GARANTIA PARA RESPONDER DE LOS DEFECTOS Y VICIOS OCULTOS DE LOS BIENES O LA CALIDAD DE LOS SERVICIOS, ASÍ

MSC.PATRAN is used to build the finite element model. Following are the steps used to create bay 2120, extending between stations “21” and “20” in the current wing-box

1- in MSC.PATRAN a new data base is created and named DLR-F6-wing-box- 3D-FEM

2- The model tolerance is set to the default. Analysis type is set to “structure” while the analysis code is chosen to be MSC/NASTRAN.

3- The set of coordinates representing the locations of the stringers and the spar caps at stations “20” and “21” are used to generate these points in MSC.PATRAN as shown in Figure (20).

Fig. (20) Points representing the locations of the spar caps and the stringers at stations “20” and “21”

4- A new group is created and named “2120_stringers”, then post this group as the current group. Using the points created in the previous step a group of lines is generated between pairs of points extending from station “21” to station “20”. The order of creating these lines must start by the lines representing the spar caps, then the lines representing the stringers are created in the order starting from the points near the front spar then proceed towards the rear spar. The reason of this order is that the stringers run out always takes place at the rear spar, i.e. a difference in the number of stringers between two stations means that there is a stringer run out equal to the difference between the number of stringers between the two successive stations and these run outs take place at the rear spars, as shown in the next figure.

Fig. (21) Group of lines representing the spar caps and stringers in bay 2120

From figure (21) it can be noticed that there is a point on the top skin and another one on the lower skin that are not employed in generating the stringer lines, this indicates that these two points are a run out of two stringers in bay 2019.

5- A group is created and named as “2120_skin” and posted as the current group. Use the lines generated in the previous step to generate surfaces extending between adjacent lines in the chord wise direction as shown in the following figure.

Fig. (22) Group of surfaces representing the bay skin and the spars webs

6- Once the geometry of the bay is created, finite elements can be generated. It is well known that increasing the number of elements in the model enhances the accuracy of the results but it increases the model cost. Accordingly, it is required to keep the minimum number of elements necessary to obtain acceptable accurate results. To do so, the number of elements along the bay is selected to be two elements in the span wise direction, and after finishing the whole bay model, the bay is tested for an arbitrary load and the results are obtained. Then the number of elements is increased to three in the span wise direction and the model is resubmitted to NASTRAN for analysis. The results obtained are compared with the results obtained from the pervious step. If a significant change is obtained in the results then, it is required to re-increase the number of elements and test again. A change in the result with in 0.05% doesn’t

require additional refining of the model. It has been found that three elements in the span wise direction results in acceptable results.

9- Elements Properties:

After creating the finite elements, the elements properties should be applied. The stringers are modeled by beam elements with a Z shape cross-section. The details of the Z-shape cross-section are shown in the next figure.

Fig. (23) The Z-shape cross-section of the beam element used in the PBEAML Card for stringer modeling [8]

A comparison between the dimensions of this Z-shape cross-section and the dimensions obtained from the optimization process in stages one and two, shows that these DIM1, DIM2, DIM3 and DIM4 dimensions can be calculated by simple transformations as follows 2 1 w a t b DIM = − (46) w t DIM2= (47) a w t b DIM3= − (48) a w t b DIM4= + (49)

Since the dimensions of the stringers vary from one station to the other, an interpolation process is used to obtain the dimensions of all elements between stations.

This is done by defining the dimensions in PATRAN as fields, where a local coordinate is created at each station with its Z-coordinate directed in the span wise direction. Set of fields are created in PATRAN defined in the station local coordinate, representing the variation of the dimension in the span wise direction. As an example, consider the dimension DIM1 of the Z-shape stringer extending between stations 21 and 20, this dimension is defined in PATRAN as a field on the form

Z DIM

DIM DIM

DIM1= 1_20+( 1_21− 1_20) (50) Similarly for all the other dimensions.

The spar caps are also modeled by beam elements but with L-shape cross-section as shown in the following figure

Fig. (24) The L-shape cross-section of the beam element used in the PBEAML Card for spar caps modeling [8]

Fig. (25) the model stringers after applying the properties in PATRAN

The skin is modeled by SHELL elements, where the thickness of the shells is also defined by fields representing the variation of the skin thickness in the span wise direction.

7- modeling of ribs:

a group of points is generated to represent the perimeter of the rib, these points have the same y-coordinate of the station, while its x-coordinate has the same x- coordinate of the corresponding stringer, while its z-c00rdinate can be defined by the following equation

s s

r z DIM

z = − 4 (51)

Where z_r is the z-coordinate of the rib perimeter point, z_s is the z-coordinate of the corresponding stringer while DIM 4_s is a dimension belongs to the stinger corresponding to this rib point.

The rib web is modeled by QUAD4 elements with PSHELL card for its properties. While the perimeter of the rib and the lightening holes are reinforced by beam elements.

The following figure shows a complete bay modeled in PATRAN.

Fig. (26) Complete bay modeled in PATRAN