c 

Army Research Laboratory 

Aberdeen Proving Ground, MD 2 1005-5069 

On the Application of Genetic 

Algorithms for Optimization 

of RTM Process Parameters 

Bruce K. Fink 

Weapons and Materials Research Directorate, ARL 

Roopesh Mathur and Suresh G. Advani 

University of Delaware 

Approved for public release; distribution is unhitd. 
Abstract 

Resin infusion processes are finding increasing applications in the manufacture of composite 

parts that have geometric and material complexities. In such cases, the placement of gates and 

vents is nonintuitive and may require expensive repetitive experimentation. Finite element-based 

resin-flow simulation codes have been successMIy used for modeling and analysis of the 

mold-filling process. Such filling simulations, when coupled with a search algorithm, can also 

prove useful for optimal design of the filljug process. Genetic algorithms (GAS) mimic natural 

selection and can efficiently “evolve” near-global optimal solutions kom a large number of 

alternative solutions. In this paper, GAS are used to optimize gate and vent locations for the 

resin-transfer molding (RTM) process in order to minimize fill times and dry-spot formation. A 

process performance index, or cost function, is defined, which incorporates the fill time and dryspot formation as primary variables. A part having material and geometric complexities was 

chosen for a case study. GA and mold-filling simulations were used interactively to search for 

optimal gate and vent locations to locate near-optimal solutions. The GA was able to find good 

solutions using less than 1% of simulations of the possible permutations of gates and vents. The 

case study was also repeated in the presence of racetrackjug channels. Agam, the optimal 

locations were found by the GA using less than 1% of all possible combinations. 

ii 
Acknowledgment 

The authors gratefully acknowledge the help of Dr. Murat Sozer from the University of 

Delaware in writing the LBASIC scripts for this work qd for his many helpful discussions. 

_.. 

111 
iv 
. 

1. Introduction . . . . . . . . . . . . . . . . . . . . *** ..*..........*...*...**.*............*...... ~.....***...~...,**....~.~.*...~....~....* 1 

2. 

3. 

3.1 Optimization of Design ....................................................................................... S 

3.2 SGA Procedure .................................................................................................... 7 

3.3 Application of SGA to Gate and Vent Location Optimization ........................... 10 

3.4 Optimization With Racetracking Effects ............................................................ 13 

4. Results . . . . . . . . . . ..*....~...~...*.*.*......*~.....~.*.*...........~***....~....~*.*.*..........***-...~.....***.....~....*.*~ 13 

5. Racetracking Study .~.*.......*~.....~..**.....~........*......~~..*..*..~.........*...........*.**.~......*........ 16 

6. Discussion .. . . . . ..****.......*..*....*..~.*................~ . . . ..~..~..........***....~......**~~....~..~.............* 19 

6.1 

6.2 

7. 

8. 

9. References .*..............*....*~..........*...~ . . . . . . . . . ..*..~........*.............................**............*.**. 2s 

Table of Contents 

Acknowledgment . . . . . ..~....**..........*........**..~.........*..*.....*... . . ..*.......*....I.~......*.*.......*...- ,.. 

111 

List of Figures . . . . . ..*...*...........**a...... . . . ...**...*..........*.......**...*.....*..*.* . . . . . . . . . . . . . . . . . ...*....* vii 

Background 3 . ..**....*......*................. ..~...~~..~...........~....~....~...........~~~..~.....*.~.. *...*.....*... 

Optimal Design and GAS ~.~..I*....~~..~.......**...~~.....*.. . . ..~........*~.~~..~....*~~.~.~.....*......~...~. S 

Racetracking Case ............................................................................................... 20 

Resin Waste Through Vent ................................................................................. 20 

Further Refinement: Finding Global Optima ..................................................... 21 

Conclusions . ..**..~~*................,,......**.**......~......*..*,..*........**......*...~..*...~...........~........*. 22 

Distribution List ~.,,............*,........****..*..............*~*. ..~....~.~.**.*~.....~.~~..~..~..........* . . ...*.* 27 

Report Documentation Page .. ..*................... . . . . . . ..~~..*.*.....~..~..*.~.....~..~...~..~.............~ 47 

V 
vi 
List of Figures 

Figure 

1. 

2. 

3. 

4. 

5. 

6. 

7. 

8. 

9. 

10. 

11. 

12. 

Processing Steps in RTM . . . ..*.....*.....*............~**.......*... .*.....,....*...*..,,......*.~~.......~.*....* 

Schematic of Optimal Design for the RTM Process .. . . . e .. . ..*...... .~.~...~.~..~...~.1..~.......~. 

A Function With Multiple Peaks: A Gradient-Based Method is Likely 

to Find the Local Peak at Point A, While a GA Will Settle on Point B, 

Near the Global Maximum *......*.......**..,...........**.* *........,.........~*.*.................*.....*.*..*. 

Schematic of LIMS-Based Optimization Using GAS ..* . . . ..*..........................*........ *.. 

Reproduction, Crossover, and Mutation Operators in GAS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..~.... 

Planar Approximation of the Bed of a Vehicle or Trailer Used for Optimization.... 

Plot of Cost Function With Generation Number for Each Case . . ...**.........*..**......**.* 

Optimal Gate and Vent Placement for Each Case . . . . . . . . . . . . . . ..*.......*...**......*.***.....*..*... 

Plot of Cost Function With Generation Number for Racebacking Study . . . . . . . . . . . . . . . . I 

Optimal Gate and Vent Placement for Racetracking Study With Two 

Gates and One Vent ..*...........*................,,..*....**.....,................*...*.....*...............*.*...*.. 

Flow-Front Locations With the Optimal Gate and Vent Locations for the 

Racetracking Case Optimized by the GA . . . . ..*..*.....*...........*........*......**.**.*................ 

Improved Optima for the Placement of Gates and Vents ..,............................... e .. . . . . . 

m 

2 

6 

7 

8 

9 

11 

14 

15 

17 

18 

19 

23 

vii 
. . . 

Vlll 
1. Introduction 

Liquid-injection molding processes, such as resin-transfer molding (RTM), are being used in 

the manufacture of composite structures that have varying material properties in aerospace and 

defense applications. These processes are attractive, since they enable the manufacture of parts 

with good strength-to-weight ratio, with material properties tailored to specifications, and in 

desired “net” shapes. 

In RTM, the reinforcement material or “preform” is placed inside a mold. The mold is 

closed, and the resin is injected into it at high pressure through inlet ports or “gates.” Outlet 

ports or “vents” are used to enable the displaced air to escape out of the mold. The resin 

impregnates the preform and polymerizes to form the solid part, which is then demolded, as 

shown in Figure 1 [ 11. The manufacture of these complex composite structures by RTM may 

lead to the problem of “dry spots,” which are areas not wetted-out by the resin due to the 

trapping of air pockets between flow fronts, thus affecting the quality of the manufactured parts. 

Mold-filling simulations can track the flow-front location during the impregnation of the 

preform, once the user has specified the locations of inlet gates and vents. However, there are as 

many choices for gate and vent locations as there are nodes in the ftite element (FE) mesh for 

the mold geometry. To find the globally optimal locations, one would have to run a large 

number of simulations. This number could be reduced if an appropriate optimization technique 

were used. Optimization of the filling process is critical, due to the need to decrease the process 

cycle time and to complete the filling before the resin starts to cure. 

For parts having material and geometric complexities, the location of gates and vents is 

nonintuitive and extensive trial and error is involved in optimizing their position. Hence, there is 

a need for a systematic search method that can be interactively coupled with filling simulation 

capabilities to determine optimally placed gates and vents in order to minimize fill times, as well 

as dry-spot formation. Of the search techniques studied, genetic algorithms (GAS) have been 

proven as powerful and robust search methods in dealing with highly nonlinear and large spaces 

1 
5. Demoldlng and Flnal 

2. Lay-up and Draping 4. Rosin InJectIon and Cure 

3. Mold Closure 

Figure 1. Processing Steps in RTM. 

having many possible local optima. In this case, the search space consists of a large number of 

nodes from FE models and, hence, the number of possibilities is formidable. In addition, with 

respect to the location of gates and vents, the trends in dry-spot formation and fill time are 

nonlinear. Hence, GAS were selected as a search method. 

In the following sections, some of the pertinent body of work on modeling and simulation of 

RTM, GAS, and model-based optimization and its application to RTM is reviewed, A 

description of the operation of a simple genetic algorithm (SGA) is given. The implementation 

of the SGA with the help of a case study is described, and the results are presented and 

discussed. It was found that GAS could efficiently locate near optimal gate and vent locations 

for the manufacture of complex composite parts by RTM, where the optimal locations are not 

obvious to the designer. The near-optimal gate locations are then used as a starting point to 

converge onto a globally optimal gate location. 

. 

2 
2. Background 

l 

The flow of resin in porous media is governed by Darcy’s Law, which states that the velocity 

of a fluid flowing through a porous medium is directly proportional to the driving pressure drop: 

where z is the average velocity, VP is the pressure gradient in the fluid, K is a second rank = 

permeability tensor, and 77 is the viscosity of the resin. This can be coupled with the continuity 

equation for incompressible flow (equation [2]) to give a Laplace equation (equation [3]) for the 

pressure field inside a fibrous porous media permeated by the fluid: 

v&o, 

and 

(2) 

(3) 

This equation can be discretized using FE methods that can be used for simulation of the filling 

of molds in RTM processes [2-51. 

The flow of resin in RTM has been modeled by the discretization of the governing partial 

differential equation (i.e., equation [3]) using the FE method [2, 31. The solution involves 

tracking a moving boundary either using control-volume techniques [4-61 or the movement of a 

saturation field [7, 81. Simulation software, such as Liquid-Injection Molding Simulation 

(LIMS), Version 4.0 [4, 91, uses control volume techniques to simulate the resin flow in 

3 
two-dimensional (2-D) molds and in thin three-dimensional (3-D) parts. One may also use the 

saturation field approach for 2-D or 3-D mold filling. However, the central processing unit 

(CPU) time is extremely large for 3-D mold filling [lo]. Nevertheless, the codes essentially 

capture the physics of the process. Jn addition, LIMS can be used to investigate phenomena such 

as racetracking effects (preferential flow along edges of a mold) and to test control schemes for 

mold filling [ 113. 

Usually, the geometry; material parameters; gate and vent positions; and pressure or the flow 

rate, or a combination of the two, are specified before the filling simulation is carried out. The 

simulation code is used to track the location of the flow fronts, estimate fill times, and account 

for racetracking effects. In addition, LIMS is capable of showing dry-spot formation and 

tracking of dry spots as filling progresses [111. Such flow simulations have also been used to 

study the effects of different configurations of gates and vents on mold filling, wherein the 

process inputs are already fixed. 

During the filling process, the area of the preform that is poorly wetted-out, or not wetted at 

all, by the resin, is called a dry spot. Dry spots have been investigated and classified both 

experimentally and numerically [ 12, 131. It has been shown that the positioning and control of 

gates and vents can lead to dry-spot reduction [ 111. 

The optimal placement of gates and vents and cure-cycle optimization have been carried out 

using GAS [ 14, 151. The method employed used a cost function that is comprised of the 

maximum difference in times at which the resin reaches the boundary of the mold. This was a 

measure of the uniformity of filling and, indirectly, of dry-spot formation. However, frequently, 

the inlets or “gates” are to be located on the edges of the mold and this cost function cannot be 

used since the resin is injected at the edges. Jn addition, the locations of gates and vents are 

dependent on each other in a complex and nonlinear fashion. The present study explicitly 

defines gate and vent locations and *formulates a cost function that accounts for the size of the 

dry spot and the fill time. These are coupled with the GA and the filling simulation to carry out 

the optimization of gate and vent locations. 

4 
3. Optimal Design and GAS 

3.1 Optimization of Design. Optimal design can be defined as the selection of the best set 

of inputs for a process to meet certain requirements using available resources. Design 

optimization proceeds in the following phases: recognition of needs and requirements (problem 

definition), creation of one or more design configurations (synthesis), the study of the 

configurations’ performance using engineering science and knowledge (analysis), and the 

selection of the “best” alternative (optimization). The design is defined as a system of design 

variables, parameters, and constants. The optimal design is selected using a criterion that is 

called an objective function. The objective function is sometimes referred to as a cost function 

since a minimum cost is often desired [161. 

The selection of an optimal design is usually an iterative process involving a search 

technique that searches for the “best” design configuration. A mathematical model of the system 

is used for evaluation of the objective function for each design configuration. The mathematical, 

or simulation-based, model is a numerical representation of the relationship between process 

inputs and process outputs. For example, the filling simulation is a very sophisticated model that 

relates the inputs (e.g., gate and vent positions, permeability data, injection pressures, etc.) to the 

outputs, such as fill times, pressure fields, and dry-spot formation and location. 

As illustrated in Figure 2, the process of optimal design for RTM involves the coupling of a 

cost function, which incorporates the important criteria for optimal design with a filling 

simulation. The variables to be optimized are gate and vent positions in order to minimize the 

fill times and area dry-spot formation. 

Conventional search techniques are gradient-based. The gradient of the objective function 

with respect to the design variables is evaluated, and the variables are adjusted along the line of 

maximum slope until a minimum is reached, where the gradient is zero. Gradient-descent-based 

techniques tend to get trapped in local minima and strongly depend on an initial guess and on the 

existence of derivatives. 

5 
. 

RIM Process Cost Function 

* . 

Figure 2. Schematic of Optimal Design for the RTM Process. 

GAS are search algorithms that mimic natural selection and genetics to “evolve” the best 

solution to a problem from a large number of alternative solutions. The solution is usually 

represented by a binary string. A sample set of solutions, or a “generation,” as represented by 

their strings is evaluated and fitness values are assigned. Two of the strings are selected at a time 

and “reproduced” using crossover and mutation operators that are defmed mathematically, and 

they produce two new strings or “offspring,” until a new set of strings or a new generation is 

produced. The probability of selection is proportional to the fitness of the string. Hence, the 

“fittest” strings have a greater chance to contribute to the next generation, imitating Darwinian 

evolution. The next generation is again evaluated and reproduces. The cycle is repeated until a 

generation having marry good solutions emerges [173. 

GAS have proven to be robust and powerful techniques for search and optimization. GAS 

search from a population of points and use payoff or fitness information with probabilistic 

transition rules. They generally produce near-global optimal solutions in large search spaces. As 

illustrated in Figure 3, for a multimodal function (i.e., a function possessing multiple peaks) a 

gradient-based search method will probably settle on a lower peak (i.e., a local optimum), while 

6 
i 

* 

X 

Figure 3. A F’unction With Multiple Peaks: A Gradient-Based Method Is Likely to Find 

the Local Peak at Point A, While a GA Will Settle on Point B, Near the Global 

Maximum. 

a GA is most likely to find a point close to the absolute maximum. This is because GAS use 

information from multiple points in parallel to explore the search space. An SGA has been 

implemented in this work [1X]. 

3.2 SGA Procedure. The SGA is a powerful yet simple search technique that involves 

partial swapping and copying of binary strings, which are representations of the optimization 

variables. The variables themselves can be continuous or discrete, since they are mapped to 

binary strings. Each string has a “fitness” value, f, associated with it. The SGA employs three 

operators: reproduction, crossover, and mutation. 

7 
The reproduction operator operates on the strings of each generation to produce the strings of 

the next generation. The strings are allocated space on a roulette wheel, with the size of the 

sector assigned to each string on the circle, being proportional to its fitness. Thus, the roulette 

wheel is biased in favor of the “fittest” members of each generation. The wheel is spun, and 

strings are selected two at a time. These two strings are operated on, by the crossover and 

mutation operators, to produce two new strings, which belong to the next generation. New 

strings are produced until the population size (i.e., the number of strings in each generation, 

which is a fixed number) is attained. This new generation is evaluated, and fitness values are 

assigned to each member of the generation. A schematic of this process is shown in Figure 4. 

(Roukttc Wheel) 

I 

Figure 4. Schematic of LIMS-Based Optimization Using GAS. 

The crossover operator takes each pair of strings selected by the reproduction operator to 

produce two new strings. It does this by randomly selecting an integer position on the string, 

dividing each of the strings at that position, and then swapping the substrings. If the strings (Sl 

8 
. 

and S2) are each of length L, a position k < L is selected and the two strings are divided into four 

substrings, two of length k (sl and s2) and two of length L-k (rl and d). The two new strings 

are sl-r2 and s2-rl. 

The reproduction and crossover operators work in tandem to use high performance strings 

having high fitness values and generate better strings having higher fitness values, thus 

emulating natural selection, which favors “survival of the fittest.” The mutation operator works 

by taking the new strings produced and randomly flipping over a few digits from 0 to 1 or 1 to 0. 

This ensures genetic diversity by producing strings that contain new material and are not totally 

derived from the previous generation. The three operators are illustrated in Figure 5. 

Reproduction Operator : Roulette Wheel Sckction 

Mutation -Ll-uuu-m 

Mutation Orxrator 

Figure 5. Reproduction, Crossover, and Mutation Operators in GAS. 

9 
In terms of optimization and search, the SGA works by searching from multiple points in the 

search space. It is a random-search technique possessing some degree of determinism. This 

ensures that the algorithm does not get trapped tin local optima. The mutation operator ensures 

that the search is not localized to a small part of the search space. Since there are no 

requirements on the fitness function, it allows a high degree of freedom in constructing the 

function. It has been shown that the SGA will usually locate near-global optima in the search 

space [18]. 

3.3 Application of SGA to Gate and Vent Location Optimization. To illustrate the 

potential and use of GAS, a composite part having material and geometric complexity was used 

for the case study. This part is a 2-D approximation of a vehicle bed with wheel wells. It is a 

large planar part and contains a thick section that provides a path of high resistance to the resin. 

The search space of possible gate and vent locations was defined. An objective function or 

process performance index (PPI) was formulated, which incorporates the fill time and dry-spot 

formation, with appropriate normalized weighting factors. 

LlMS 4.0 [ 111 incorporates the LBASIC script language. A script was written to simulate 

the filling process with sets of gates and vents arranged in a sequential manner and that abandon 

the filling simulation when a tolerance on the fill time and dry-spot area is exceeded. Initially, a 

random set of configurations is evaluated using LIMS and the objective function. The SGA, 

coded in C++, was then used to generate successive sets or “generations” of configurations, with 

the IJMS-based simulations supplying the cost information for each set. It was observed that the 

average costs for successive generations showed a decrease, and several optimal configurations 

were obtained. 

The optimization problem solved here, is that of finding optimal gate and vent locations to 

minimize fill time and dry spot formed for the selected mold geometry and material parameters 

(Figure 6). The composite part has thicker sections at the center corresponding to the wheel 

wells. The penneabilities of the preform material are K11 = I& = 10e7m2 for the thin section 

and two orders of magnitude lower, K 11 = K22 = 10sgm2, for the thick section. 

10 
I 2.4dm 1 

Figure 6. Planar Approximation of the Bed of a Vehicle or Trailer Used for Optimization. 

The injection at the gate is performed under constant pressure, which was chosen to be 

10 atm at each gate (i.e., a standard injection pressure for RTM of vinyl-ester resins). The vents 

are at atmospheric pressure. The resin viscosity was chosen to be 0.231 Pa-s, which is a typical 

value for vinyl-ester resin. The mold geometry was discretized using the PATRAN FE 

preprocessor [ 191. 

The optimal@ criterion was represented by the following objective function that is to be 

minimized: 

J=& tf (1+ 99H (t - Q,rd 1) 

+4 

%Void (1+99H (%Void - %Void,,)) (4) 

5 snax %Void max 

The PPI formulated incorporated the importance of fill time and voids, although one may 

include other outputs if necessary. Voids or dry spots are represented by the number of unfilled 

nodes in the FE model at the end of the simulation. The functions H(t - tf,,J and 

11 
H(%Void - %Void,,) are Heaviside penalty functions, which add a penalty if tolerance limits 

on time and void formation are exceeded. The variables 4 and 4 are weighting factors that can 

be adjusted according to the relative importance of each term. The tolerance time is usually less 

than the time to initiate gelling and the tolerance on void formation is less than a fraction of a 

percent for structural applications and a few percent for nonstructural applications. 

The optimization problem was attempted for case (a), the ideal case of two gates and vents 

everywhere (i.e., no vents specified, hence, no dry spots are formed, so the objective function 

was limited to fill times only); case (b), two gates and one fixed-vent location; and case (c), two 

gates and four vents. Since the mold geometty has left-right symmetry, the flow in only the left 

section with one gate specified considered. In case (c), there are two vents in the left section 

placed symmetrically about the centerline; hence, only one vent needs to be independently 

specified. The search area was initially restricted to the boundary of the mold, which was 

divided into 128 parts; as in many cases, the mold is held in a press and it is generally costly to 

inject from the top or the bottom face. Each gate or vent location corresponds to a node in the 

FE mesh and is represented by a seven-digit binary number. Hence, the gates in cases (a) and (b) 

are represented by seven-digit binary strings in the GA. In case (c), the gate and two vents are 

represented by two seven-digit strings joined together. 

The worst case for filling is with one gate at the center of the thick section with fixed vent 

location. The fill time is 62,979 s with 638 unfilled nodes. It was observed that, in case (b), the 

fill times in the first generation were distributed with 75% of the cases having fill times below 

6,500 s and, in case (c), fill times were below 9,500 s. The values of the weighting factors were 

A, = 10 and il, = 5; and were chosen so that both terms in the cost function have equal 

importance. 

In each case, an initial population of 6-8 strings was generated randomly. These were 

decoded to gates and vents and the mold-filling simulations were performed using the LBASIC 

script. The cost function was evaluated. The GA uses the cost function to calculate the fitness of 

each string, using the linear scaling function, fitness(x) = l,OOO-cost(x), and produces the next 

12 
generation, which is decoded and evaluated. This optimization loop was continued for several 

generations, until the average cost function over each generation was below a preset value. 

3.4 Optimization With Racetracking Effects. Racetracking channels are created when 

there is a gap between the preform and the mold wall. The channels provide a path of least 

resistance to the flow and dramatically afTecthe flow-front movement of the resin in the mold. 

Thus, the optimal locations of gates and vents to minimize fill time and dry-spot formation, as 

previously defined, will change. 

In the previous study, the boundaries of the mold were considered for the location of gates 

and vents. In this study, with racetracking effects included, the boundary cannot be the location 

of both a gate and a vent, since the mold will not fill as the racetracking channel provides a 

conduit of least resistance from the gate to the vent. However, if one of them were to be located 

on the mold boundary and the other in the center of the mold, then there exists a possibility for 

the mold to fill. Hence, for this study, the centerline of the mold was also included in the search 

space. The geometry on this case study was identical to the previous one, except that a 

racetracking channel of width 2.54 cm and depth 0.64 cm around the boundary of the mold was 

incorporated into the FE model of the mold. The total number of possible nodes that could serve 

as a gate or vent was 304. The optimization problem was solved for the case of two gates placed 

symmetrically about the centerline of the mold and a single vent placed on the centerline of the 

mold. &ch configuration was represented by a 15-digit binary string, where the first 8 digits 

correspond to the gate, which can be anywhere on the racetracking channel and the centerline, 

and,the last 7 bits represent the vent, which is restricted to the centerline. 

4. Results 

The GA was first applied for the three cases without the racetracking effect, as described in 

the previous section, with five to six generations being evolved in each case. The average values 

of the cost function per generation are plotted in Figure 7. The best configurations are shown for 

each case in Figure 8. 

13 
Case (a) 

Case (b) 

Case (c) 

1 2 3 4 5 6 

Generation Number 

g300- 

9 250- 

co 

stmP 

PI) ‘xi - 

roo- 

!TQ01 

6 

400 

350 

300 

E 

B 250 

ti 

s 200 

t 150 

a 

100 

50 

1 2 3 4 5 6 

GeneratIon Number 

Note: Case (a): Two Gates, Vents Everywhere. 

Case (b): Two Gates, One Fixed Vent. 

Case (c): Two Gates, Four Vents, No Racetracking. 

Figure 7. Plot of Cdst Function With Generation Number for Each Case. 

14 
i 

Note: Case (a): Two Gates, Vent Everywhere, Fill Time = 3,292 s. 

Case (b): Two Gates, One Fixed Vent, Fill Time = 4,291.6 s. 

Case (q): Two Gates, Four Vents, Fill Time = 4,407 s. 

Figure 8. Optimal Gate and Vent Placement for Each Case. 

15 
In case (a), when it is assumed that the vent is present everywhere, the average value of the 

cost function was 3.62 for the first generation and 1*82 for the sixth generation. The best time to 

fill was 3,290 s, with the gate being located next to the thick section. This makes sense and can 

be explained as follows: the optimal gate location is as close to the centerline of the part as 

possible since the resin has to travel the minimum distance. But the thick section is located at 

the center of the part, and a gate location in the thick section would require a very high time to 

fill since the flow is at constant pressure and will be forced to go through the high resistance to 

flow in the thick section. Hence, the optimal gate location is at the edge of the thick section. 

The number of gates evaluated was 16 out of a possible 32. 

In case (b), the gate was allowed to float along the edge of the mold and the vent was fixed at 

the position shown in Figure 8(b). The average cost value decreased from 390.7 to 12.9 in five 

generations. The best solution was calculated to take a fill time of 4,292 s and unfilled nodes = 

23 or 0.008% dry-spot formation. The number of gates evaluated was 25 out of a possible 128. 

In case (c), the vent was free to move in addition to the gate location. The average value of 

the cost function, as expressed in equation (4), decreased from 3X8.3 to 14.23 in six generations. 

The best solution was fill time = 4,407 s, unfilled nodes = 17 or 0.006% dry-spot formation. 

The number of gate and vent configurations evaluated were 40 out of a possible 16,256 gate and 

vent configurations. One can see that, as the number of possible configurations increased, the 

utility of the GA becomes evident, as it was able to locate an optimal solution with fewer than 

1% possible evaluations. The vent location was very close to the line of symmetry. A local 

search showed that the vent should be at the symmetry line, as shown in Figure 8(c). 

5. Racetracking Study 

In the racetracking study, from 83,000 possible configurations, the GA took 6 generations 

and 48 simulations to arrive at a near-optimal solution. The average cost function decreased with 

successive generations and is plotted in Figure 9. Two optimal solutions were obtained that 

minimized the time to fill and low dry-spot formation using just 0.14% of possible evaluations. 

16 
600 

El 

f 200 

h 

100 

0 

1 2 3 4 5 6 

Generation Number 

Figure 9. Plot of Cost Function With Generation Number for Racetracking Study. 

These ae shown in Figure 10. The optimal fill times are much less than those in the case 

without racetracking channels. The flow contours for the best gate and vent configurations are 

plotted in Figure 11. 

In the previously mentioned case study, the simulation of resin flow in the mold was stopped 

at a critical time, reflecting the need to complete the mold filling in a finite time, which may be 

dependent on cycle time requirements, or gel on time of the resin. However, it may be 

imperative to fill the mold completely in order to obtain good-quality parts. Thus, the resin 

injection has to be continued for some time until the mold filling is complete. Since the thick 

section is the last to fill and the vent here is in the thin section, there will be considerable resin 

wastage through the vent. 

The continuous injection was undertaken for the best configuration of two gates and a vent. 

The mold was filled in 5,309 s (i.e., 20% more time than the 3839.2 s previously considered). 

The amount of resin wasted through the vent increased to 20% of the total inflow through the 

gate. 

17 
% Vent 

I 

I 

Gate 

4.5 

Note: Case (a): Fill Time = 3J89.2 s, Dry Spot = 0.7% , Wastage = 6.0%. 

Case (b): Fill Time = 3J39.2 s, Dry Spot = 0.61%, Wastage = 6.7%. 

Figure 10. Optimal Gate and Vent Placement for Racetracking Study With Two Gates 

and One Vent. 

18 
Figure 11. Flow-Front Locations With the Optimal Gate and Vent Locations for the 

Racetracking Case Optimized by the GA. 

6. Discussion 

For the case with no racetracking, when a vent is present in the mold and once the resin 

reaches the vent, it tends to flow from the gate into the vent, as that is the path of least resistance. 

Hence, if the vent is in the proximity of the gate, then this path is established quickly and the 

time to fill will be high due to the leakage of resin through the vent and/or with large dry spots 

19 
being formed. Thus, the optimal gate location will involve a trade-off between maximum 

distance between gates and vents and minimum distance from the centerline. This is reflected in 

the best gate and vent locations determined by the GA for cases (b) and (c). 

It was observed that the average value of the cost function decreased with succeeding 

generations in each case. A number of possibly optimal solutions for each problem were 

generated. The number of simulations required before the GA found optimal points was much 

less than the possible number of simulations. 

6.1 Racetracking Case. For the case with racetracking, the best gate locations should be 

placed on the racetsacking channel, while the best vent locations should be placed close to the 

center of the part. This is because the resistance to the flow of resin is the least when it is on the 

empty racetracking channel. When the gate is on the racetracking channel, it fills quickly, due to 

low resistance, and acts as a gate. The resin reaches the vent rapidly and then flows through it. 

This leads to an undesirable quantity of waste resin. Hence, the vent has to be as far away from 

the racetracking channel as possible. The optimal gate and vent configurations generated by the 

GA reflect this behavior (Figure 11). 

6.2 Resin Waste Through Vent, In the present study, it was observed that there is waste 

due to the flow of resin through the vent. It can also be seen from the flow contours that the last 

point to fill is in the thick section, due to its low permeability and a very high resistance to flow. 

The question arises whether a single vent in each of the thick sections will eliminate the waste of 

resin altogether as this is the last point to fill. 

However, a vent is introduced into the mold in order to allow the entrapped air in the mold to 

escape. In a large and complex mold, there will be many areas where the air can be entrapped. 

In the mold considered here, air pockets will form not only in the thick section, but also along the 

centerline, at the intersection of the two flow-fronts. Hence, if the vent on the centerline were to 

be eliminated, a dry spot would form in the center of the finished part. However, a vent in the 

thick section is necessary, in any case. An issue that arises is that of minimizing the resin waste. 

This minimization is implicit here because, if a greater amount of resin were wasted due to the 

20 
suboptimal placement of the vent, the fill time would be higher. Hence, the cost function reflects 

this and the best configurations obtained here have low resin w&e (Figure 10). 

7. Further Refinement: Finding Global Optima 

The GA here has proven adept at fmding good configurations of gates and vents to minimize 

the fill times and areas of dry spots formed. However, the GA is a search technique that has 

incorporated an element of randomness. This randomness and the fact that it is a multipoint 

search technique enables one to quickly find points of interest (i.e., good configurations of gates 

and vents). For this same reason, these configurations are likely not to be global optima (i.e., the 

absolute minimum) that one could obtain using an exhaustive search through the thousands of 

possible configurations. Indeed, GAS have been shown to find near-global optima, when applied 

to well-known optimization problems. Hence, it is likely that the configurations obtained here 

lie close to global optima (as in Figure 3). The results can be further refined using a local search 

technique, such as an exhaustive search or a gradient search, and better configurations can be 

discovered with very little computational cost. In addition, physical insight obtained from the 

analysis of the gate and vent configurations can be used for further experimentation. 

In the case with no racetraking and dealing with the optimal placement of two gates and four 

vents, the best solution obtained has the gate near the thick section, while the vents are very close 

to the centerline (Figure 7). Thus, the globally optimal solution would be to have a vent at both 

ends of the centerline and the gates near the thick section. 

hi the case with racetracking, it can be seen from the flow contours that the best vent 

locations are close to the center of the part, while the gate locations are again close to the thick 

section. Since the racetracking channel is also present there, the gate can be placed on the 

portion of the racetracking channel near the thick section. Hence, the globally optimal solution 

will be to have the gate at the center of this portion and the vent at the center of the part. A 

simulation of this configuration yields a time of 3,555 s to fill 99.4% of the part (i.e., a dry spot 

occupying 0.6% volume was formed), if the filling is stopped at this point. This optimal 

configuration is likely to have been found if the cost function severely penalized the resin 

21 
wastage. Continuing the filling process, it takes 5,56 1 s to completely fill the part with 17.1% of 

the resin wastage. The global optima for both cases (with and without racetracking) are 

illustrated in Figure 12. Since the points to fill last are always in the thick section, it may also be 

necessary to have a vent at its center. 

8. Conclusions 

To determine optimal location of gates and vents, so as to reduce fill times and improve part 

quality, is a nonlinear problem for the design of molds for RTM, for the manufacture of 

composite parts with geometric and material complexities. The solution of this problem requires 

extensive experimentation on a trial-and-error basis. 

A simple GA coupled interactively with finite-element-based simulations has been used as an 

effective search technique for determining optimal gate and vent configurations, which minimize 

fill times and dry-spot formation. A PPI was formulated, which incorporates fill time and 

dry-spot formation directly, with penalties for exceeding performance tolerances. The case study 

was extended by adding channels that introduce racetracking effects. The solutions obtained 

made physical sense and can be easily improved using a local search technique. 

The approach used here can be applied to obtain solutions to mold design quickly, where the 

placement of gates and vents may be nonintuitive. The search space can be restricted to a small 

part of the mold where the placement of gates and vents is feasible. A cost function can be 

defined, which reflects the process requirements and penalizes bad performance. A GA is an 

efficient and practical tool, which can determine good configurations of gates and vents from a 

large number of possibilities. The analysis was carried out by coupling the GA with our 

mold-filling simulation software, LJMS. The analysis of these configurations and the 

improvement of the solutions yields valuable insight into the placement of gates and vents in the 

mold. This would reduce expensive mistakes during the manufacturing of the composite part. 

22 

. 
X Vent 

@ Gatr: 1,22m ! -l 

. . 

1 

I 

3.05 

Note: (a) No Racetracking Channel, Fill Time = 4,407 s, Dry Spot = 0.006%. 

(b) Racetracking Channel Incorporated, Fill Time = 3,555 s, Dry Spot = 0.6%. 

Figure 12. Improved Optima for the Placement of Gates and Vents. 

23 
24 
9. References 

I 

1. 

I 

2. 

3. 

4. 

5. 

6. 

7. 

8. 

9. 

Fong, L., and S. G. Advani. Lubin’s Handbook of Composites H S. T. Peters (editor), 

1998. 

Bruschke, M. V., and S. G. Advani. “RTM: Filling Simulation of Complex ThreeDimensional Shell-Like Structures.” SAMPE Quarterly, pp. 2-l 1, 199 1. 

Lee, L. J., W. B. Young, and R. J. Lin. “Mold Filling and Cure Modeling of RTM and 

SRIM Processes.” Composite Structures, vol. 27, no. l-2, 1994. 

Trochu, F., R. Gauvin, D. M. Gao, and J. F. Boudreault. “RTMI?LOT - An Integrated 

Software Environment for the Computer Simulation of the Resin Transfer Molding 

Process.” Journal of Reinforced Plastics and Ceramics, vol. 13, no. 3, 1994. 

Bruschke, M. V., and S. G. Advani. “A Numerical Approach to Model Non-Isothermal, 

Viscous Flow With Free- Surfaces Through Fibrous Media.” International Journal of 

Numerical Methods in Fluids, vol. 19, pp. 575-603, 1991. 

Bruschke, M. V., and S. G. Advani. “A Finite Element/Control Volume Approach to Mold 

Filling in Anisotropic Porous Media.” Polymer Composites, vol. 11, pp* 398-4-05, 1990. 

Gallez, X. E., and S. G. Advani. “Numerical Simulations for Impregnation of Fiber 

Preforms in Composites Manufacturing.” Proceedings of the Fourth Intern&or& 

Conference on Flow Processes in Composite Materials, University of Wales, 1996. 

Mohan, R. V., N. D. Ngo, K. K. Tamma, and K. D. Fickie. “On a Pure Finite Element 

Based Methodology for Resin Transfer Mold Filling Simulations.” Numerical Methods in 

Thermal Problems, Proceedings of the Ninth International Conference, Part 2, 1995. 

Advani, S. G. “Numerical Issues and Approaches in Simulation of VARTM Processes.” 

Proceedings of the ASME Annual Winter Meeting, Dallas, TX, 1997. 

10. Simacek, P., E. M. Sozer, and S. G. Advani. User Manual for DRAPE 1 .I and LIMS 4.0. 

University of Delaware Center for Composite Materials, 1998. 

r 

11. Liu, D., S. Bickerton, and S. G. Advani. “Modeling and Simulation of RTM: Gate Control, 

Venting and Dry Spot Prediction.” Composites, vol. 27A, no, 135, 1996. 

12. Han, K., and L. K. Lee. “Dry Spot Formation and Changes in Liquid Composite Molding: 

I-Experimental.” Journal of Composite Materials, vol. 30, no. 13, 1996. 

25 
13. Han K., L. K. Lee, and S. Nakamura. 

Composite Molding: 

“Dry Spot Formation and Changes in Liquid 

II-Modeling and Simulation.” Journal of Composite Materials, 

vol. 30, no. 13, 1996. 

14. Young W. B. “Gate Location Optimization in Liquid Composite Molding Using Genetic 

Algorithms.” Journal of Composite Materials, vol. 28, no. 12, 1994. 

15. Young, W. B., and W. H. Yu. “Optimal Design of Process Parameters for Resin Transfer 

Molding.” Journal of Composite Materials, vol. 3 1, no. 11, 1997. 

16. Papalambros, P. Y., and D. E. Wilde. Principles of Optimal Design: Modeling and 

Computation. Cambridge University Press, 1988. 

17. Mitchell, M. E. An Introduction to Genetic Algorithms. MIT Press, 1996. 

18. Goldberg, D. E. Genetic Algorithms in Search, Optimization and Machine Learning. 

Addison-Wesley, 1997. 

19. PDA Engineering: PATRAN Division. PATRAN Users Manual: Version 5. PDA, 1997. 

26 

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G CAMPONESCHI 

235 1 JEFFBRSON DAVIS Hwy 

ARLINGTON VA 22242-5 165 

1 EXFEDIT1ONARY WARFARE DIV N85 

F SHOW 

2000 NAVY PENTAGON 

WASHINGTON DC 20350-2000 

NO. OF 

COPES WN 

2 

AFRL MLBC 

2941 P ST RM 136 

WRIGHT PATTERSON AF’B OH 

45433-7750 

AFRL MISS 

P 

R THOMSON 

2179 12TH ST RM 122 

WRIGHT PATTERSON AFB OH 

45433-7718 

FABRAMS 

J BROWN 

BLDG 653 

2977 P ST STE 6 

WRIGHT PATTERSON AFB OH 

45433-7739 

AFRLMLSOL 

L COULT’ER 

7278 4TH ST 

BLDG 100 BAY D 

HILL AFB UT 84056-5205 

OSD 

JOINT CCD TEST FORCE 

OSD JCCD 

RWILLIAMS 

3909 HALLS FERRY RD 

VICKSBURG MS 29180-6199 

DEFENSE NUCLEAR AGENCY 

INNOVATIVE CONCEPTS DIV 

6801 TELEGRAPH RD 

ALEXANDRIA VA 223 lo-3398 

WATERWAYS EXPERIMENT 

D SCOTT 

3909 HALLS FERRY Ru SC c 

VICKSBURG MS 39 180 

DARE’A 

M VANFOSSEN 

SWAX 

L CHRISTODOULOU .- 

3701 N FAIRFAX DR 

ARLINGTON VA 22203-1714 

34 
NO. OF 

COPIES B 

2 SERDP PROGRAM OFC 

PM P2 

C PELLERJN 

B SMITH 

901 N STUART ST STE 303 

ARLJNGTON VA 22203 

1 FAA 

MIL HDBK 17 CHAJR 

L ILCEWICZ 

1601 LIND AVE SW 

ANM 115N 

RENTON VA 98055 

2 FAA 

TECH CENTER 

D OPLINGER AAR 43 1 

P SHYPRYKEVICH AAR 43 1 

ATLANTIC CITY NJ 08405 

1 US DEPT OF ENERGY 

OFC OF ENVIRONMENTAL 

MANAGEMENT 

P RITZCOVAN 

19901 GERMANTOWN RD 

GERMANTOWN MD 208741928 

1 DIRECTOR 

LLNL 

F ADDESSI MS B216 

PO BOX 1633 

LOS ALAMOS NM 87545 

5 DIRECTOR 

LLNL 

R CHRISTENSEN 

S DETERESA 

F MAGNESS 

M FINGER MS 313 

MMURF’HYL282 

PO BOX 808 

LIVERMORE CA 94550 

1 OAK RIDGE NATIONAL 

LABORATORY 

R M DAVIS 

PO BOX 2008 

OAK RIDGE TN 37831-6195 

NO. OF 

COPIES 

7 

I 

1 

4 

ORGANIZATION 

NIST 

R PARNAS 

J DUNKERS 

M VANLANDINGHAM MS 8621 

5 CHIN MS 8621 

D HUNSTON MS 8543 

J MARTIN MS 8621 

D DUTHINH MS 8611 

100 BUREAU DR 

GAITHERSBURG MD 20899 

OAK RIDGE NATIONAL 

LABORATORY 

C EBERLE MS 8048 

PO BOX 2009 

OAK RIDGE TN 3783 1 

OAK RJDGE NATIONAL 

LABORATORY 

C D WARREN MS 8039 

PO BOX 2009 

OAK RIDGE TN 37922 

LOCKHEED MARTIN MISSILES 

& EIRE CONTROL 

R TAYLOR 

PO BOX 650003 M S WT 93 

DALLAS TX 75265-0003 

HYDROGEOLOGIC INC 

SERDP ESTCP SPT OFC 

S WALSH 

1155 HERNDON PKWY STE 900 

HERNDON VA 20170 

DIRECTOR 

SANDIA NATIONAL LABS 

APPLIED MECHANICS DEPT 

DIV 8241 

WKAWAHARA 

R PER4NO 

D DAWSON 

P NIELAN 

PO BOX 969 

LIVERMORE CA 94550-0096 
NO. OF 

COPIES 

3 

ORGANIZATION 

NASA LANGLEY RSCH CTR 

AMSRL vs 

W ELBER MS 266 

F BARTLETT JR MS 266 

G FARLEY MS 266 

HAMPTON VA 2368 l-0001 

NASA LANGLEY RSCH CTR 

T GATES MS 188E 

HAMF’TON VA 23661-3400 

USDOT FEDERAL RAILRD 

MFATEHRDV31 

WASHINGTON DC 20590 

DOT FHWA 

J SCALZI 

400 SEVENTH ST SW 

3203 HNG 32 

WASHINGTON DC 20590 

FHWA 

E MUNLEY 

6300 GEORGETOWN PIKE 

MCLEAN VA 22101 

CENTRAL INTLLGNC AGNCY 

OTI WDAG GT 

W L WALTMAN 

PO BOX 1925 

WASHINGTON DC 20505 

MARINE CORPS INTLLGNC ACTVTY 

D KOSITZEUZ 

3300 RUSSELL RD STE 250 

QUANTICO VA 221345011 

DIRECTOR 

NATIONAL GRND JNTLLGNC CTR 

IANGTMT 

220 SEVENTH ST NE 

CHARLOTTESVJLLE VA 

22902-5396 

DIRECTOR 

DEFENSE INTLLGNC AGNCY 

TA5 

K CRELLING 

WASHINGTON DC 203 10 

36 

NO. OF 

COPIES 

1 

I 

1 

3 

2 

4 

2 

1 

ORGANIZATION 

GRAPHITE MASTERS INC 

J WILLIS 

3815 MEDFORD ST 

LOS ANGELES CA 90063-1900 

ADVANCED GLASS FIBER YARNS 

T COLLINS 

281 SPRING RUN LANE STE A 

DOWNINGTON PA 19335 

COhhPOSITE MATERIALS INC 

D SHOR’IT 

19105 63 AVE NE 

PO BOX 25 

ARLINGTON WA 98223 

COhh’OSI’TE MATERIALS INC 

R HOLLAND 

11 JEWELCT 

ORlNDA CA 94563 

COdPOSlTE MATERIALS INC 

C RILEY 

1453b S ANSON AVE 

SANTA FE SPRINGS CA 90670 

COMPOSIX 

D BLAKE 

L DJXON 

120ONEILLDR 

HEBRUN OHIO 43025 

CYtiC FIBERITE 

RDUNNE 

D KOHL1 

M GILL10 

RMAYHEW 

1300 REVOLUTION ST 

HAVRJZ DE GRACE MD 21078 

SIMULA 

J COLTMAN 

RHUYETT 

10016 S 51ST ST 

PHOENIX AZ 85044 

SIOUX MFG 

BKRJEL 

PO BOX 400 

FT TOTTEN ND 58335 
NO. OF 

COPIES 

2 

3 

2 

1 

1 

2 

1 

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PROTECTION MATERLALS INC 

MMJLLER 

F CRILLEY 

14000 NW 58 CT 

MIAMI LAKES FL 33014 

FOSTER MILLER 

J J GASSNER 

M ROYLANCE 

WZUKAS 

195 BEARHILLRD 

WALTHAM MA 02354-l 196 

ROM DEVELOPMENT CORP 

ROMBARA 

136 SWINEBURNE ROW 

BRICK MARKET PLACE 

NEWPORT RI 02840 

TEXTRON SYSTEMS 

T FOLTZ 

M TREASURE 

201 LOWELL ST 

WILMINGTON MA 08870-2941 

JPS GLASS 

L CARTER 

PO BOX 260 

SLATER RD 

SLATER SC 29683 

0 GARA HESS & EISENHARDT 

M GILLESPIE 

9113 LESAINT DR 

FAIRFIELD OH 45014 

MILLIKEN RSCH CORP 

HKUHN 

M MACLEOD 

PO BOX 1926 

SPARTANBURG SC 29303 

CONNEAUGHT INDUSTRIES JNC 

J SANTOS 

PO BOX 1425 

COVENTRY RI 02816 

NO. OF 

COPIES 

1 

ORGANIZATION 

BATTELLE 

C R HARGREAVES 

505 KING AVE 

COLUMBUS OH 43201-2681 

BATTELLE NATICK OPNS 

J CONNORS 

B HALPIN 

209 W CENTRAL ST STE 302 

NATICK MA 01760 

BATIELLE NW DOE PNNL 

THALLMSK231 

BATIELLE BLVD 

RICHLAND WA 99352 

PACLFIC NORTHWEST LAB 

MSMJTH 

G VAN ARSDALE 

R SFUPPELL 

PO BOX 999 

RICHLAND WA 99352 

ARMTEC DEFENSE PRODUCTS 

S DYER 

85 901 AVE 53 

PO BOX 848 

COACHELLA CA 92236 

ADVANCED COMPOSITE 

MATERIAJ.,s CORP 

P HOOD 

J RHODES 

1525 S BUNCOMBE RD 

GREER SC 2965 l-9208 

GLCC INC 

JRAY 

M BRADLEY 

103 TRADE ZONE DR ST-E 26C 

WEST COLUMBIA SC 29170 

AMOCO PERFORMANCE 

PRODUCTS 

M MICHNO JR 

J BANJSAUKAS 

4500 MCGINNIS FERRY RD 

ALPHARETTA GA 30202-3944 

37 
NO. OF 

CDpIEs -ON 

1 SAIC 

M PALMER 

2109AIRPARKRDSE 

ALBUQUERQUE NM 87106 

1 SAIC 

G CHRYSSOMALLIS 

3800 W SOTH ST STE 1090 

BLOOMINGTON MN 5543 1 

1 AAI CORPORATION 

T G STASTNY 

PO BOX 126 

HUNTVALLEYMD21030-0126 

1 JOHN HEBERT 

PO BOX 1072 

HUNT VALLEY MD 21030-0126 

1 APPLIED coMFosITEs 

W GRISCH 

333 NORTH SIXTH ST 

ST CHARLES IL 60174 

12 ALLIANT TECHSYSTEMS INC 

CCANDLAND 

CAAKHUS 

R BECKER 

B SEE 

NVLAHAKUS 

R DOHRN 

S HAGLUND 

D FISHER 

WWORRELL 

R COPENHAFER 

M HISSONG 

DKAMDAR 

600 SECOND ST NE 

HOPKINS MN 55343-8367 

3 ALLIANT TECHSYSTEMS INC 

J CONDON 

E LYNAM 

J GERHARD 

WV01 16 STATE RT 956 

PO BOX 210 

ROCKET CENTER WV 

26726-0210 

NO. OF 

COPIES 

1 

1 

2 

5 

3 

1 

ORGANIZATION 

PROJECTILE TECHNOLOGY INC 

515 GILES ST 

HAVRE DE GRACE MD 21078 

CUSTOM ANALYTICAL 

ENG SYS INC 

A ALEXANDER 

13000 TENSOR LANE NE 

FLINTSTONE MD 21530 

LORAL VOUGHT SYSTEMS 

G JACKSON 

K COOK 

1701 W MARSHALL DR 

GRAND PRAIRIE TX 7505 1 

AEROJET GEN CORP 

D PILLASCH 

T COTJLTER 

CFLYNN 

D RUBAREZUL 

M GREEdER 

1100 WEST HOLLYVALE ST 

AZUSA CA 9 1702-0296 

HEXCEL INC 

R BOE 

F POLICELLI 

J POESCH 

PO BOX 98 

MAGNA UT 84044 

HERCULES INC 

HERCULES PLAZA 

WILMINGTON DE 19894 

BRIGS COMPANY 

J BACKOFEN 

2668 PETERBOROUGH ST 

HERNDON VA 2207 l-2443 

ZERNOW TECHNICAL SERVICES 

LZERNOW 

425 W BONITA AVE STE 208 

SAN DIMAS CA 91773 

38 
NO. OF 

cQa.Es 

NO. OF 

COPIES 

1 

ORGANIZATION ORGANIZATION 

2 OLIN CORPORATION 

FLINCHBAUGH DIV 

E STEINER 

B STEWART 

PO BOX 127 

RED LION PA 17356 

BOEING 

R BOHLMANN 

PO BOX 516 MC 5021322 

ST LOUIS MO 63 166-05 16 

2 BOEING DFNSE & SPACE GP 

W HAMMOND 

J RUSSELL S 4X55 

PO BOX 3707 

SEATTLE WA 98 124-2207 

1 OLIN CORPORATION 

L WHITMORE 

10101 NINTH ST NORTH 

ST PETERSBURG FL 33702 

2 BOEING ROTORCRAFT 

P MLNGURT 

P HANDEL 

800 B PUTNAM BLVD 

WALLINGFORD PA 19086 

5 SIKORSKY AIRCRAFT 

G JACARUSO 

T CARSTENSAN 

BRAY 

S GARBO MS S33OA 

J ADELMANN 

6900 MAIN ST 

PO BOX 9729 

STRATFORD CT 06497-9729 

1 BOEING 

DOUGLAS PRODUCTS DIV 

LJHARTSMITH 

3855 LAKEWOOD BLVD 

D800-0019 

GKN AEROSPACE LONG BEACH CA 90846-0001 

D OLDS 

15 STERLING DR 

WALLINGFORD CT 06492 

1 LOCKHEED MARTIN 

S REEVE 

8650 COBB DR 

D 73 62 MZ 0648 

MARIETTA GA 30063-0648 

PRAl-r&WHITNEY 

D HAMBRICK 

4OOMAlNSTMS 11437 

EAST HARTFORD CT 06108 1 LOCKHEED MARTIN 

SKUNK WORKS 

D FORTNEY 

1011 LOCKHEED WAY 

PALMDALE CA 93599-2502 

AEROSPACE CORP 

G HAWKINS M4 945 

2350 E EL SEGUNDO BLVD 

EL SEGUNDO CA 90245 

LOCKHEED MARTIN 

R FIELDS 

1195 IRmcr 

WINTER SPRINGS FL 32708 

CYTEC F’IBERITE 

MLIN 

WWEB 

144ONKRAEMERBLVD 

ANAHEIM CA 92806 MATERIALS SCIENCES CORP 

B W ROSEN 

500 OFC CENTER DR STE 250 

FT WASHINGTON PA 19034 

1 

1 HBXCEL 

T BITZER 

11711 DUBLIN BLVD 

DUBLIN CA 94568 

. 

39 
NO. OF 

cQm5 

1 

2 

1 

1 

3 

ORGANIZATION 

NORTHRUP GRUMMAN CORF 

ELECTRONIC SENSORS 

& SYSTEMS DIV 

E SCHOCH MS V 16 

1745A W NURSERY RD 

LINTHICUM MD 21090 

NORTHROP GRUMMAN 

ENVIRONMENTAL PROGRAMS 

R OSTERMAN 

AYEN 

8900 E WASHINGTON BLVD 

PICO RIVERA CA 90660 

UDLP 

D MARTIN 

PO BOX 359 

SANTA CLARA CA 95052 

UDLP 

G THOMAS 

PO BOX 58123 

SANTA CLARA CA 95052 

UDLP 

R BARRETT MAIL DROP M53 

V HORVATICH MAlL DROP M53 

328 W BROKAW RD 

SANTA CLARA CA 95052-0359 

UDLP 

GROUND SYSTEMS DIVISION 

M PEDRAZZI MAIL DROP NO9 

ALEEMAILDROPNll 

M MACLEAN MAIL DROP NO6 

1205 COLEMAN AVE 

SANTA CLARA CA 95052 

UDLP 

R BRYNSVOLD 

P JANKE MS 170 

T GIOVANETTI MS 236 

BVANWYKMS389 

4800 EAST RIVER RD 

MINNEAPOLIS MN 55421-1498 

40 

NO. OF 

COPIES ORGANIZATION 

2 GDLS 

D REES 

M PASM 

PO BOX 2074 

WARREN MI 48090-2074 

1 GDLS DMSION 

D BARTLE 

PO BOX 1901 

WARREN MI 48090 

1 GDLS 

MUSKEGON OPERATIONS 

W SOMMERS JR 

76 GE-ITY ST 

MUSKEGON MI 49442 

1 GENERAL DYNAMICS 

AMPHIBIOUS SY S 

SURVIVABILITY LEAD 

G WALKER 

991 ANNAPOLIS WAY 

WOODBRIDGE VA 22191 

5 INST FOR ADVANCED 

TECH 

TK 

HFAIR 

P SULLIVAN 

WREINECKE 

I MCNAB 

4030 2 W BRAKER LN 

AUSTIN TX 78759 

2 CIVIL ENGR RSCH FOUNDATION 

PRESIDENT 

H BERNSTEIN 

R BELLE 

1015 15TH ST NW STE 600 

WASHINGTON DC 20005 

1 ARROW TECH ASS0 

1233 SHELBURNE RD STE D 8 

SOUTH BURLINGTON VT 

05403-7700 

1 R EICHELBERGER 

CONSULTANT 

409 W CATHERINE ST 

BEL AIR MD 21014-3613 
NO. OF 

COPIES 

1 

2 

1 

1 

1 

1 

1 

ORGANIZATION 

UCLA MANE DEPT ENGR IV 

HTHAHN 

LOS ANGELES CA 90024- 1597 

UNIV OF DAYTON 

RESEARCH INST 

RYKIM 

AKROY 

300 COLLEGE PARFZ AVE 

DAYTON OH 45469-0168 

MIT 

P LAGACE 

77 MASS AVE 

CAMBRIDGE MA 01887 

IIT RESEARCH CENTER 

D ROSE 

201 hILL ST 

ROME NY 13440-6916 

GA TECH RSCH lNST 

GA INST OF TCHNLGY 

P FRJEDERICH 

ATLANTA GA 30392 

MICHIGAN ST UNIV 

MSM DEPT 

R AVERILL 

3515 EB 

EAST LANSING MI 488241226 

UNIV OF KENTUCKY 

L PENN 

763 ANDERSON HALL 

LEXINGTON KY 40506-0046 

UNIV OF WYOMING 

D ADAMS 

PO BOX 3295 

LARAMCE WY 82071 

UNIV OF UTAH 

DEPT OF MECH & 

INDUSTRIAL ENGR 

S SWANSON 

SALT LAKE CITY UT 84112 

NO. OF 

COPrES 

2 

1 

ORGANIZATION 

PENN STATE UNIV 

R MCNITT 

C BAKIS 

212 EARTH ENGR SCIENCES BLDG 

UNIVERSITY PARK PA 16802 

PENN STATE UNIV 

R S ENGEL 

245 HAMMOND BLDG 

UNIVERSITY PARK PA 16801 

PURDUEUNIV 

SCHOOL OF AERO & ASTRO 

CTSUN 

W LAFAYETTE IN 47907-1282 

STANFORD UNIV 

DEPT OF AERONAUTICS 

& AEROBALLISTICS 

S TSAI 

DURANT BLDG 

STANFORD CA 94305 

UNIV OF DAYTON 

JMWHJTNEY 

COLLEGE PARK AVE 

DAYTON OH 45469-0240 

UNIV OF DELAWARE 

CTR FOR COMPOSITE MTRLS 

J GILLESPIE 

M SAN-I-ARE 

G PALMESE 

S YARLAGADDA 

s ADVANI 

D HEIDER 

D KUKICH 

201 SPENCER LABORATORY 

NEWARK DE 19714 

TJNIV OF ILLINOIS AT 

URBANA CHAMPAIGN 

NATIONAL CENTER 

FOR COMPOSITE 

MATERIALS RESEARCH 

J ECONOMY 

216 TALBOT LABORATORY 

104 S WRIGHT ST 

URBANA IL 61801 

41 
NO. OF 

COPIES 

3 THEUNIVOF 

TEXAS AT AUSTIN 

CTR FOR ELECTROMECHANICS 

J PRICE 

A WALLS 

J KITZMJLLER 

10100 BURNET RD 

AUSTIN TX 78758-4497 

VA POLYTECHNICAL 

INST & STATE UNJV 

DEPT OF ESM 

MWHYER 

K REJFSNJDER 

R JONES 

BLACKSBURG VA 24061-0219 

NORTH CAROLINA STATE UNIV 

CIVIL ENGINEERING DEPT 

W RASDORF 

PO BOX 7908 

RALEIGH NC 27696-7908 

UNIV OF MARYLAND 

DEPT OF AEROSPACE ENGNRNG 

AJVIZZINI 

COLLEGE PARK MD 20742 

DREXEL UNJV 

ASDWANG 

32ND & CHESTNUT ST 

PHILADELPHIA PA 19104 

SOUTHWEST RSCH INST 

ENGR & MATL SCIENCES DIV 

J RIEGEL 

6220 CULEBRA RD 

PO DRAWER 28510 

SAN ANTONIO TX 78228-0510 

NO. OF 

CoeJEs 

1 

1 

108 

ORGANIZATION 

ABERDEEN PROVING GROUND 

US ARMY MATERIEL 

SYSTEMS ANALYSIS 

P DJETZ 

392 HOPKINS RD 

AMXSY BTD 

APG MD 21005-5071 

DIRECTOR 

US ARMY RESEARCH LAB 

AMSRLOPAPL 

APG MD 21005-5066 

DJR USARL 

AMSRL CI 

AMSRL CI H 

W STUREK 

AMSRL CI s 

AMARK 

AMSRL cs IO FI 

M ADAMSON 

AMSRL SL B 

J SMITH 

AMSRL SL BA 

AMSRL SL BL 

D BELY 

R HENRY 

AMSRL SL BG 

A YOUNG 

AMSRL SL I 

AMSRLWMB 

A HORST 

E SCHMIDT 

AMSRL WM BA 

W D AMICO 

F BRANDON 

AMSRJ., WM BC 

P PLOSTJNS 

D LYON 

J NEWILL 

S WILKERSON 

A ZJELINSKI 

AMSRL WM BD 

B FORCH 

RFJFBR 

R PESCE RODRIGUEZ 

BRICE 

42 
NO. OF 

C_OPIESB 

ABERDEENPROVINGClRQUND(CQEIT) 

AMSRL WM BE 

C LEVERITT 

D KOOKER 

AMSRL WM BR 

C SHOEMAKER 

J BORNSTEIN 

AMSRLWMM 

D VIECHNICKI 

G HAGNATJER 

J MCCAULEY 

B TANNER 

AMSRL WM MA 

R SHUFORD 

P TOUCHET 

N BECK TAN 

DFLANAGAN 

L GHJORSE 

DHARRIS 

S MCKNIGHT 

P MOY 

S NGYUEN 

P PATTERSON 

G RODRIGUEZ 

A TEETS 

RYIN 

AMSRL WM MB 

BFINK 

J BENDER 

T BLANAS 

T BOGETTI 

R BOSSOLI 

L BURTON 

K BOYD 

S CORNELISON 

P DEHMER 

R DOOLEY 

W DRYSDALE 

G GAZONAS 

S GHIORSE 

D GRANVJLLE 

D HOPKINS 

C HOPPEL 

D HENRY 

R KASTE 

M KLUSEWITZ 

M LEADORE 

R LIEB 

NO. OF 

COPIES ORGANIZATION 

ABERDEEN PROVING GROUND ICONTl 

AMSRLWMMB 

E RJGAS 

J SANDS 

D SPAGNUOLO 

W SPURGEON 

J TZENG 

E WETZEL 

AABRAHAMXAN 

M BERMAN 

AFRYDMAN 

TLI 

W MCINTOSH 

E SZYMANSKI 

AMRSL WM MC 

J BEAT-N 

J SWAB 

ECHIN 

J MONTGOMERY 

A WERECZCAK 

J LASALVIA 

J WELLS 

AMSRLWMMD 

W ROY 

S WALSH 

AMSRL WM T 

B BURNS 

AMSRL WM TA 

W GJLLICH 

T HAVEL 

J RUNYEON 

M BURKINS 

E HORWATH 

B GOOCH 

W BRUCHEY 

AMSRL WM TC 

R COAT.& 

AMSRLWMTD 

A DAS GUPTA 

T HADUCH 

T MOYNIHAN 

F GREGORY 

ARAJENDRAN 

M RAFI’ENBERG 

M BOTELER 

T WEERASOORIYA 

DDANDEKAR 

A DIETRICH 
NO. OF 

COPIES ORGANIZAT_ION 

c ABERDEEN 

AMSRLWMTE 

A NIILER 

J POWELL 

AMSRL SS SD 

H WALLACE 

AMSRL SS SE R 

R CHASE 

AMSRL SS SE DS 

R REYZER 

R ATKINSON 

AMSRL SE L 

RWEINRAUB 

J DESMOND 

D WOODBURY 
NO. OF 

COPIES ORGANIZATION 

1 LTD 

R MARTLN 

MERL 

TAMWORTH RD 

HERTFORD SG13 7DG 

UK 

1 PW LAY 

SMC SCOTLAND 

DERA ROSYTH 

ROSYTH ROYAL DOCKYARD 

DUNFERMLINEFIFEKY 112XR 

UK 

1 CIVIL AVIATION 

ADMINSTRATION 

T GOTTESMAN 

PO BOX 8 

BEN GURION INTERNL AIRPORT 

LOD 70150 ISRAEL 

NO. OF 

COPIES 

2 

1 

1 

1 

1 AEROSPATIALE 

SANDRE 

A BTE CC RTE MD132 

316 ROUTE DE BAYONNE 

TOULOUSE 3 1060 

FRANCE 

1 DAIMLER BENZ AEROSPACE 

J BAUER 

D 81663 MUNCHEN 

MUNICH 

GERMANY 

3 DRA FORT HALSTEAD 

P N JONES 

D SCOTT 

M HINTON 

SEVEN OAKS KENT TN 147BP 

UK 

1 DEFENSE RESEARCH ESTAB 

VALCARTIER 

F LESAGE 

COURCELE’ITE QUEBEC COA 

IRO CANADA 

45 

1 

1 

1 

ORGANIZATION 

ROYAL MILITARY COLLEGE OF 

SCIENCE SHRIVENHAM 

D BULMAN 

B LAWTON 

SWlNDON WILTS SN6 8LA 

UK 

SWISS FEDERAL ARMAMENTS 

WKS 

w LANZ 

ALLMENDSTRASSE 86 

3602 THUN 

SWITZERLAND 

ISRAEL INST OF 

TECHNOLOGY 

S BODNER 

FACULTY OF MECHANICAL ENGR 

HAlFA 3200 ISRAEL 

DSTO MATERIALS RESEARCH LAB 

NAVAL PLATFORM VULNERABILITY 

SHIP STRUCTURES & MTRLS DIV 

NBURMAN 

PO BOX 50 

ASCOT VALE VICTORIA 

AUSTRALIA 3032 

ECOLE ROYAL MILITAIRE 

E CELENS 

AVE DE LA RENAISSANCE 30 

1040 BRUXELLE 

BELGIQUE 

DEF RES ESTABLISHMENT 

VALCARTIER 

A DUPUIS 

2459 BOULEVARD PIE XI NORTH 

VALCARTIER QUEBEC 

CANADA 

PO BOX 8800 COURCELETI-E 

GOA IRO QUEBEC CANADA 

INSTITUT FRANC0 ALLEMAND 

DE RECHERCHES DE SANIT LOUIS 

DE M GIRAUD 

5 RUE DU GENERAL CASSAGNOU 

BOITE POSTALE 34 

F 68301 SAINT LOUIS CEDEX 

FRANCE 
NO. OF 

COPIES 

1 

0 m 

ECOLE POLYTECH 1 ERNST MACH JNSTITUT EM1 

J MANSON A STILP 

DMX LTC ECKBRSTRASSE 4 

CH 1015 LAUSANNE 7800 FREIBURG 

SWITZERLAND GERMANY 

TN0 PRINS MAURITS 

LABORATORY 

R IJSSELSTEIN 

LANGE KLEIWEG 137 

PO BOX 45 

2280 A4 RIJSWIJK 

THENETHERLANDS 

FOA NAT L DEFENSE RESEARCH 

ESTAB 

DIR DEPT OF WEAPONS & 

PROTECTION 

B JANZON 

R HOLMLJN 

S 172 90 STOCKHOLM 

SWEDEN 

DEFENSE TECH s4 PROC AGENCY 

GROUND 

ICREWTHER 

GENERAL HERZOG HALTS 

3602 THIN 

SWITZERLAND 

MINJSTRY OF DEFENCE 

RAFAEL 

ARMAMENT DEVELOPMENT 

AUTH 

M MAYSELESS 

PO BOX 2250 

HAIFA 31021 ISRAEL 

DYNAMEC RESEARCH AB 

A PERSSON 

BOX 201 

S 15123 SODERTALJE 

SWEDEN 

ERNST MACH INSTITUT EMI 

DIRECTOR 

HAUPTSTRASSE 18 

79576 WEIL AM RHEIN 

GERMANY 

NO. OF 

COPIES ORGANIZATION 

1 TN0 DEFENSE RESEARCH 

I H PASMAN 

POSTBUS 6006 

2600 JA DELFT 

THENETHERLANDS 

1 B HIRSCH 

TACHKEMONY ST 6 

NETAMUA 426 11 

ISRAEL 

1 DEUTSCHE AEROSPACE AG 

DYNAMICS SYSTEMS 

M HELD 

PO BOX 1340 

D 86523 SCHROBENHAUSEN 

GERMANY 

46 
Bruce K. Fink, Rmpesh Mlathur,* and Suresh G. Advani* 

Aberdeen Proving Ground, MD 21005-5069 MS-I-R-23 17 

Wniversity of Delaware, Newark, DE 19716 

12a. DlSTRlBUTWAVAlLlLlTY STATEMENT 12b. DISTRIBUTION CODE 

Spproved for public release; distribution is unlimited. 

13. ABSTRACT(Marlmwn 200 MS) 

Resin infusion processes are finding increasing applications in the manufacture of composite parrs that have 

geometric and material complexities. In such W, the placement of gates and vents is nonintuitive and may require 

:xpensive repetitive experimentation. Finite element-based resin-flow simulation codes have &en successllly used 

br modeling and analysis of the mold-filling process. Such filling simulations, when coupled with a search 

dgorithm, can also prove useful for optimal design of the filling process. Genetic algorithms (GAS) mimic natural 

&&on and wn efkiently “evolve” near-global optimal solutions from a large number of alternatibe solutions. In 

his paper, GAS are used to optimize gate and vent locations for the resin-transfer molding (RTMJ process in order to 

ninimize fill times and dry-spot formation. A pm performance index, or cost function, is defined, which 

ncorpomtes the fill time and dry-spot formation as primary variables. A part having material and geometric 

~mplexities was chosen for a case study. GA and mold-filling simulations were. used interactively to search for 

)ptimaI gate and vent locations to locate nc~+ptimaI solutions. The GA was able to find good solutions using lc~ 

than 1% of simulations of the possible permutations of gates and vents. The case study was also repeated in thy 

presence of racetracking channels. Again, the optimal locations were found by the GA using less than 1% of all 

Fssible combinations. 

14. SUBJECT TERMS f5. NUMBER OF PAGES 

composite material, genetic altgorithm, resin transfer m&ling, process optimization 51 

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17. SECURITY ClASSiFlCAllON 18. ElXURlTY CLASSIFkXTDtd 19. SECURITY CLASSIFICATION 

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20. LIMITATION OF ABSTRACT 

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UNCLASSIFlED UNCLASSIFIED UNCLASSIFIED UL 

JSN 75404%28p5500 

47 Standard Fom? 298 (Rev. 2-69) Pracrltmd ty ANSI Std. 23918 298-m 
48 
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