Simulating Postbuckling Behaviour and Collapse of Stiffened CFRP Panels

Advanced composite materials are well known for their outstanding potential in weight-related stiffness and strength leading to an ever increasing share in aerospace structural components out of Carbon Fibre Reinforced Plastics (CFRP). In order to fully exploit the load-carrying capacity of such structures an accurate and reliable simulation is indispensable. Local buckling is not necessarily the load bearing limit for stiffened panels or shells; their full potential can be tapped only by utilizing the postbuckling region. That, however, requires fast tools which are capable of simulating the structural behaviour beyond bifurcation points including material degradation up to collapse. The most critical structural degradation mode is skin stringer separation; delamination, especially within the stringer, is a critical material degradation. A reliable prediction of collapse requires knowledge of degradation due to static as well as low cycle loading in the postbuckling region. Earlier projects have shown that it needs considerable experience in simulating the postbuckling behaviour. Though a great deal of knowledge about CFRP structural and material degradation is available its influence on collapse is not yet sufficiently investigated. It is the aim of the project COCOMAT (Improved MATerial exploitation at safe design of COmposite airframe structures by accurate simulation of COllapse) to develop means for and gain experience in fast and accurate simulation of the collapse load of stringer stiffened CFRP curved panels taking degradation and cyclic loading as well as geometric nonlinearity into account. COCOMAT is a Specific Targeted Research Project supported by the EU 6th Framework Programme; it started 2004 and runs for 4 years. Main deliverables are: • test results for buckling and collapse of undamaged and pre-damaged stiffened CFRP panels under static and cyclic loading, • improved material properties and degradation models, computational tools for design and certification of stiffened fibre composite panels which take postbuckling behaviour, degradation and collapse into account, • and finally design guidelines and industrial validation. The work will lead to an extended experimental data base, relevant degradation models and improved simulation tools for certification as well as for design. These results should allow setting up a future design scenario which exploits the existing reserves in primary fibre composite structures. The paper starts out from results provided by the forerunners of COCOMAT, describes the main objectives of the project, gives a general status of the progress reached so far and presents first results

Design and Analysis of Composite Panels

European aircraft industry demands for reduced development and operating costs, by 20% and 50% in the short and long term, respectively. Contributions to this aim are provided by the completed project POSICOSS (5thFP) and the running follow-up project COCOMAT (6thFP), both supported by the European Commission. As an important contribution to cost reduction a decrease in structural weight can be reached by exploiting considerable reserves in primary fibre composite fuselage structures through an accurate and reliable simulation of postbuckling up to collapse. The POSICOSS team developed fast procedures for postbuckling analysis of stiffened fibre composite panels, created comprehensive experimental data bases and derived design guidelines. COCOMAT builds up on the POSICOSS results and considers in addition the simulation of collapse by taking degradation into account. The results comprise an extended experimental data base, degradation models, improved certification and design tools as well as design guidelines. The projects POSICOSS and COCOMAT develop improved tools which are validated by experimental results obtained during the projects. Because the new tools must consider a wide range of different aspects a lot of different structures had to be tested. These structures were designed under different design objectives. For the design process the consortium applied already available simulation tools and brought in their own design experience. This paper deals with the design process within both projects and the analysis procedure applied within this task. It focuses on the experience of DLR on the design and analysis of stringer stiffened CFRP panels gained in the frame of these projects

Neural networks for time-varying data

This paper reviews some basic issues and methods involved in using neural networks to respond in a desired fashion to a temporally-varying environment. Some popular network models and training methods are introduced. A speech recognition example is then used to illustrate the central difficulty of temporal data processing: learning to notice and remember relevant contextual information. Feedforward network methods are applicable to cases where this problem is not severe. The application of these methods are explained and applications are discussed in the areas of pure mathematics, chemical and physical systems, and economic systems. A more powerful but less practical algorithm for temporal problems, the moving targets algorithm, is sketched and discussed. For completeness, a few remarks are made on reinforcement learning

Description and training of neural network dynamics

Attractor properties of a popular discrete-time neural network model are illustrated through numerical simulations. The most complex dynamics is found to occur within particular ranges of parameters controlling the symmetry and magnitude of the weight matrix. A small network model is observed to produce fixed points, limit cycles, mode-locking, the Ruelle-Takens route to chaos, and the period-doubling route to chaos. Training algorithms for tuning this dynamical behaviour are discussed. Training can be an easy or difficult task, depending whether the problem requires the use of temporal information distributed over long time intervals. Such problems require training algorithms which can handle hidden nodes. The most prominent of these algorithms, back propagation through time, solves the temporal credit assignment problem in a way which can work only if the relevant information is distributed locally in time. The Moving Targets algorithm works for the more general case, but is computationally intensive, and prone to local minima

Time trials on second-order and variable-learning-rate algorithms

The performance of seven minimization algorithms are compared on five neural network problems. These include a variable-step-size algorithm, conjugate gradient, and several methods with explicit analytic or numerical approximations to the Hessian

The 'moving targets' training algorithm

A simple method for training the dynamical behavior of a neural network is derived. It is applicable to any training problem in discrete-time networks with arbitrary feedback. The algorithm resembles back-propagation in that an error function is minimized using a gradient-based method, but the optimization is carried out in the hidden part of state space either instead of, or in addition to weight space. Computational results are presented for some simple dynamical training problems, one of which requires response to a signal 100 time steps in the past

Useful ideas for exploiting time to engineer representations

Commentary on target article "From simple associations to systematic reasoning: a connectionist representation of rules, variables, and dynamic bindings using temporal synchrony", by L. Shastri and V. Ajjangadde, pp. 417-49

How many thoughts can you think?

In ordinary computer programs, the relationship between data in a machine and the concepts it represents is defined arbitrarily by the programmer. It is argued here that the Strong AI hypothesis suggests that no such arbitrariness is possible in the relationship between brain states and mental experiences, and that this may place surprising limitations on the possible variety of mental experiences. Possible psychology experiments are sketched which aim to falsify the Strong AI hypothesis by indicating that these limits can be exceeded. It is concluded that although such experiments might be valuable, they are unlikely to succeed in this aim

The moving targets algorithm for difficult temporal credit assignment problems

The 'moving targets' algorithm for training recurrent networks is reviewed and applied to a task which demonstrates the ability of this algorithm to use distant contextual information. Some practical difficulties are discussed, especially with regard to the minimization process. Results on performance and computational requirements of several different 2nd-order minimization algorithms are presented for moving target problems