Structural Optimization by a Combinational Approach of ANSYS Analyzer and an Improved

Structural Optimization by a Combinational Approach of ANSYS Analyzer and An improved ACO Algorithm

Jianfeng Zhou

Guilin University of Electronic Technology, Guilin, 541004, China

Email:

Abstract. It is significant to improve the efficiency of structural repeat analysis. In this paper, the commercial FEM procedure, namely ANSYS which has high efficiency and precision in the computation, was applied to serve as a tool solving the structural analysis. An interface was built to link the ANSYS software and the user-defined structual optimization algorithm. By this interface, a combinational approach of optimization algorithm, such as Ant Colony Optimization (ACO) algorithm, and ANSYS analyzer for structural optimization problem was provided. Several numerical examples were presented and solved by the combinational approach. The comparisons between the combinational approach here and some published materials had been obtained in terms of effectiveness. The comparisonsprove that because of combining both advantage of the ANSYS Analyzer and optimization algorithm, the efficiency of structural optimization were greatly improved. And this combinational approach of optimization algorithms and ANSYS analyzer was efficient, effective, practical and convenient for structural optimization.It was also emphasized that in this paper, an improved ACO algorithm was presented.

Key words:Optimization; ANSYS; ACO; FEM

Introduction

Structural optimization has been and continues to be a large field of active research. It is well known that mathematical programming (MP) and optimality criterion methods have received great interest and application in structural optimization successfully[1]. Moreover, some evolutionary algorithm, such as GA (Genetic Algorithm), ACO (Ant Colony Optimization) algorithm has been adopted to effectively solve the structural optimization, which belongs to soft computing techniques and can avoid the complexity of implementation of MP approach, such as the need of the derivatives [1].

Generally, strucutural optimization procedure includes two parts. The one is the structural analysis, which mostly use Finite Element Analysis mehtods. The other one is structural optimization algorithm. The relationship between the structural analysis and structural optimization algorithm is generally shown like this:

Fig 1 general procedure of structure optimization Fig2 process of combinatioal procedure

FEA has become a standard method of structural analysis. However coding ones own element codes required great effort and lengthy time. Moreover, in most case once the character of structure optimization problems is changed, the FEA codes should be rewritten corresponding.

In this paper, a combinational approach of optimization algorithms and ANSYS analyzer is presented. Namely, the commerciall FEA software ANSYS is applied to serve as an analyzer to solve the structural analysis. And some advanced and effective algorithm is used to be an optimizer. Once one build the finite element model in the analyzer, set the user-defined interface between the analyzer and optimizer,no programming effort or user extra intervention is requested to conduct the optimization process. This combinational approach provides the ease in structure analysis and design, flexibility to conduct multidisciplinary analysis and significant saving in terms of time and money partly due to the advantages of FEA software. The optimization algorithm which serve as the optimizer is also can easily replaced. Discrete and continuous designvariables can be handled.

In this paper, we choose the ACO algorithm as the optimizer, and improved the ACO algorithm by improving the pheromeon trails update rule. Several numerical examples were presented and solved by the combinational approach.

ant colony algorithm for strucutural otpimzation

As a new evolutional optimization method, ACO algorithmhas been successful applied to solve several NP-hard combination optimization problems, such as TSP (Traveling Salesman Problem), QAP (Quadratic Assignment Problem) and so on[2][3][4][5]. The advantage of ACO algorithm, which includes positive feeding-back, coordination and implicit parallelism, make it has a broad future in application. Application of ACO algorithm to structural optimization was studied by Li, Q.Y [6], Serra, M et al [7], just to name a few. It is proved that ACO algorithm is a promising method to solving the structural optimization.

Ant colonies could always find the shortest path between the nest and the food source. When an ant is walking on a path, it will deposit on its road a certain kind of chemical substance called pheromone which can be evaporated gradually as time goes on and can recognized by other ants. The probability of the path being chosen by later ants is proportional to the amount of the pheromone on it. A trial with more pheromone will be more likely to be chosen by other antsFinally, the shortest path will have the most pheromone on it and ants will choose the specific path to walk.

The improved ant colony optimization algorithm

How to take advantage of pheromone trails and heuristic information is the key of ACO algorithm. In order to promote the efficiency of pheromone trails, the pheromone trail update rule is improved as followed:

(2)

Herein, CC is the initial intensity of pheromone trails, cycle is the number of iteration and L is the value of objective function. aretwouser-defined parameters, which distribute in [0－1]. L is the length of the tour, p is the pheromone trail evaporation rateAll the feasible tour can release the pheromone, including the best tour. The relation among the number of iteration, the initial intensity of pheromone trail and the increment of pheromone is built.

The method of calculated the increment of pheromone is the one of most important factors in the ACO algorithm. Different increment of pheromone in one train will directly affect its probability to be chosen in next generation, and eventually, change and affect the directions of ant search road. In equality (2), the increment of pheromone is proportional the reciprocal of the objective value. Thus the objective is bigger, the increment is less. It is logical and necessary to preserve the “good” trail and discard the “bad” trail currently. Moreover , the equality (2), as a penalty function, CC*(1-P)cycle presents the average value of current amount of the pheromones. The introduction of parameters can adjust the velocity of pheromone increment, in order to keep the increment of pheromone to a suitable amount. In that way, the increment of pheromon will neither grow too fast or too slow. As a result, the “bad” trail can be preserved longer and the probability to be chosen increased. That is to say, the character of diversity in ant colonies can be substained steadly. Consequently, the prematurely of algorithm can be avoided.The optimal result can be more robust.

Dynamic data exchanging between optimizer and analyzer

The FEA software used to interface with the optimizer is ANSYS. ANSYS architecture provided easy integrated pre-and post-processing. Building a finite element mode is a very easy task. More importantly, ANSYS allow user to exploit secondly in the environment of ANSYS with the aid of ANSYS parametric design language (APDL). A structural analysis input file coded by user contains in APDL language contains the FEA model data which is required in solving, for example, the area and the length of the truss and bar. This input file can be sent to ANSYS and executed by ANSYS each iteration. An output file which contains much result data, such as stresses, displacement and so on was generated by analyzer. The optimizer can availably extract the concern data from the above output file. If the convergencecriteria are satisfied, the program stops and the best design is output to the screen.

The process of the overall procedure for structural optimization is shown in Fig2.

Numerical examples

Example1: 10 bar truss [6]

The 10 bar cantilever truss problem have been used as a benchmark problem to verify the efficiency of diverse optimization methods. The initial geometry of the structure is shown in Fig3, and the loading conditions, material properties and constraints are given in reference [6].

Fig3. 10 bar truss, initial geometry Fig 4. 72 bar space truss, initial geometry

The optimal design given by ACO based combinational approach and other algorithm are compared and listed in table 2.

In our studies, the continuous value field of the design variables is equally divided to discrete segment.

It can be also seen from the table 2 that the optimal result (5070.49) given by ACO algorithmis just with a weight about 0.06% higher than the best design obtained (5067.3) by Ringertz in Ref.8 by now.

TABLE 2. Comparison of the design variables and objective values for 10 bar truss
Conf. / This paper / Ref 13 / Ref9 / Ref9 / Ref10 / Ref8
method / ACO based / ANSYS
One order / zigzag / DDDU / PGA / GLM
1 / 30.812 / 30.374 / 30.9662 / 30.902 / 29.355 / 30.9662
2 / 0.100 / 0.55216 / 0.1000 / 0.100 / 0.5172 / 0.1000
3 / 23.483 / 26.281 / 23.7568 / 23.545 / 24.566 / 23.7568
4 / 14.758 / 15.504 / 14.9362 / 14.960 / 14.936 / 14.9362
5 / 0.100 / 0.13732 / 0.1000 / 0.100 / 0.2082 / 0.1000
6 / 0.449 / 0.42772 / 0.3063 / 0.297 / 0.8460 / 0.3063
7 / 7.778 / 7.2686 / 7.4698 / 7.611 / 7.0222 / 7.4698
8 / 21.040 / 20.610 / 21.2322 / 21.275 / 21.237 / 21.2322
9 / 21.389 / 21.762 / 21.1226 / 21.156 / 22.334 / 21.1226
10 / 0.100 / 0.1000 / 0.1000 / 0.100 / 0.10030 / 0.1000
weight / 5070.49 / 5119.42 / 5067.71 / 5069.4 / 5116.416 / 5067.3
TABLE 4. Comparison of the design variables and objective values for 72 bar truss
section number / This paper / Ref 9 / Ref 11 / Ref 12
1 / 0.16 / 0.1564 / 0.1585 / 0.1571
2 / 0.71 / 0.5457 / 0.5936 / 0.5385
3 / 0.33 / 0.4106 / 0.3414 / 0.4156
4 / 0.51 / 0.5692 / 0.6076 / 0.5510
5 / 0.46 / 0.5237 / 0.2643 / 0.5082
6 / 0.505 / 0.5171 / 0.5408 / 0.5196
7 / 0.1 / 0.1000 / 0.1000 / 0.1000
8 / 0.1075 / 0.1001 / 0.1509 / 0.1000
9 / 0.96 / 1.2683 / 1.1067 / 1.2797
10 / 0.5125 / 0.5116 / 0.5792 / 0.5149
11 / 0.1 / 0.1000 / 0.1000 / 0.1000
12 / 0.1 / 0.1000 / 0.1000 / 0.1000
13 / 1.7375 / 1.8862 / 2.0784 / 1.8931
14 / 0.47 / 0.5123 / 0.5034 / 0.5171
15 / 0.1 / 0.1000 / 0.1000 / 0.1000
16 / 0.1 / 0.1000 / 0.1000 / 0.1000
Weight(kg) / 373.467 / 379.62 / 388.63 / 379.67

Example 2: 72 bar space truss

A 72 bar truss structure is shown in Fig 4. The listing of member grouping can be found in Ref [9]. The material constants, load case and constraint values are also given in table [9].

The optimal design given by improved ACO based combinational approach and other algorithm are compared and listed in table 4. It is can be seen from the table4, the combinational approach behaved as well as other algorithms.

Conclusion

A combinational approach of improved ACO optimization and ANSYS analyzer for structural optimization has been presented in this paper. The final designs of twostructural optimization problems have been obtained using this approach and compared with the previously obtained designs. The comparison shows the optimal result given by this approach is as well as that given by optimality criteria method and mathematic programming method. However, this combinational approach provides more flexibility, ease in structural optimization.

References

1. Jose Herskovits et al, Proceedings of 6th world congress on structural and multidisciplinary optimization. Rio de Janeiro, 30 May-3 june 2005.

2. Colorni A, Dorigo M, Mariezzo V., Distributed optimization by Ant colonies, Proc. of the 1st Euro. Conf. on artificial life, France: Elsevier publishing 1991, 134-142.

3. Colorni A, Dorigo M, Maniezzo V., An investigation of some properties of an ant algorithm, Proc. Of the parallel problem solving from nature conference (PPSN’92), Belgium: Elsevier publishing, 1992, 509-520.

4. Zhang Jihui, Xu Xinhe., A new evolutionary algorithm –ant colony algorithm, Systems engineering―Theory & Practice， 1999，(3)：84-87. (in Chinese)

5. Ma Liang, Ant algorithm for the degree-constrained minimum spanning tree., Journal of systems engineering. 1999, 14(3):211-214. (in Chinese)

6. Yubing Gong, Quanyong Li et al, The Application of Ant Algorithm in structural optimization, Proceedings of WCSM06, 2005, NO.4101

7. Serra, M., Venini, P., On some application of Ant Algorithm Optimization metaheuristic to structural optimization problems, Proceedings of WCSM06, 2005, NO.3101

8. Ringertz, U.T., Onmethods for Discrete Structural Optimization. Eng. Opt. 1988, Vol.13:47-64

9. Qian Lingxi, Optimization design for engineering structures. Beijing: Hydro-Electric Press, 1983 (in Chinese)

10. Wu, J.Y. , Wang, X.C.，A parallel genetic design method with coarse grain. Chinese Journal of Computational Mechanics, 2002, Vol. 19, No.2: 148-153 (in Chinese)

11. Schmit, L.A., Farshi,B., Some approximation concept for structural synthesis. AIAA J.12(2) 231-233(1974).

12. Berk , L., Khot,N.S., Use of optimal criteria methods for large scale systems. AGARD lectures series No.70, Structural optimization 1-29(1974)

13．Xie, Z.X., A structural optimal design based on ANSYS, Degree’s thesis, Guilin University of Electronic Technology, 2005( in Chinese).