Metamodel-based uncertainty quantification for the mechanical behavior of braided composites

The main design requirement for any high-performance structure is minimal dead weight. Producing lighter structures for aerospace and automotive industry directly leads to fuel efficiency and, hence, cost reduction. For wind energy, lighter wings allow larger rotor blades and, consequently, better performance. Prosthetic implants for missing body parts and athletic equipment such as rackets and sticks should also be lightweight for augmented functionality. Additional demands depending on the application, can very often be improved fatigue strength and damage tolerance, crashworthiness, temperature and corrosion resistance etc. Fiber-reinforced composite materials lie within the intersection of all the above requirements since they offer competing stiffness and ultimate strength levels at much lower weight than metals, and also high optimization and design potential due to their versatility. Braided composites are a special category with continuous fiber bundles interlaced around a preform. The automated braiding manufacturing process allows simultaneous material-structure assembly, and therefore, high-rate production with minimal material waste. The multi-step material processes and the intrinsic heterogeneity are the basic origins of the observed variability during mechanical characterization and operation of composite end-products. Conservative safety factors are applied during the design process accounting for uncertainties, even though stochastic modeling approaches lead to more rational estimations of structural safety and reliability. Such approaches require statistical modeling of the uncertain parameters which is quite expensive to be performed experimentally. A robust virtual uncertainty quantification framework is presented, able to integrate material and geometric uncertainties of different nature and statistically assess the response variability of braided composites in terms of effective properties. Information-passing multiscale algorithms are employed for high-fidelity predictions of stiffness and strength. In order to bypass the numerical cost of the repeated multiscale model evaluations required for the probabilistic approach, smart and efficient solutions should be applied. Surrogate models are, thus, trained to map manifolds at different scales and eventually substitute the finite element models. The use of machine learning is viable for uncertainty quantification, optimization and reliability applications of textile materials, but not straightforward for failure responses with complex response surfaces. Novel techniques based on variable-fidelity data and hybrid surrogate models are also integrated. Uncertain parameters are classified according to their significance to the corresponding response via variance-based global sensitivity analysis procedures. Quantification of the random properties in terms of mean and variance can be achieved by inverse approaches based on Bayesian inference. All stochastic and machine learning methods included in the framework are non-intrusive and data-driven, to ensure direct extensions towards more load cases and different materials. Moreover, experimental validation of the adopted multiscale models is presented and an application of stochastic recreation of random textile yarn distortions based on computed tomography data is demonstrated

Seismic risk assessment of frame structures using stochastic beam-column elements

Εθνικό Μετσόβιο Πολυτεχνείο--Μεταπτυχιακή Εργασία. Διεπιστημονικό-Διατμηματικό Πρόγραμμα Μεταπτυχιακών Σπουδών (Δ.Π.Μ.Σ.) "Analysis and Design of Earthquake Resistant Structures

Numerical evaluation on shell buckling of empty thin-walled steel tanks under wind load according to current American and European design codes

Liquid storage steel tanks are vertical above-ground cylindrical shells and as typical thin-walled structures, they are very sensitive to buckling under wind loads, especially when they are empty or at low liquid level. Previous studies revealed discrepancies in buckling resistance of empty tanks between the design method proposed by the American Standard API 650 and the analytical formulas recommended by the European Standard EN1993-1-6 and EN1993-4-2. This study presents a comparison between the provisions of current design codes by performing all types of numerical buckling analyses recommended by Eurocodes (i.e. LBA-linear elastic bifurcation analysis, GNA-geometrically nonlinear elastic analysis of the perfect tank and GNIA-geometrically nonlinear elastic analysis of the imperfect tank). Such analyses are performed in order to evaluate the buckling resistance of two existing thin-walled steel tanks, with large diameters and variable wall thickness. In addition, a discussion is unfolded about the differences between computational and analytical methods and the conservatism that the latter method imposes. An influence study on the geometric imperfections and the boundary conditions is also conducted. Investigation on the boundary conditions at the foot of the tank highlights the sensitivity to the fixation of the vertical translational degree of freedom. Further, it is indicated that the imperfection magnitude recommended by the EN1993-1-6 is extremely unfavorable when applied to large diameter tanks. Comments and conclusions achieved could be helpful in order to evaluate the safety of the current design codes and shed more light towards the most accurate one

Structural analysis of composite wind turbine blade with the finite element method

104 σ.Σε μία ανεμογεννήτρια τα πτερύγια είναι ένα πολύ κρίσιμο και σημαντικό τμήμα όσον αφορά τον σχεδιασμό, διότι η επίδοσή της εξαρτάται από παράγοντες όπως τα υλικά του πτερυγίου, το σχήμα, η γωνία συστροφής κτλ. Εξετάζεται ο σχεδιασμός του εσωτερικού του πτερυγίου όπως επίσης και η κατάλληλη επιλογή των υλικών μίας μεγάλης ισχύος ανεμογεννήτριας που καταπονείται από ένα στατικό φορτίο κάθετο στην μεγάλη επιφάνεια του πτερυγίου (φόρτιση flap-wise). Αναπτύσσεται ένα πολύ λεπτομερές μοντέλο πεπερασμένων στοιχείων που προσομοιώνει την εσωτερική στήριξη του πτερυγίου (σε σχήμα «κουτιού»), με δεδομένα το μέγεθος, το αεροδυναμικό σχήμα, τον τύπο και την ακριβή τοποθέτηση των εσωτερικών δοκών (spar-caps) και υποστυλωμάτων (shear-webs). Για την στήριξη αυτή χρησιμοποιούνται προχωρημένα και καινοτόμα σύνθετα υλικά με υψηλούς λόγους αντοχής – και ακαμψίας – προς βάρος, όπως πολυμερή οπλισμένα με ίνες γυαλιού και ίνες άνθρακα. Με τη βοήθεια εξειδικευμένων λογισμικών πεπερασμένων στοιχείων παράγονται αποτελέσματα που αφορούν τις τάσεις και τις μετατοπίσεις χρησιμοποιώντας επίπεδα στοιχεία και τρισδιάστατα στοιχεία κελύφους, με γραμμικές και μη γραμμικές αναλύσεις (παραδοχές μικρών και μεγάλων μετατοπίσεων). Εφαρμόζεται επίσης ένα κριτήριο αστοχίας σύνθετων υλικών για περαιτέρω συμπεράσματα όσον αφορά τα μεγέθη των τάσεων. Ο κύριος στόχος της εργασίας είναι η μελέτη της συμπεριφοράς του πτερυγίου μίας μεγάλης ισχύος ανεμογεννήτριας σε επίπεδο διατομής, που καταπονείται από στατικό φορτίο ισοδύναμο με μία μέση φόρτιση ανέμου και γενικότερα η έρευνα γύρω από τη συμπεριφορά των κατασκευών αυτών με έμφαση στην επιλογή των υλικών, με σκοπό πάντα τη βελτιστοποίηση της απόδοσής τους.In wind turbines, blades are critical design members because performance depends on blade material, shape, twist angle, etc. The problem of internal, mechanical design and material selection for a prototypical -high power- horizontal axis wind turbine blade under static, flap-wise loading is investigated in this study. A very detailed finite element model is developed representing the load-carrying box girder of the blade with a given airfoil shape, size, and the type and position of the interior load-bearing longitudinal beams/shear-webs. The materials used in the internal support are innovative, highly advanced composites that have high strength – and stiffness – to weight ratios such as E-Glass fiber reinforced plastic and Carbon fiber reinforced plastic. Results concerning displacements and stresses are generated using both plane and shell finite elements with linear and non-linear analyses. A failure criterion for composite materials is also applied, in order to obtain some more results about the stresses. The main objective of this study is to help further advance the use of computer – aided engineering methods and tools (e.g. geometrical modeling of the box girder, structural analysis and material-selection methodologies) to the field of design and development of composite wind turbine blades and in general to shed some more light into the behavior of wind turbine blade structures.Μπαλόκας Α. Γεώργιο

Multiscale analysis of braided composites via surrogate modeling

Probabilistic analysis in engineering sciences takes into account the uncertainties that may exist and affect a certain physical system in an a priori unknown manner. As the design of structures gets increasingly complex over the years, the impact of those uncertainties onto the system response has to be studied in order to implement numerical procedures for virtual testing platforms. Especially the variations in the output of a model with regards to some inputs are of much interest. For all the above reasons, quantifying the relative importance of each uncertain input parameter through sensitivity analysis becomes a necessity. This work implements global sensitivity analysis to study the effect of uncertainties on multiscale analysis of braided composite materials. Several surrogate models (or meta-models e.g. neural networks, polynomial chaos expansions and Gaussian process expansions or Kriging models) are used to overcome the excessive cost of sensitivity analysis for a high-fidelity engineering simulation. Attention is given to non-intrusive approaches and order reduction techniques. The curse of dimensionality is handled through special truncation schemes aiming for a limited set of runs of the original multiscale model. Applicability of the selected modeling techniques is discussed as well as error monitoring and training procedures. All mathematical tools used in this study account for nonlinearities, hence strength prediction is feasible and probabilistic models of failure processes through the scales can also be developed. Results offer a perspective on the variability influence of the random parameters, an overview of the performance of several surrogate models and also highlight the importance of realistic uncertainty quantification. Moreover, this paper provides a useful guidance for training and handling advanced non-intrusive metamodeling techniques for uncertainty propagation assessment

Robustness Analysis of CFRP structures under thermomechanical loading uncluding manufacturing defects

Carbon fibre reinforced plastics (CFRP) show superior weight-specific properties compared to metals. However, the structural behavior is more complex when exposed to thermomechanical load conditions, for instance in engine, turbine or battery environments or in space applications. The properties of CFRP decrease with increasing service temperature due to the temperature-dependency of their plastic matrix system. Yet, within current industrial design processes, temperature limits are defined with high conservatism. Therefore, additional load carrying capabilities at higher temperatures, before complete loss of mechanical performance, are not exploited. This study is presenting an enhanced analysis process for robust composite design by considering temperature-dependent material behavior, effects from manufacturing deviations and uncertainties from thermomechanical loading conditions. A sequential finite element (FE) analysis strategy is utilized to assess the mechanical performance of a structure under thermal load conditions until glass transition temperature. The current investigations use nonlinear temperature-dependent material models to account for the corresponding stiffness and strength reduction. Based on the thermal load conditions and the structural concept, different temperature distribution will occur within the part and therefore, thermal expansion results in varying development of structural deformation and stress. Moreover, the temperature field causes locally decreased material properties. Evaluation of forces, stresses and strains allows assessing the structural performance. Inherent material uncertainties, local property knock-down resulting from fibre-placement defects and deviations of thermal load conditions are introduced to analyze the structural robustness. The work focuses on the analysis strategy and describes the approach of material modelling and applied uncertainties. Finally, results of the presented methodology are shown for a thin-walled stiffened CFRP structure