2. Optimal design procedure

#### 2.1. Basic structural configuration and FEA design parameters

In this work, hat stiffeners and plates were selected as basic elements for parametric analysis and for constructing an analytical solution. The plate element is an orthotropic laminated element with material, number of plies, stacking sequence, width, length, and thickness parameters. The hat stiffener element is also parametrically defined in terms of several geometric parameters as shown in Figure 3.

Design Optimization and Higher Order FEA of Hat-Stiffened Aerospace Composite Structures http://dx.doi.org/10.5772/intechopen.79488 59

Figure 3. Hat stiffener basic element with geometric parameters.

FEM was utilized to produce sensitivity of structural behavior (deflection, stresses) to basic elements' parameters and for comparing final experimental results with modeling. Laminated plate, hat-stiffener, hat-stiffener bonded to base plate were modeled in MSC NASTRAN for this purpose. Laminated plate modeling in FEM is routine and therefore not discussed for the sake of brevity. The hat stiffener (with and without plate to which it is bonded) are modeled as follows. Height of the stiffener web (h), width of the stiffener cap (W1), bottom width in between stiffener flanges (W2), width of the stiffener flange (due to symmetric, the left and right width are the both L1) are the geometric parameters considered in addition to thickness of a ply, ply orientation and the stacking sequence. The length of the hat stiffener is fixed at 508 mm (which is 20 inches).

Material properties are taken from Cytec information sheet CYCOM 5320 [12–37]. These unidirectional fiber tape tensile properties are:

E1 = 1.59E5 MPa;

allow quick, easy and accurate topology and geometry model creation with design constraints, implicit parameterization for easy model variation, integrated Finite Element generator, models and components storage in library for generation of knowledge database and reusability, shape and size optimization in a closed batch loop, on-the-fly definition of design variables and design space, and integration of specific applications like commercial optimization and design tools. In this work, we plan to utilize these aspects to create a Higher Order Abstract

The goals and key feature of this work include analyzing the geometric parameter sensitivity of the hat stiffener, and developing and demonstrating a proof-of-concept theoretical model which is a parametric analytical solution that is theoretically equivalent to hat-stiffener stiffened panels in mechanical response. The analytical solution contains parametric information incorporating geometric, design allowables, and manufacturing information such as laminate stacking order. The constructions of these equivalent analytical models will be stored in a

1. Select composite ply materials and corresponding stochastic material properties for track-

2. Explore the design space and using Finite Element Method (FEM) to analyze the para-

3. Develop an equivalentmodel using analytical solution and run case studies for various loading conditions to develop the empirical relationships between design parameters and allowables/ performance. This takes into account the key geometric and material parameters and gives a

4. Manufacture hat-stiffened composite panel and perform experimental investigation to compare its mechanical response with FEA models' prediction and the mechanical response bounds resulting from the analytical models. Finally, this work would provide the aviation industry with a parametric databases of hat stiffener design and analysis.

In this work, hat stiffeners and plates were selected as basic elements for parametric analysis and for constructing an analytical solution. The plate element is an orthotropic laminated element with material, number of plies, stacking sequence, width, length, and thickness parameters. The hat stiffener element is also parametrically defined in terms of several geo-

metrical sensitivity of the basic composite structural elements: hat stiffeners.

higher and lower boundary of the relatively equivalent hat-stiffener stiffened panel.

database from which they can be easily retrieved and parametrically modified.

Achieving the above requires specific technical objectives including:

2.1. Basic structural configuration and FEA design parameters

Structural Elements, later abbreviated as HOASE.

ing them to parametric design allowables.

2. Optimal design procedure

metric parameters as shown in Figure 3.

1.2. Objectives and structure

58 Optimum Composite Structures

E2 = 9.3E3 MPa;

Poisson's Ratio v = 0.336;

Shear modulus G12 = G13 = 5.6E3 MPa.

QUAD4 MSC Nastran element and PCOMP material properties input was used for analysis. A uniform pressure of 6.89E-2 MPa is applied on each of the two bottom flange surfaces for the hat-stiffener simulation. For the second set of simulations, same magnitude of pressure, 6.89E-2 MPa is applied on the plate to which hat-stiffener is bonded. Longitudinal edges are free to rotate but not translate (Tx = Ty = Tz = 0). The transverse direction edges are free. These longitudinal edge boundary conditions represent fixed edges rather than simply supported, because edge cross sections are constrained from rotation. Same boundary conditions for flat plates will represent simply supported conditions.

Longitudinal edges (the two edges of the skin plate only, not including hat stiffener web and top cap) are simply supported as Tx = Ty = Tz = 0 for hat stiffener bonded to the plate. The transverse edges of the plate are subjected to the boundary conditions Tx = Ry = Rz = 0, corresponding to all four edges simply supported. These boundary conditions are chosen to demonstrate extreme sensitivity of structural response to boundary conditions.

#### 2.2. Parametric sensitivity analysis on hat-stiffener structures

To study the sensitivity of hat-stiffener's geometric parameters, hat-stiffener models are created first. The hat-stiffener element is modeled and analyzed using MSC NASTRAN to construct parametric design space. As presented in the last section, design parameters were defined for hat-stiffeners. The parametric range and increments we defined here covered most of the practical design exploration space and are summarized in Table 2.

These parametric variations represent 1680 models and design points. A smaller set of parameter combinations are analyzed to get the design trends. We explored maximum specific bending rigidity contribution of hat-stiffeners to membrane skin which is designed to take torsional shear. Representative 10 psi uniform pressure loading and simply supported boundary conditions on a 508 mm (20 inches) long hat cross section beam are analyzed. The cross-sectional area of hat-stiffeners varies with design parameters. A baseline configuration with minimum cross-sectional area is chosen to illustrate effect of parameters on bending. This configuration represents 12.7 mm (0.5 inch) bottom flange length, 25.4 mm (1 inch) bottom hat width, 12.7 mm (0.5 inch) top hat width, 12.7 mm (0.5 inch) hat height, 1.016 mm (0.04 inch) thickness and [0/90/45/45]s stacking order.

Figure 4 shows the mid-point transverse deflection and maximum flexural stress at mid-point on the beam as a percent change from the baseline configuration. Stacking sequence and therefore corresponding laminate thickness is kept constant. The ratio of top and bottom hat widths is kept constant at 0.5 for all parametric variations. Three curve-sets show variation of deflection and flexural longitudinal stress with hat height, width and bottom flange length, respectively. As expected, it is evident that bottom flange length contribution is minimal to the


flexural behavior of the stiffener. The maximum change in bending rigidity is achieved by

Design Optimization and Higher Order FEA of Hat-Stiffened Aerospace Composite Structures

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A proof-of-concept analytical model consists of a rectangular plate stiffened by several hat

Figure 5 shows steps incorporated in constructing the analytical model. Composite ply properties, stacking sequence for hat and plate laminates, plate and hat stiffener geometric parameters, stiffener spacing, boundary conditions and loading are specified for the analytical model. Orthotropic plate properties are obtained by scaling, homogenizing and distributing stiffener

Let θ be the angle between x-axis (stiffener longitudinal direction) and j is the ply fiber direction in sections plane, a is the equal distance between stiffeners. The bottom and top flanges as well as webs are defined as continuous plies of the orthotropic plate as follows:

changing hat height up to three times the top flange width.

2.3. Analytical solution of hat stiffener with base plate

stiffeners was established in MATLAB.

Figure 4. Hat stiffener basic element bending behavior.

For bottom flange:

properties over the space between the stiffeners.

Figure 5. Equivalent orthotropic plate for hat-stiffener stiffened skin.

Table 2. Hat-stiffener parametric design exploration space.

Figure 4. Hat stiffener basic element bending behavior.

flexural behavior of the stiffener. The maximum change in bending rigidity is achieved by changing hat height up to three times the top flange width.

#### 2.3. Analytical solution of hat stiffener with base plate

A proof-of-concept analytical model consists of a rectangular plate stiffened by several hat stiffeners was established in MATLAB.

Figure 5 shows steps incorporated in constructing the analytical model. Composite ply properties, stacking sequence for hat and plate laminates, plate and hat stiffener geometric parameters, stiffener spacing, boundary conditions and loading are specified for the analytical model. Orthotropic plate properties are obtained by scaling, homogenizing and distributing stiffener properties over the space between the stiffeners.

Let θ be the angle between x-axis (stiffener longitudinal direction) and j is the ply fiber direction in sections plane, a is the equal distance between stiffeners. The bottom and top flanges as well as webs are defined as continuous plies of the orthotropic plate as follows:

For bottom flange:

corresponding to all four edges simply supported. These boundary conditions are chosen to

To study the sensitivity of hat-stiffener's geometric parameters, hat-stiffener models are created first. The hat-stiffener element is modeled and analyzed using MSC NASTRAN to construct parametric design space. As presented in the last section, design parameters were defined for hat-stiffeners. The parametric range and increments we defined here covered most

These parametric variations represent 1680 models and design points. A smaller set of parameter combinations are analyzed to get the design trends. We explored maximum specific bending rigidity contribution of hat-stiffeners to membrane skin which is designed to take torsional shear. Representative 10 psi uniform pressure loading and simply supported boundary conditions on a 508 mm (20 inches) long hat cross section beam are analyzed. The cross-sectional area of hat-stiffeners varies with design parameters. A baseline configuration with minimum cross-sectional area is chosen to illustrate effect of parameters on bending. This configuration represents 12.7 mm (0.5 inch) bottom flange length, 25.4 mm (1 inch) bottom hat width, 12.7 mm (0.5 inch) top hat width, 12.7 mm (0.5 inch) hat height, 1.016 mm (0.04 inch) thickness and [0/90/45/45]s stacking

Figure 4 shows the mid-point transverse deflection and maximum flexural stress at mid-point on the beam as a percent change from the baseline configuration. Stacking sequence and therefore corresponding laminate thickness is kept constant. The ratio of top and bottom hat widths is kept constant at 0.5 for all parametric variations. Three curve-sets show variation of deflection and flexural longitudinal stress with hat height, width and bottom flange length, respectively. As expected, it is evident that bottom flange length contribution is minimal to the

demonstrate extreme sensitivity of structural response to boundary conditions.

of the practical design exploration space and are summarized in Table 2.

2.2. Parametric sensitivity analysis on hat-stiffener structures

Table 2. Hat-stiffener parametric design exploration space.

order.

60 Optimum Composite Structures

Figure 5. Equivalent orthotropic plate for hat-stiffener stiffened skin.

$$\overline{Q}\_{11b\not\!\!/} = \frac{2L1}{a} \left[ Q\_{11}^{\not\!\!/} \cos 4\theta + Q\_{22}^{\not\!\!/} \sin 4\theta + 2 \left( Q\_{12}^{\not\!\!/} + 2 Q\_{66}^{\not\!\!/} \right) \sin 2\theta \cos 2\theta \right] \tag{1}$$

For top flange:

$$\overrightarrow{Q}\_{11f}^{\circ} = \frac{w1}{a} \left[ \overrightarrow{Q}\_{11}^{\circ} \cos 4\theta + \overrightarrow{Q}\_{22}^{\circ} \sin 4\theta + 2 \left( \overrightarrow{Q}\_{12}^{\circ} + 2 \overrightarrow{Q}\_{66}^{\circ} \right) \sin 2\theta \cos 2\theta \right] \tag{2}$$

For webs, define:

$$\cos x = \frac{h}{\left[\left(\frac{w\_2 - w\_1}{2}\right)^2 + h^2\right]^{1/2}}\tag{3}$$

Simulation of panel-level hat-stiffeners requires understanding of global and local effects of the parameters. One should consider local maximum deflection occurring in between the stiffeners on the panel, because that may become a dominant parameter for deformation constraints

Design Optimization and Higher Order FEA of Hat-Stiffened Aerospace Composite Structures

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63

To validate the modeling prediction of the center point deflection of the stiffened panel, a composite panel bonded with multiple hat-stiffeners was manufactured as a demonstrator part. During fabrication of the structural element and the final demonstration part, unidirectional Cytec Cycom 5320 prepreg material, out-of-autoclave curing, and secondary bonding

The basic structural elements comprise of flat panels and hat cross section beams. The assembly of these basic structural elements forms the demonstrator part represented by a large panel stiffened by four equidistant hat beams, as shown in Figure 7. To accurately predict and compare with the FEA results, the demonstration part has identical set up with the MSC

The demonstration part was tested under near-uniform 1 psi loading and the center point deflection was recorded so it can be compared with FEA results. Photographs of the testing setup are shown in Figure 8. The experimental testing of the demonstrator part involves simply supporting the edges and subjecting it to a uniform pressure loading condition by placing sandbags at the center. Experimentally measured panel displacements are then com-

The demonstration plate midpoint deflections are experimentally obtained for 150, 225, 300, 375 and 400 lb. load are 0.022, 0.032, 0.039, 0.045 and 0.047 in, respectively. The first increment

pared to predictions from both analytical constructs as well as FEA models.

satisfaction.

technique were used.

2.5. Manufacturing of the demonstration part

Figure 6. Midpoint deflection of the demonstration part FEA model.

Nastran FEA model built and explained in the last section.

2.6. Testing and validation of the demonstration part

And therefore, contribution from two web laminates is:

$$\overline{Q}\_{11\text{web}}^{\dot{}} = \frac{2}{a\cos x} \sum\_{j=1}^{n} t\_{\dot{}} \left[ Q\_{11}^{j} \cos 4\theta + Q\_{22}^{j} \sin 4\theta + 2 \left( Q\_{12}^{j} + 2 Q\_{66}^{j} \right) \sin 2\theta \cos 2\theta \right] \tag{4}$$

These equivalent Q<sup>j</sup> <sup>11</sup> contributions can be used in traditional ABD matrix construction. Similarly, other Qs, the equivalent reduced stiffness matrix components are also calculated, and their contributions are used in the traditional A, B and D matrix construction. The analytical solution of the equivalent panel was input into MATLAB for the center point deflection prediction. Future work will be focusing on analytically representing the homogenized panel equivalent to the stiffened panel with multiple hat-stiffeners on it. Also, it should be noted that for the analytical solution for large panel with a sparse distribution of multiple stiffeners, these relationships may not be valid but may still give the bounding values of the possible deflection of points on the plate.

#### 2.4. FEA model for the demonstration part: Panel with multiple hat-stiffeners

To better understand and predict the mechanical behavior of the structure, a demonstration FEA model of one panel with multiple hat stiffeners bonded onto it was built in MSC Nastran (Figure 6). A few composite ply material properties were selected from the Cytec Cycom 5320 prepreg data sheet for creating the model and database.

For the geometric configuration of the model: this demonstrator model comprises a base panel of in-plane dimensions 304.8 mm (which is 12 inches) � 863.6 mm (which is 3 inches) with four hat stiffeners on it., each separated by approximately 85.725 mm (which is 3.37 inches). The bottom width of the hat stiffener is approximately 86.36 mm (which is 3.4 inches) with 60.96 mm (which is 2.4 inches) as the distance between the lower two corners of the hat stiffeners and 12.7 mm (which is 0.5 inch) overhang (i.e., flange) on the either side. The base panel has 8 plies of laminates with 5320 unidirectional prepreg properties and they are in a quasi-isotropic layup as follows: [90,�45,+45,0]S. Each of the four hats also consists of eight unidirectional fiber plies in the same quasi-isotropic layup.

Design Optimization and Higher Order FEA of Hat-Stiffened Aerospace Composite Structures http://dx.doi.org/10.5772/intechopen.79488 63

Figure 6. Midpoint deflection of the demonstration part FEA model.

Qj

62 Optimum Composite Structures

Qj

For top flange:

For webs, define:

Qj

These equivalent Q<sup>j</sup>

of points on the plate.

<sup>11</sup>web <sup>¼</sup> <sup>2</sup>

a cos x

<sup>11</sup>bf <sup>¼</sup> <sup>2</sup>L<sup>1</sup> a Qj

<sup>11</sup>tf <sup>¼</sup> <sup>w</sup><sup>1</sup> a Qj

<sup>11</sup> cos 4<sup>θ</sup> <sup>þ</sup> <sup>Q</sup><sup>j</sup>

<sup>11</sup> cos 4<sup>θ</sup> <sup>þ</sup> <sup>Q</sup><sup>j</sup>

And therefore, contribution from two web laminates is:

Xn j¼1

prepreg data sheet for creating the model and database.

unidirectional fiber plies in the same quasi-isotropic layup.

tj Q<sup>j</sup>

<sup>22</sup> sin 4<sup>θ</sup> <sup>þ</sup> <sup>2</sup> Qj

<sup>22</sup> sin 4<sup>θ</sup> <sup>þ</sup> <sup>2</sup> <sup>Q</sup><sup>j</sup>

cos <sup>x</sup> <sup>¼</sup> <sup>h</sup> w2�w<sup>1</sup> 2

<sup>11</sup> cos 4<sup>θ</sup> <sup>þ</sup> <sup>Q</sup><sup>j</sup>

2.4. FEA model for the demonstration part: Panel with multiple hat-stiffeners

h i

h i

<sup>22</sup> sin 4<sup>θ</sup> <sup>þ</sup> <sup>2</sup> <sup>Q</sup><sup>j</sup>

larly, other Qs, the equivalent reduced stiffness matrix components are also calculated, and their contributions are used in the traditional A, B and D matrix construction. The analytical solution of the equivalent panel was input into MATLAB for the center point deflection prediction. Future work will be focusing on analytically representing the homogenized panel equivalent to the stiffened panel with multiple hat-stiffeners on it. Also, it should be noted that for the analytical solution for large panel with a sparse distribution of multiple stiffeners, these relationships may not be valid but may still give the bounding values of the possible deflection

To better understand and predict the mechanical behavior of the structure, a demonstration FEA model of one panel with multiple hat stiffeners bonded onto it was built in MSC Nastran (Figure 6). A few composite ply material properties were selected from the Cytec Cycom 5320

For the geometric configuration of the model: this demonstrator model comprises a base panel of in-plane dimensions 304.8 mm (which is 12 inches) � 863.6 mm (which is 3 inches) with four hat stiffeners on it., each separated by approximately 85.725 mm (which is 3.37 inches). The bottom width of the hat stiffener is approximately 86.36 mm (which is 3.4 inches) with 60.96 mm (which is 2.4 inches) as the distance between the lower two corners of the hat stiffeners and 12.7 mm (which is 0.5 inch) overhang (i.e., flange) on the either side. The base panel has 8 plies of laminates with 5320 unidirectional prepreg properties and they are in a quasi-isotropic layup as follows: [90,�45,+45,0]S. Each of the four hats also consists of eight

h i

<sup>11</sup> contributions can be used in traditional ABD matrix construction. Simi-

<sup>12</sup> <sup>þ</sup> <sup>2</sup>Q<sup>j</sup> 66

<sup>12</sup> <sup>þ</sup> <sup>2</sup>Q<sup>j</sup> 66

� �

sin 2θ cos 2θ

sin 2θ cos 2θ

sin 2θ cos 2θ

� �<sup>2</sup> <sup>þ</sup> <sup>h</sup><sup>2</sup> h i<sup>1</sup>=<sup>2</sup> (3)

<sup>12</sup> <sup>þ</sup> <sup>2</sup>Q<sup>j</sup> 66

� �

(1)

(2)

(4)

� �

Simulation of panel-level hat-stiffeners requires understanding of global and local effects of the parameters. One should consider local maximum deflection occurring in between the stiffeners on the panel, because that may become a dominant parameter for deformation constraints satisfaction.

#### 2.5. Manufacturing of the demonstration part

To validate the modeling prediction of the center point deflection of the stiffened panel, a composite panel bonded with multiple hat-stiffeners was manufactured as a demonstrator part. During fabrication of the structural element and the final demonstration part, unidirectional Cytec Cycom 5320 prepreg material, out-of-autoclave curing, and secondary bonding technique were used.

The basic structural elements comprise of flat panels and hat cross section beams. The assembly of these basic structural elements forms the demonstrator part represented by a large panel stiffened by four equidistant hat beams, as shown in Figure 7. To accurately predict and compare with the FEA results, the demonstration part has identical set up with the MSC Nastran FEA model built and explained in the last section.

#### 2.6. Testing and validation of the demonstration part

The demonstration part was tested under near-uniform 1 psi loading and the center point deflection was recorded so it can be compared with FEA results. Photographs of the testing setup are shown in Figure 8. The experimental testing of the demonstrator part involves simply supporting the edges and subjecting it to a uniform pressure loading condition by placing sandbags at the center. Experimentally measured panel displacements are then compared to predictions from both analytical constructs as well as FEA models.

The demonstration plate midpoint deflections are experimentally obtained for 150, 225, 300, 375 and 400 lb. load are 0.022, 0.032, 0.039, 0.045 and 0.047 in, respectively. The first increment

components from these parametric modeling constructs will be matured, implemented and validated to demonstrate the benefits of starting the design with validated parametric design

Design Optimization and Higher Order FEA of Hat-Stiffened Aerospace Composite Structures

http://dx.doi.org/10.5772/intechopen.79488

65

This work has illustrated the process of developing an analytical model and the design and analysis of the parametric composite hat-stiffened panels. The amount of the work involved in designing to this level of abstraction is a significant part of the design of an aircraft. This work is needlessly repeated by designers again and again and can be standardized to abbreviate the design process, and has successfully shown most of the processes involved in creating parametric models with a hat-stiffener stiffened composite laminated plate model development.

Most commercial CAD/FEA software includes some form of parameterization of design variables. Basic research level higher order structural elements have also been developed. These tools allow quick, easy and accurate topology and geometry model creation with design constraints; implicit parameterization for easy model variation; integrated Finite Element generator; models and components storage in library for generation of knowledge database and reusability; shape and size optimization in a closed batch loop; on-the-fly definition of design variables and design space; and integration of specific applications like commercial optimization and design tools. Our future work includes integrating these models in similar design tools, such as a combination of MSC Nastran, ABAQUS, MATLAB and C++ platform.

Authors would like to appreciate Brian Casey, Senior Engineer of MSC NASTRAN Development, for his important suggestions and the time he has spent on proof-reading the manuscript.

elements.

3. Conclusions

Figure 9. Midpoint deflection of the demonstration part.

Acknowledgements

Figure 7. Manufacturing and assembly of basic structural elements into a demonstration part.

Figure 8. Simply supported hat-stiffened composite panel under near-uniform pressure loading.

(150 lb) was using lead balls filled bags providing close to uniform loading. The remaining increments were obtained using iron discs that did not provide as uniform loading as lead balls filled bags would have. As the results are shown in Figure 9, the midpoint deflection is 1.52 mm (0.06 in) for 1 psi uniform loading while FEA simulation gave 1.83 mm (0.07 in).

The analytical bounds for stiffened plates were also obtained. The midpoint deflection from the homogenized orthotropic plate gives the lower bound and simply supported idealized plate between the stiffeners gives upper bound. The lower bound provides better approximation for plates with closely spaced stiffeners. The real deformation starts to approach the upper bound as spacing between stiffeners increases. The lower bound for midpoint deflection under 1 psi is 0.133 mm (0.0052 in) and the upper bound is 2.85 mm (0.11 in).

The work performed establishes the basis for continuing future work to further develop a set of parametric models. The conceived process of designing advanced composite aircraft structural

Figure 9. Midpoint deflection of the demonstration part.

components from these parametric modeling constructs will be matured, implemented and validated to demonstrate the benefits of starting the design with validated parametric design elements.

## 3. Conclusions

(150 lb) was using lead balls filled bags providing close to uniform loading. The remaining increments were obtained using iron discs that did not provide as uniform loading as lead balls filled bags would have. As the results are shown in Figure 9, the midpoint deflection is 1.52 mm (0.06 in) for 1 psi uniform loading while FEA simulation gave 1.83 mm (0.07 in).

The analytical bounds for stiffened plates were also obtained. The midpoint deflection from the homogenized orthotropic plate gives the lower bound and simply supported idealized plate between the stiffeners gives upper bound. The lower bound provides better approximation for plates with closely spaced stiffeners. The real deformation starts to approach the upper bound as spacing between stiffeners increases. The lower bound for midpoint deflection under

The work performed establishes the basis for continuing future work to further develop a set of parametric models. The conceived process of designing advanced composite aircraft structural

1 psi is 0.133 mm (0.0052 in) and the upper bound is 2.85 mm (0.11 in).

Figure 7. Manufacturing and assembly of basic structural elements into a demonstration part.

64 Optimum Composite Structures

Figure 8. Simply supported hat-stiffened composite panel under near-uniform pressure loading.

This work has illustrated the process of developing an analytical model and the design and analysis of the parametric composite hat-stiffened panels. The amount of the work involved in designing to this level of abstraction is a significant part of the design of an aircraft. This work is needlessly repeated by designers again and again and can be standardized to abbreviate the design process, and has successfully shown most of the processes involved in creating parametric models with a hat-stiffener stiffened composite laminated plate model development.

Most commercial CAD/FEA software includes some form of parameterization of design variables. Basic research level higher order structural elements have also been developed. These tools allow quick, easy and accurate topology and geometry model creation with design constraints; implicit parameterization for easy model variation; integrated Finite Element generator; models and components storage in library for generation of knowledge database and reusability; shape and size optimization in a closed batch loop; on-the-fly definition of design variables and design space; and integration of specific applications like commercial optimization and design tools. Our future work includes integrating these models in similar design tools, such as a combination of MSC Nastran, ABAQUS, MATLAB and C++ platform.

## Acknowledgements

Authors would like to appreciate Brian Casey, Senior Engineer of MSC NASTRAN Development, for his important suggestions and the time he has spent on proof-reading the manuscript.
