**3.1. The procedure and first results**

6 Advances in Computational Stability Analysis

**2.5. Conclusions** 

validation

these limits a knock-down factor is derived.

The work for the stochastic approach consists in checking which structural parameters substantially influence the buckling load and defining realistic limits for their deviations from the nominal values, in varying them within the limits and performing buckling load computations for these variations. The results are evaluated stochastically in order to define a guideline for the lower limits of the buckling loads within a certain given reliability. From

**Figure 4.** Scatter of buckling load due to the scatter of non-traditional imperfections

From all this it becomes obvious that a great deal of knowledge is accumulated concerning the buckling of cylindrical shells under axial compression. However, the NASA guideline for the knock-down factors from 1968 is still in use, and there are no appropriate guidelines for unstiffened cylindrical CFRP shells. To define a lower bound of the buckling load of CFRP structures a new guideline is needed which takes the lay-up and the imperfections into account. This can be for instance a probabilistic approach or the Single-Perturbation-Load approach, combined with a specific stochastic approach. In the following the second one is considered in more detail. Independent of the approach dozens of additional tests are necessary, in order to account for statistical scatter as well as for software and guideline Figure 5 summarises the future design scenario for imperfection sensitive composite structures in comparison to the current design scenario. Currently, the buckling load of the perfect structure FPerfect has to be multiplied by the knock-down factor NASA from the NASA SP 8007 guideline. This approach was developed for metallic structures in 1968 and does not at all allow exploiting the capacities of composite structures. Accordingly, with the new design scenario FPerfect is multiplied by 1 which results from SPLA and 2 which comes from the specific stochastic approach.

**Figure 5.** Future design scenario for composite structures

First studies (cf. [2]) demonstrated the high potential of this combined approach which is summarized in Figure 6. In this example a composite cylinder (R/t=500) with 4 layers was designed according the current and the future design scenarios. The classical buckling load was calculated and utilized as reference (scaled buckling load ρ=1.0, marked by a star). The buckling load calculated by the SPLA was at ρ=0.58 (marked by a star). All experimentally extracted results revealed first buckling beyond the one calculated by the SPLA (safe design). The knock down factor from the SPLA was found to be 0.58 (times 0.8 from stochastic), whereas the one form NASA SP was 0.32. The result was that the load carrying capacity could be increased by 45%. It corresponds to approximately 20% weight reduction for the same load. In [2] the results were validated by tests on 10 nominally identical structures.

The improvement of load carrying capacity by 45% for the investigated 4-ply laminate can be considered to be representative for the following reasons: That laminate set-up was chosen because of its remarkable imperfection sensitivity known from foregoing investigations. With high imperfection sensitivity NASA SP 8007 is not as conservative as with a lower one, nevertheless the improvement of load carrying capacity came to 45%. With lay-ups leading to low imperfection sensitivity the NASA SP 8007 is extremely conservative because it is overestimating the negative influence of imperfections. In that case the improvement of load carrying capacity may be even higher than 45%. Thus the margin of 45% is at the lower limit of improvement of load carrying capacity, and it is not relevant for the expected improvement due to the novel approach whether the 4-ply laminate is optimal or representative for the real construction.

Dealing with Imperfection Sensitivity of Composite Structures Prone to Buckling 9

The buckling test facility is the main instrument to investigate buckling phenomena and to validate software simulations. Figure 7 shows on the left the axial compression configuration and on the right the compression-shear-configuration of the buckling test facility of the DLR Institute of Composite Structures and Adaptive Systems. The test facility

**Figure 7.** DLR's buckling test facility, axial compression configuration (left), compression-shear-

The axial compression configuration is best suited for investigation of imperfection sensitivity on cylindrical structures. All parts of the test device are extremely stiff. The test specimen is located between an axially supporting top plate and a lower drive plate. The top plate can be moved in vertical direction on three spindle columns in order to adapt the test device to various lengths of test specimens. Due to the great sensitivity of stability tests against non-uniform load introduction even the small necessary clearance inside the spindle drives is fixed during the tests by automatically operating hydraulic clamps. The top plate functions as a counter bearing to the axial force that is applied to the movable lower drive plate by a servo-controlled hydraulic cylinder. The drive plate acts against the specimen, which itself acts against a stout cylindrical structure that is meant to distribute the three concentrated forces coming from three load cells at its upper surface, into a smooth force distribution. The test specimen is placed between the load distributor and the drive plate. Although the test device and test specimen are manufactured with particular care one can not expect, that the fixed upper plate and the load distributor are perfectly plane and parallel to each other, nor can one expect the end plates or clamping boxes of the test specimen to be perfectly plane and parallel. To make sure, that the test specimen will be uniformly loaded, thin layers of a kind of epoxy concrete, i.e. epoxy reinforced with a

configuration (right)

can be changed from one configuration to another according to the test requirements.

**Figure 6.** Potential of the future design scenario [2] Example: CFRP cylindrical shell (R/t = 500, 4 layers), Fperfect = 32 kN

## **3.2. The key role of experiments**

New design methods or new software tools in the engineering have to be validated by test results. In addition, stochastic approaches require comprehensive data bases. In order to achieve suitable results appropriate test facilities and measurement systems, but also experience is needed. In the following, facilities and procedures are listed as currently used at DLR, cf. [16].

The buckling test facility is the main instrument to investigate buckling phenomena and to validate software simulations. Figure 7 shows on the left the axial compression configuration and on the right the compression-shear-configuration of the buckling test facility of the DLR Institute of Composite Structures and Adaptive Systems. The test facility can be changed from one configuration to another according to the test requirements.

8 Advances in Computational Stability Analysis

laminate is optimal or representative for the real construction.

**Figure 6.** Potential of the future design scenario [2]

**3.2. The key role of experiments** 

at DLR, cf. [16].

Example: CFRP cylindrical shell (R/t = 500, 4 layers), Fperfect = 32 kN

New design methods or new software tools in the engineering have to be validated by test results. In addition, stochastic approaches require comprehensive data bases. In order to achieve suitable results appropriate test facilities and measurement systems, but also experience is needed. In the following, facilities and procedures are listed as currently used

The improvement of load carrying capacity by 45% for the investigated 4-ply laminate can be considered to be representative for the following reasons: That laminate set-up was chosen because of its remarkable imperfection sensitivity known from foregoing investigations. With high imperfection sensitivity NASA SP 8007 is not as conservative as with a lower one, nevertheless the improvement of load carrying capacity came to 45%. With lay-ups leading to low imperfection sensitivity the NASA SP 8007 is extremely conservative because it is overestimating the negative influence of imperfections. In that case the improvement of load carrying capacity may be even higher than 45%. Thus the margin of 45% is at the lower limit of improvement of load carrying capacity, and it is not relevant for the expected improvement due to the novel approach whether the 4-ply

**Figure 7.** DLR's buckling test facility, axial compression configuration (left), compression-shearconfiguration (right)

The axial compression configuration is best suited for investigation of imperfection sensitivity on cylindrical structures. All parts of the test device are extremely stiff. The test specimen is located between an axially supporting top plate and a lower drive plate. The top plate can be moved in vertical direction on three spindle columns in order to adapt the test device to various lengths of test specimens. Due to the great sensitivity of stability tests against non-uniform load introduction even the small necessary clearance inside the spindle drives is fixed during the tests by automatically operating hydraulic clamps. The top plate functions as a counter bearing to the axial force that is applied to the movable lower drive plate by a servo-controlled hydraulic cylinder. The drive plate acts against the specimen, which itself acts against a stout cylindrical structure that is meant to distribute the three concentrated forces coming from three load cells at its upper surface, into a smooth force distribution. The test specimen is placed between the load distributor and the drive plate. Although the test device and test specimen are manufactured with particular care one can not expect, that the fixed upper plate and the load distributor are perfectly plane and parallel to each other, nor can one expect the end plates or clamping boxes of the test specimen to be perfectly plane and parallel. To make sure, that the test specimen will be uniformly loaded, thin layers of a kind of epoxy concrete, i.e. epoxy reinforced with a

mixture of sand and quartz powder, are applied between the end plates or clamping boxes of the test specimens and the adjacent parts of the test device. This has the side effect of securing the test specimens against lateral displacement. In order to determine the offset of the load measurement it is required, that at least one side of the specimen may be separated temporarily from the test facility. This is achieved by using a separating foil between the top plate and the upper epoxy layer. Two displacement transducers (LVDT) are used to measure axial shortening of the specimen during the tests. Their signals are recorded and, moreover, used for control purposes as actual values. Hence, the test device is displacement controlled. According to the particular arrangement of the transducers the elastic deformation of the test device does not influence the control by shortening at quasi-static loading. Table 1 summarizes the characteristics of the test facility.

Dealing with Imperfection Sensitivity of Composite Structures Prone to Buckling 11

**Camera system 4**

> **Camera system 3**

**4 camera systems**

**Figure 8.** Measured geometric imperfections (ATOS)

**Camera system 1**

**The 4 subareas are joined together without any transition by photogrammetry with TRITOP®**

**Figure 9.** 360° Measurement on a cylinder

**Figure 10.** High Speed ARAMIS Set-Up

loading and unloading sequence)

**Figure 11.** Results of a 360° Measurement on a CFRP cylinder (selected deformation patterns of one

**Camera system 2**


**Table 1.** Characteristics of the DLR buckling test facility

*Before testing* geometric and material imperfections are measured by the following systems (or equivalent)


*During testing* the deformations are measured by the ARAMIS system:

It is based on photogrammetry (precision: 0.02 mm). The system used allows also a 360° measurement of shell surface displacements on a CFRP cylinder (cf. Figure 9 and Figure 11).

All measured full field displacements are transferred to a global coordinate system of the cylinder by means of at least three reference points in each area. The reference points are allocated to the global coordinate system by TRITOP, another photogrammetric system. The result of this procedure is a complete 3-D visualisation of the cylinder deformation (cf. Figure 9). The four camera pairs can also be placed on one part of the structure which allows a quadruplicating of the number of taken pictures per time (Figure 10). A 360° survey of a CFRP cylinder (selected deformation patterns of one loading and unloading sequence) is presented in Figure 11.

Dealing with Imperfection Sensitivity of Composite Structures Prone to Buckling 11

**Figure 8.** Measured geometric imperfections (ATOS)

10 Advances in Computational Stability Analysis

**Geometry limits of the test structure**

**Table 1.** Characteristics of the DLR buckling test facility

**Load case** 

(or equivalent)

improve the visibility 2. Ultrasonic inspection

presented in Figure 11.

mixture of sand and quartz powder, are applied between the end plates or clamping boxes of the test specimens and the adjacent parts of the test device. This has the side effect of securing the test specimens against lateral displacement. In order to determine the offset of the load measurement it is required, that at least one side of the specimen may be separated temporarily from the test facility. This is achieved by using a separating foil between the top plate and the upper epoxy layer. Two displacement transducers (LVDT) are used to measure axial shortening of the specimen during the tests. Their signals are recorded and, moreover, used for control purposes as actual values. Hence, the test device is displacement controlled. According to the particular arrangement of the transducers the elastic deformation of the test device does not influence the control by shortening at quasi-static

loading. Table 1 summarizes the characteristics of the test facility.

Axial compression Max. 1000 kN Torsion Max. 20 kNm Internal pressure Max. 800 kPa External pressure Max. 80 kPa Shear Max. 500 kN

Length Max. 2100 mm Width (diameter) Max. 1000 mm **Load frequency (axial compression only)** Max. 50 Hz

*Before testing* geometric and material imperfections are measured by the following systems

1. ATOS: The ATOS system is based on photogrammetry (precision: 0.02 mm), Figure 8 illustrates an example of measured imperfections which are scaled by a factor of 100 to

It is based on photogrammetry (precision: 0.02 mm). The system used allows also a 360° measurement of shell surface displacements on a CFRP cylinder (cf. Figure 9 and Figure 11). All measured full field displacements are transferred to a global coordinate system of the cylinder by means of at least three reference points in each area. The reference points are allocated to the global coordinate system by TRITOP, another photogrammetric system. The result of this procedure is a complete 3-D visualisation of the cylinder deformation (cf. Figure 9). The four camera pairs can also be placed on one part of the structure which allows a quadruplicating of the number of taken pictures per time (Figure 10). A 360° survey of a CFRP cylinder (selected deformation patterns of one loading and unloading sequence) is

*During testing* the deformations are measured by the ARAMIS system:

**Figure 9.** 360° Measurement on a cylinder

**Figure 10.** High Speed ARAMIS Set-Up

**Figure 11.** Results of a 360° Measurement on a CFRP cylinder (selected deformation patterns of one loading and unloading sequence)

Figure 12 illustrates the measured load-shortening curves of 10 tests with three selected pictures extracted from ARAMIS measurement obtained from the 360° measurement. Picture A and B are from the pre-buckling and Picture C from the early post-buckling state. Figure 13 compares the post-buckling pattern between test and Finite-Element simulation. The left picture is obtained by the 360° ARAMIS measurement. It agrees quite well with the simulation in the right figure. This buckling pattern was observed for all 10 cylinders. More details can be found in [2].

Dealing with Imperfection Sensitivity of Composite Structures Prone to Buckling 13

The main objective of DESICOS is to establish an approach on how to handle imperfection sensitivity in space structures endangered by buckling, in particular for those made from fiber composite materials. It shall substitute the NASA SP 8007, which is extremely

The DESICOS consortium merges knowledge from 2 large industrial partners (ADTRIUM-SAS from France and Astrium GmbH from Germany), one enterprise belonging to the category of SME (GRIPHUS from Israel), 2 research establishments (DLR from Germany and CRC-ACS from Australia) and 7 universities (Politecnico di Milano from Italy, RWTH Aachen, Leibniz University and the Private University of Applied Sciences Göttingen from Germany, TECHNION from Israel, TU-Delft from Netherlands and Technical University of Riga from Latvia). The large industrial enterprises and the SME bring in their specific experience with designing and manufacturing of space structures as well as their long grown manufacturing philosophies for high quality stiffened composite structures. The academic partners and the research organisations provide their special knowledge in methods and tool development as well as testing. This consortium composition assures the

 **WP1:** Benchmarking on selected structures with existing methods: Benchmarks are defined for method evaluation purposes. The objective is the knowledge of the abilities

 **WP2:** Material characterisation and design of structures for buckling tests: The first focus is on the design of structures which will be manufactured and tested in WP4. For that purpose, small specimens will be built and tested in order to characterise the

 **WP3:** Development and application of improved design approaches: In this workpackage new design approaches are developed, modelling and analysis strategies are derived. Finally, all methods are validated by means of the experimental results

 **WP4:** Manufacture, inspection and testing of structures designed in WP 2: This workpackage deals with the manufacturing and testing of structures. The objective is to extend the data base on buckling of imperfection sensitive structures. Based on the designs from WP2 as input, a total of 14 (monolithic, sandwich, stiffened and

 **WP5:** Design handbook and industrial validation: WP5 comprises the final technical part; all the results of the project are assembled in order to derive the final design guidelines and to validate them as well as the new methods. The output is summarized

unstiffened, cylindrical and conical) structures will be considered.

conservative and not really applicable for composite structures, cf. Figure 5.

expected rapid and extensive industrial application of the DESICOS results.

The partners co-operate in the following technical work packages:

and deficiencies of existing approaches.

specific composite material properties.

obtained from the other workpackages.

**4. DESICOS project** 

**4.1. Main objective** 

**4.2. Workpackages** 

**Figure 12.** Load shortening curves of 10 tested cylinders and ARAMIS measurement

**Figure 13.** Postbuckling pattern. Left: Test results obtained by ARAMIS – Right: Simulation results
