Von Mises stresses is shown in Figure 8.

Fig.8. Von Mises stresses – Size optimization – Case II Two previous cases are tipical samples of size optimization. After size optimization, shape optimization was performed. Shape of the bracket was defined by BSpline, which is shown in Figure 9. Optimal value of 30

Fig.11. Inner hole defined by B-Spline

Optimal value of objective function in this case was 80645,354 mm3 . Apperance of Von Mises stresses is

shown in Figure 13. Better control of shape can be done by using more control points. In that case optimization model becomes more complex, and computational time and effort becomes enormous. Furthermore, changes of design vairables during optimization process can produce anomalous shape of inner hole. In some cases inner contour can interrupt themself or outer contour. Then stress distribution becomes abnormal and huge stress concetration appears in some points. That rapid stress growth causes significant violation of constrain in optimization model and optimization process can fall down. This weakness can be avoided by including new implicit constraints on design variables, thus optimization model becomes more and more complex.

Fig.14. Von Mises stresses – Integrated optimization – Case I Reduction of objective function values, for diferent optimization cases is shown in Figure 15. Objective function value [ mm3 ]

Objective function reduction [%]

164486,962

0

Fig.12. Von Mises stresses – Integrated optimization – Case I

126532,280

23,07

In the second case of integrated optimization inner hole was defined by the triangle whose sides are parallel to outer sides of bracket. Corners of triangle are rounded because of stress concetration (Figure 13).

114584,458

30,33

80645,354

50,97

67591,169

58,91

Optimization case

1.8E+05

Fig.13. Inner hole defined by triangle Optimal value of objective function in this case was 67591,169 mm3 . Apperance of Von Mises stresses is shown in Figure 14. Optimization results show successive improvement of objective function values i. e. decrease of bracket volume. Through five stages of optimization, initial optimal bracket volume value of 164486,962 mm3 decreases to 67591,169 mm3 , or about 60 percent.

Objective function

1.6E+05 1.4E+05 1.2E+05 1.0E+05 8.0E+04 6.0E+04 4.0E+04 2.0E+04 0.0E+00 1

2

3

4

5

Optimization case Fig.15. Objective function values for different optimization cases 31

5. CONCLUSION In this paper one way of integrating structural optimization and CAD tools is presented. Structural optimization is an automated synthesis of a mechanical component based on structural properties. In the first part of this paper two methods of CAD based optimization are described. Imbedded optimization has an optimization engine integrated in CAD (PLM) software. Stand alone optimization considers CAD independent optimization engine (software). Structural optimization is defined as an automated synthesis of a mechanical component based on structural properties, or as a method that automatically generates a mechanical component design that exhibits optimal structural performance. Structural optimization always considers some kind of stress and/or deformation analysis, which is performed using CAE (Computer Aided Engineering) tools. Three types of structural optimization are elaborated. Integrated structural optimization as method proper for structural optimization in concrete CAD software is particularly described. As illustration of suggested approach optimization of bracket clamped on the left side and saddled on right side by the vertical force is performed. Modeling, FEM analysis and optimization are performed using different workbenches in PLM software CATIA V5. Optimization results indicate improvement of objective function value of about 60 percent. Proposed approach is designer oriented. The designer is fully involved in optimization process, as well as in design process. This approach assures practical implementation of optimization results.

[7] SCHUMACHER A., Parameter-based optimization for crashworthiness structures, 6th World Congresses of Structural and Multidisciplinary Optimization, Rio de Janeiro, June 2005., Brazil, pp. 1 – 10. [8] MING H., H., YEH L. H., Interpreting threedimensional structural topology optimization results, Computer and Structures, 83 (2005), pp. 327 – 337. [9] WALL A. W, FRENCEL M. A, Cyron C., Isogeometric structural shape optimization, Computer Methods in Applied Mechanics and Engineering, 197 (2008), pp. 2976 – 2988. [10] BELYTSCHKO T., XIAO S. P., PARTIMI C., Topology optimization with implicit function and regularization, International Journal for Numerical Methods in Engineering, 2003., 57, pp. 1177 – 1196. [11] TCHERNIAK D., SIGMUND O, A web-based topology optimization program, Structural Multidis. Optim., 22, 2001., pp. 179. 187. [12] PAPADRAKAKIS M., TSOMPANIKIS Y., Advanced solution methods in topology optimization and shape sensitivity analysis, Engineering Computations, Vol. 13, No. 5, 1996., pp 57 – 90.

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Nenad MARJANOVIC, Prof. D.Sc. Eng. University of Kragujevac Faculty of Mechanical Engineering in Kragujevac S. Janjic street, 6 34000 Kragujevac, Serbia [email protected] Biserka ISAILOVIC, B.Sc., Eng. Car factory “ZASTAVA AUTOMOBILI” Profit center “Zastitna radionica” 4 Trg topolivaca, 34000 Kragujevac, Serbia [email protected] Mirko BLAGOJEVIC, Assist. Prof. D.Sc., Eng. University of Kragujevac Faculty of Mechanical Engineering in Kragujevac S. Janjic street, 6 34000 Kragujevac, Serbia [email protected]