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WP 3: Application of dynamic loading

The work within WP3 will consist of investigating the particular loading phenomena that may cause (unwanted) conservatism, and translating these results into design variables that can be applied to the current design process. The targets of WP3 are:

  • Compare results between static and dynamic sizing loads by means of parametric
    analysis
  • Define new structural concepts able to absorb dynamic loads

WP leader: Enrique Villarreal Jurado, Aernnova Engineering Solutions SAU

WP 3 Results

Within Work Package 3,  a parametric dynamic analysis has been carried out with the following aims and characteristics:

  • Select the worst structural response by means of parametric analysis. This is done by means of condensed like beam models (Stick Models).
  • Investigate the effect of the time varying loading on the structure. This is accomplished by means of Stick Models and different Hybrid Models (Figs. 1 to 5).
  • Investigate the frequency content of the load history as well as the corresponding frequency content of the response.
  • Investigate dynamic effects for different duration loads at panel level (Figs. 6 and 7).

Within WP 3, various damping and energy dissipation models in FE programs have been studied by the partners involved. The FE programs include ABAQUS, B2000++, NASTRAN, and STRIPE. 

Implementing damping and energy dissipation models in FE programs requires the computational models to be validated. FE material models can be tested against known analytical material models with unidirectional tests or analytical solutions. This has been demonstrated by AAEM (NASTRAN), AES (ABAQUS), and SMR (B2000++).

Once damping and energy dissipation models are in place they can be applied to specimen, structural parts, and global FE models.

  • Specimen FE models have been studied by AAEM and SMR.

  • Structural parts FE models (composite plates and panels) have been studied by POLIMI and SMR.

  • Global FE model has been studied by SMR.

Damping and dissipation FE models studied include linear viscous damping models and linear and nonlinear transient solution methods, the linear ones limiting the behaviour to a model vibrating at a single frequency, and the nonlinear ones being valid for a range of frequencies limited by the experimental data. More specifically, the DAEDALOS consortium has addressed the issues described in the following. 

AAEM has used the linear viscoelastic material model of NASTRAN, studying the error induced by the linear assumption, i.e. selecting a loss factor η at a given frequency f. If the excitation frequency is near f, the error is less than 10% if the stress amplitude is in the range of 60 MPa (aluminum).

AES did first a parametric analysis, varying the global damping factor and see how the von Mises stress evolves, the idea being to simulate the local dissipation effect on a typical fastened joint structure representing the wing panel fastened to the wing spar. Adaptation of the hybrid model was done, duplicating grids and, separating the skin from the rest and simulating fasteners as linear CBUSH elements. In order to have an estimation of the loss factor of every fastener, an ABAQUS simulations were done for several cases. In all of them viscoelasticity of the aluminum parts as well as friction between contact faces was introduced. Results of the ABAQUS simulation for a typical excitation frequency (4 Hz) were introduced in the properties of the CBUSH elements in the hybrid models, with no success of seeing the local dissipation energy effects.

ALE has analysed a composite coupon with the homogenized viscoelastic material. The generalized Maxwell material parameters were obtained via an optimization procedure reducing the error at the measured data points.

BUT has studied composite panels representing parts of a wing structure with the DYTRAN code. Simulations were focused on energy dissipation. Results for different loading speeds and loading levels in the form of dependencies force-displacement and in the form of figures with deformed shape of the panel are presented. In addition, dissipated energy is estimated.  

FOI has implemented the generalized Maxwell material model for finite strains.

POLIMI has studied damping properties for calculating dissipation in composite plates based on modal damping of composite plates. These parameters were used in simulations of composite plates performed by SMR.

SMR has shown that experimental data can be processed and applied to linear viscoelastic material models for composites and aluminum. Experimental cyclic forced vibration of unidirectional materials can be reconstructed with the numerical model. The generalized Maxwell material parameters are obtained via an optimization procedure reducing the error continuously along the spectrum. A method for calculating the dissipated energy per unit volume and the energy dissipation rate has been tested with FE models of specimens and structural elements. However, nonlinear effects as the ones observed by (RWTH) with aluminum require nonlinear viscoelastic material models already at low stress levels for more accurately representing the response.

TECHNION has studied damping properties of aluminum and composite specimens. AAEM has used the linear viscoelastic material model of NASTRAN, studying the error induced by the linear assumption, i.e. selecting a loss factor η at a given frequency f. If the excitation frequency is near f, the error is less than 10% if the stress amplitude is in the range of 60 MPa (aluminum).

 

Video: Transient analysis of composite plate with viscous damping
Composite plate specimen in non-linear transient analysis with viscoelastic damping (sinusoidal (steady-state) out-of-plane excitation of central node with a frequency equal to 0.7 of the first harmonic). The video shows deformation and energy dissipated per unit volume, both as a function of time.

Video: Dynamic response of full model of DAEDALOS aircraft
Dynamic response of full A/C FE model due to landing case (main gear only). B2000++ transient analysis with 3% percent damping (Rayleigh damping with vibration modes around 15 Hz)

Video: Dynamic response of hybrid model of DAEDALOS aircraft
Response of the metal DAEDALOS aircraft (deformations are scaled 5x) due to the critical vertical gust load case defined in deliverable 2.3. Hybrid wing model was created in metal and composite by ALE. Result plotted is the Von Mises stress. 

 

Work Package 3 has also studied the force redistribution that occurs due to geometrically nonlinear effects (instability, large deflections). Various static and dynamic FE analyses at panel level using detailed panel model have been conducted.

IAI addressed the quasi-static response of the composite test panels (designed and manufactured by IAI) to axial compressive loading. Non-linear numerical analysis was performed using MSC.NASTRAN commercial software. The post-buckling behaviour and stress redistribution were traced till the panel's collapse (defined at the maximum allowed stress level in an individual ply). According to FEA, the panels' collapse is expected due to the stiffeners failure in compression. The results obtained may be validated in the future against the experimental data (the panels are planned to be tested by POLIMI).

AES has studied, in collaboration with POLIMI, the internal force redistribution due to instability for a composite wing panel. POLIMI has further studied the internal force redistribution due to instability for a fuselage panel proposed by IAI, and a tailplane panel proposed by AAEM. The wing panel has been investigated in collaboration with AES. The dynamic analyses have been performed using ABAQUS and considering pulse compressive loads with different durations. As stiffened panels subjected to dynamic loads do not exhibit large changes in dynamic response, dynamic buckling curves have been determined with a radial displacement criterion, and the obtained data were compared with the respective static buckling values. The results have shown an increase of internal force redistribution for pulse load shorter than 5 ms, and a decrease between 5 ms and 20 ms, that can be important for the design of the structures subjected to dynamic loading.

ALE has evaluated the behavior towards buckling, damage initiation and evolution and load redistribution of the 70% wing span upper panel in its test configuration. Load redistribution takes place due to buckling onset, while the damage mechanisms are not involved as they take place in a later loading stage. On the same panel, eigenfrequency and eigenmode analysis are performed in order to characterize its behavior. Finally the chosen panel is applied a dynamic impulsive load in order to evaluate the evolution of the damage Initiation parameters. The load duration needed to reach matrix damage initiation is evaluated.

BUT has studied the response of the flat (wing) panel on different loading speeds using MSC Dytran. Special attention was given to the non-linear part of the loading curve (post-buckling). Different shapes of force - displacement curves were studied for different loading speeds and simulated displacements. As a result, 3D graphs representing results were created, including “Max. Force-Displacement-Load Case Time“, “Buckling Force-Displacement-Load Case Time“, and “Max. Displacement Force-Displacement-Load Case Time“ plots. Furthermore, deformations on panels were analysed.

LUH has studied the load redistribution at panel level due to nonlinear effects (in particular geometrical nonlinearity), for the detailed model of the fuselage panel introduced in WP 2(“longeron-type panel”). Buckling load levels (load levels at which large response amplitudes occur) have been established using transient Finite Element Analysis, and a comparison with results based on static analysis has been made. The results depend significantly on the character (shape and duration) of the applied dynamic load. The possibility of an appropriate coupling between panel level models and a coarse finite element model of the full aircraft has been investigated.

In SMR’s contribution specific panels have been studied  with the goal of applying proper dynamic loads and damping properties, and testing and applying a global-local approach in structural dynamics. SMR coupled the local FE model by means of SMR's L2-norm coupling method to the local FE model. The different types of convergence and accuracy studies on panels allow for obtaining better estimates of the load redistribution due to instability. The panel-only global-local study is an intermediate/validation study for determining the influence of the L2 norm coupling method on the accuracy of the solution, specifically at the coupling interface, since this effect is important when estimating the load redistribution due to instability.

An investigation on modelling the force redistribution in a larger part of the aircraft has been carried out in the context of a hybrid model containing a detailed FE model of a larger part of the aircraft. In the DLR contribution, force redistributions due to instabilities were studied on the barrel level. First, an appropriate hybrid model was created which was then used for dynamic nonlinear simulations using a landing load case. Preliminary force distributions along the circumference of the barrel are extracted along with the radial displacement to assess the force redistribution in the structure. The final results of the study regarding the force redistribution as well as a comparison of the element stresses to the stresses resulting from the current (static) design approach will be released at a later point in time.

The analysis of force redistributions in a dynamic analysis, even at panel level, requires very large, detailed FE models, which require a considerable computational effort and their results are often difficult to interpret.

For this reason, in Work Package 3 fast tools (both semi-analytical and FE based reduced-order models) for the dynamic analysis at panel level have been developed. AES has studied the buckling and the modal analysis of aircraft skin panel in static and dynamic conditions. First, the study has been focused on the effect of the boundary rotational stiffness due to stringers on the buckling load factor and the first natural frequency of an orthotropic plate. The aim of this part is the development of an approximated analysis based on variational calculation which is computationally faster than FEA. This analysis enable one to develop parametric studies therefore allows finding alternative design solutions or understands the effect of different variables, i.e. getting buckling interaction graphs. In the second view, the study tries to quantify the panel curvature effect on the buckling load factor of a wing panel, again for static and dynamic loading.

In order to gain insight in the characteristics of the nonlinear dynamic behaviour of panel structures and to reduce the computational effort of the nonlinear transient Finite Element calculations, the LUH has developed modal-based reduced-order models (fast tools) for geometrically nonlinear dynamic analysis. The approach has been applied to the postbuckling behaviour of a benchmark stiffened composite panel under dynamic in-plane loading. In order to obtain accurate representations of the response in complicated Analysis cases such as the one investigated, extension of the reduced order approach to a multi-mode analysis is required.

Several general conclusions regarding the studies on the force redistribution which occurs due to geometrically nonlinear effects that have been performed within this Work Package, can be drawn. At panel level the failure load levels under dynamic analysis can considerably differ from the load levels obtained for a static analysis. The redistribution at panel level has been thoroughly investigated. In order to obtain insight in the load distributions at aircraft level, extended models (models in which larger parts of the aircraft are represented with detailed FE models) are required.

 

 

Figure 1: Wing Hybrid Model for parametric analysis.
Figure 2: Detailed part of Wing Hybrid Model.
Figure 3: Detailed part of Wing Hybrid Model: Lower skin.
Figure 4: Detailed part of Wing Hybrid Model: Upper skin.
Figure 5: Time history of axial stress at typical elements at Rib15 under gust loading (gust gradient distance H = 350 ft, MTOW).
Figure 6: Composite test panel with three stringers, out of plane displacement for 15 ms load duration at 47 kN, at 12.5 ms.
Figure 7: Dynamic buckling load of composite test panel with three stringers.
 
Figure 8: Using dynamic analyses, it is possible to account for strain rate dependent material behavior. Taking into account material damping results in lower, more realistic stresses. It is noted that in certain cases, a static analysis can underestimate the actual stress level. ALE results are shown.