Dissertations / Theses on the topic 'Blade Loading'

Thesis: S.M., Massachusetts Institute of Technology, Department of Mechanical Engineering, 2015.
Cataloged from PDF version of thesis.
Includes bibliographical references (pages 117-119).
Changes in loss generation associated with altering the rotor tip loading of an embedded compressor stage is assessed. Steady and unsteady three-dimensional computations, complemented by control volume analyses, for varying rotor tip loading distributions provided results for determining if aft-loading rotor tip would yield a stage performance benefit in terms of a reduction in loss generation. Aft-loading rotor blade tip yields a relatively less-mixed-out tip leakage flow at the rotor exit and a reduction in overall tip leakage mass flow hence a lower loss generation; however, the attendant changes in tip flow angle distribution are such that there is an overall increase in the flow angle mismatch between tip flow and main flow leading to higher loss generation. The latter outweighs the former so that rotor passage loss from aft-loading rotor tip is marginally higher unless a constraint is imposed on tip flow angle distribution so that associated induced loss is negligible; a potential strategy for achieving this is proposed. In the course of assessing the benefit from unsteady tip leakage flow recovery in the downstream stator, it was determined that tip clearance flow is inherently unsteady with a time-scale distinctly different from the blade passing time. The disparity between the two timescales: (i) defines the periodicity of the unsteady rotor-stator flow, which is an integral multiple of blade passing time; and (ii) causes tip leakage vortex to enter the downstream stator at specific pitchwise locations for different blade passing cycles, which is a tip leakage flow phasing effect. Because of an inadequate grid resolution defining the unsteady interaction of tip flow with downstream stator, the benefit from unsteady tip flow recovery is the lower bound of its actual benefit. A revised design hypothesis is thus as follows: "rotor should be tip-aft-loaded and hub-fore-loaded while stator should be hub-aft-loaded and tip-fore-loaded with tip/hub leakage flow angle distribution such that it results in no additional loss". For the compressor stage being assessed here, an estimated 0.15% enhancement in stage efficiency is possible from aft-loading rotor tip only.
by Aniwat Tiralap.
S.M.

The current drive to generate energy from sustainable renewable resources has led to an increased interest in generating power through exploiting the kinetic energy in faster flowing tidal streams. Much of the knowledge gained from the development of wind turbines has been applied to the tidal stream turbine. However, the hostile marine environment introduces new technological challenges. The tidal turbine operates under highly unsteady, turbulent flow conditions and the occurrence of marine biofouling adds further complication to the issue. The main objective of the present work is to advance the understanding of the effect marine fouling has on the unsteady hydrodynamic loading and performance of tidal turbine blade sections. To investigate this challenging fluid phenomenon, a series of two-dimensional static and unsteady experiments were designed and conducted in the dynamic stall test rig at the University of Glasgow's Handley Page wind tunnel facility. The test matrix was constructed to cover the full operating envelope of a blade from MW-scale turbines, and included three thicker, cambered blade sections from two radial positions on the blade - a NACA 63-619 and two proprietary AHH designs. Chordwise integrated force and pitching moment coefficients were obtained from surface pressure measurements for three representative blade fouling configurations: an aerodynamically clean baseline; a light level of widely distributed microfouling roughness; and the addition of macrofouling with a single instrumented barnacle protuberance. This work has generated what is believed to be a unique database of unsteady tidal turbine blade section performance and, more importantly, the negative impact marine biofouling is likely to have on these investigated parameters. The approach followed through the work has been to assess the impact of marine biofouling on the individual blade sections and then assess the consequences of marine biofouling on the turbine by combining the blade section findings in a BEMT numerical performance model.

Detailed surface pressure measurements have been made on a NACA 0015 immersed in two grid generated homogenous flows at Re = 1.17 x 10^6 for a = 0°, 4°, 8°, 12°, 16°, and 20°. The goal of this measurement was to reveal and highlight mean loading and turbulence scale effects on surface pressure fluctuations resulting from turbulence/airfoil interaction. Also, measurements are compared with the theory of Amiet (1976a,b). The surface pressure response shows a dependance on angle of attack, the nature of which is related to the relative chord/turbulence scale. The dependance on turbulence scale appears to be non-monotonic at low reduced frequencies, wr = Pi*f*c/U with both an increase and decrease in unsteady pressure magnitude occuring with increasing mean load. A reduced frequency overlap region exists at wr > 10 where the two different scale flows begin to produce similar effects on the surface pressure with increasing angle of attack manifesting as a rise in unsteady surface pressure magnitude. Also, the interaction of the full 3-dimensional wavenumber spectrum affects the distance over which pressure fluctuations correlate and the extent of correlation is affected by angle of attack as demonstrated in the chordwise and spanwise pressure correlation. Amietâ s theory is shown to agree favorably with measurements in the leading edge region although demonstrates insufficiencies in predicting unsteady pressure phasing.
Master of Science

Stratification of water in large reservoirs occurs in summer, or at anytime in hot climates where the water surface is exposed long-term to sunlight and the water surface is heated. Natural mixing will not occur due to the cooler and denser water always staying at the lower levels. Therefore, mechanical circulators are designed to prevent water quality problems related to stratification and depletion of dissolved oxygen. Impellers that produce the flow in mechanical circulators are available in different sizes and these impellers are designed to produce different flow rates. Due to hydraulic loadings, impellers have to be strong and durable. Loadings on impellers depend on their geometries and therefore, a durable impeller is a good combination of the use of correct materials and good geometry. Long and slender impellers are prone to failure when subjected to high hydrodynamic loadings. Nowadays, designers have very limited information on predicting the stresses on impellers and the deflection patterns of impellers because there are no design rules in designing these impeller blades and there is no such thing as "best geometry". A good impeller blade design is by guesswork and experience. In order to design the geometry that suits this application, trial-and-error finite element analyses have been conducted in this project to minimize stress levels on the blades. This research involves the use of finite element analysis (FEA) to predict stress and deflection of impeller blades used on large (5m diameter) ducted axial flow impellers as the first step in the design process. Then, based on the results, improvements have been done to the models until the final design was made. As far as the author has been able to determine, this has not been researched before. Finite Element Analysis has been used on wind turbine blades, rudders and hulls of boats but not on axial flow impeller blades of the type used in this project. For the purpose of this project, commercial finite element computer program packages STRAND6 and STRAND7 were used as the main analysis tools. A static line load increasing linearly with radius along the blade has been used to simulate the assumed hydrodynamic loading, and applied to all FEA blade models. The analysis results proved the stresses on blades are largely dependant on the blade geometry. From the analysis results, the author modified the stacking arrangement of the FEA elements in order to minimize both the tensile stresses and the displacements of the blades at the tip. Parametric studies have been done in order to obtain the best FEA impeller blade model.

Inlet distortion is an important consideration in fan performance. Distortion can be generated through flight conditions and airframe-engine interfaces. The focus of this paper is a series of high-fidelity, time-accurate Computational Fluid Dynamics (CFD) simulations of a multistage fan, investigating distortion transfer, distortion generation, and the underlying flow physics under different operating conditions. The simulations are full annulus and include 3 stages and the inlet guide vane (IGV). The code used to carry out these simulations is a modified version of Overflow2.2 that was developed as part of the Computational Research and Engineering Acquisition Tools and Environment (CREATE) program. The inlet boundary condition is a single revolution (sinusoidal pattern with one period over the circumference ) total pressure distortion. Simulations at choke, design, and near stall are analyzed and compared to experimental data. Distortion transfer and generation is analyzed under these different operating conditions. Analysis includes the phase and amplitude of total temperature and pressure distortion through each stage of the fan, level of distortion transfer and generation in each stage, and blade loading. An understanding of the flow physics associated with distorted flows will help fan designers account for unsteady flow physics at design and off-design operating conditions, in order to build more robust fans offering a greater stability margin.

This paper presents the results of stator clocking investigations at a design point and an operating point near the stability limit in a low-speed research compressor (LSRC). The unsteady flow field of the LSRC at several clocking configurations was investigated using a three-dimensional unsteady, viscous solver. The unsteady pressure on the rotor blades at midspan (MS) was measured using time-resolving piezoresistive miniature pressure transducers. The effect of clocking on the unsteady pressure fluctuation at MS on the rotor blades is discussed for different operating points. Based on the unsteady profile pressures, the blade pressure forces were calculated. The peak-to-peak amplitudes of the unsteady blade pressure forces are presented and analysed for different clocking positions at both the design point and the operating point near the stability limit of the compressor.

Thesis (M.S.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 1988.
Title as it appeared in M.I.T. Graduate List, Sept. 1987: Calculations of helicopter blade loading using an axisymmetric vortex sheet and free wake method.
Bibliography: leaves 75-77.
by Kevin Huh.
M.S.

Dynamic Substructuring is a powerful tool for simplification of the analysis of complex structures and it has been well established along the years in analytical calculations by means of the Craig-Bampton technique. Recently, a new branch of substructuring, the Experimental Dynamic Substrucuring, appeared as a promising field of research for the engineering community. This area presents several intrinsic difficulties, evincing a need to develop the traditional substructuring methods towards obtaining better results using the experimental approach. In this scenery, the Transmission Simulator technique emerges as an instrument for potential improvement of the achieved results. This work represents a study on the use of the Transmission Simulator technique in the analysis of an Ampair A600 wind turbine blade subjected to loads at the interface to the hub, and it is a part of the benchmarking studies of SEM (Society of Experimental Mechanics). The work consisted of collecting experimental data via vibration tests of a single blade connected to different sizes of transmission simulators. After that, a mathematical representation of the blade was obtained via subtraction of the effect of the transmission simulators via substructuring technique. The computed model was subsequently coupled to a model of the remainder of the wind turbine (the hub plus two blades), and the results were compared to data acquired in tests of the whole assembly. The final findings did not reflect the theory prospects and further investigation is necessary to evaluate the effectiveness of the used methodology.

Many questions exist regarding the structural integrity of wind turbine blades, and this thesis aimed to answer some of these as a means to increase future reliability. One of the key problems with the blade structural response under high static loads was the occurrence of a geometrically non-linear bending phenomenon known as the Brazier effect. This research aimed to better understand the consequences of this effect on the lightweight material used, and this was achieved by performing laboratory scale specimen tests on representative material. A key outcome was that the box girder suction side web was identified as a critical component and most likely to fail via an interfacial disbond. A related finding was that the presence of an interlaminar delamination in the sandwich web material would significantly reduce the load bearing capacity of that section of web. The percentage reduction in load bearing ability appeared to be a function of skin to core thickness ratio and delamination size. Another key outcome was the identification that either the growth of matrix cracks or the presence of pre-existing delaminations were paramount in the development of interlaminar cracks in the laminate caps. This research has demonstrated that, should future blade flexibility be increased, reinforcing layers in the cap should be introduced. The suggested design of this reinforcement was a modification to the current layup that introduced transverse layers along the inner side of the cap. This was proven to increase the flexural rigidity by 107%. Additionally, for future blade certification and monitoring, web delaminations should be identified, potentially by use of digital image correlation or acoustic emissions monitoring, both of which were demonstrated as being capable techniques.

Thesis (MScEng)--Stellenbosch University, 2012.
ENGLISH ABSTRACT: Axial flow fans used in large-scale air-cooled steam condensers (ACSCs) may operate under distorted inflow conditions. These conditions occur due to the prevailing wind conditions, the presence of buildings, and the location of the fan within the ACSC. Fans located on the periphery of the ACSC are affected the most due to their exposure to strong winds and the inner fans drawing in air past them. Distorted inflow conditions cause varying fan blade and gearbox loading conditions. The purpose of the investigation was to simultaneously measure the inlet air flow and the resultant blade and gearbox loading conditions of a single fan located on the periphery of a large-scale ACSC. Inlet and heat exchanger bundle outlet air flow velocities were measured using a combination of ultrasonic and propeller anemometers while blade loading was measured with strain gauges attached at the neck of the specific blade being monitored. Strain gauges were also attached to the low-speed fan shaft to measure gearbox loading. Measurements were recorded over a period of 8 days where it was found that increased wind resulted in increased air flow in the axial direction of the fan, which then caused a reduction in average blade loading. This was due to a decreased static pressure rise over the fan. The fan blade was found to vibrate at its own natural frequency of 6 Hz when excited by the variable aerodynamic loading. The aerodynamic loading was extracted from the measured data and was found to correlate well with previous experimental work performed by Bredell et al. (2006a). Shaft bending stresses and torque were found to oscillate at the fan’s rotational frequency of 2Hz with a large torque exerted on the shaft during fan start-up.
AFRIKAANSE OPSOMMING: Aksiaalvloeiwaaiers wat by groot lugverkoelde stoomkondensors gebruik word, werk dikwels onder verwronge inlaat lugvloei toestande wat geskied as gevolg van heersende winde, die teenwoordigheid van geboue en die posisie van die waaier in die kondensor. Waaiers wat geleë is op die rand van die kondensor word die meeste beïnvloed as gevolg van blootstelling aan die sterk winde en dwarsvloei wat deur die binneste waaiers geïnduseer word. Verwronge inlaat lugvloei veroorsaak gevolglik variërende waaierlem en ratkas belastingstoestande. Die doel van hierdie ondersoek was om terselfdetyd die inlaat lugvloei asook waaierlem en ratkas belastingstoestande van ’n enkele waaier wat op die rand van ’n grootskaalse lugverkoelde stoomkondensor geleë is, te meet. Waaier inlaat en warmteruiler uitlaat lugvloei snelhede is gemeet met ’n kombinasie van ultrasoniese- en skroefwindsnelheidsmeters terwyl die lem en ratkas belastings gemeet is met rekstrokies. Metings is oor ’n tydperk van 8 dae geneem. Die bevindinge toon dat ’n toename in windsnelheid ’n toename in aksiale lugvloei tempo, deur die waaier veroorsaak. ’n Afname in die gemiddelde lembelasting is waargeneem as gevolg van ’n afname in die waaier statiese druk. Daar is ontdek dat die waaierlem teen ’n natuurlike frekwensie van 6 Hz vibreer wanneer dit opgewek word deur die wisselende aerodinamiese belasting. Die aerodinamiese belasting is verkry uit die gemete data en vergelyk goed met die numeriese werk van Bredell et al. (2006a). Daar is ook bevind dat waaier-as buigspannings en wringkragte ossileer teen die waaier se rotasiefrekwensie van 2Hz met ’n groot wringkrag wat op die as uitgeoefen word wanneer die waaier aangeskakel word. iii

This thesis presents the results of a study performed in the Virginia Tech low speed linear cascade wind tunnel operating at a Reynolds number of 382,000 designed to model an axial compressor rotor. To simulate the flow created by the junction of a set of inlet guide vanes and the compressor casing, vortex generators were glued to a moving end wall. In this investigation, the tip clearance was varied from 0.83% to 12.9% chord. Measurements of the midspan and the tip blade loading were made using static pressure taps. The tip loading shows that the minimum suction surface pressure coefficient increases in magnitude linearly up to a tip clearance of 7.9% chord. Unsteady pressure was measured on the pressure and suction surfaces at the tip of two cascade blades using an array of 23 microphones mounted subsurface. These measurements reveal that the unsteady pressure at the blade tip is a linear function of tip clearance height. The instantaneous pressure shows that the surface pressure at the blade tip has the same character regardless of whether or not the blade is disturbed by the inflow vortices. This suggests that the vortex generators simply stimulate and organize the existing response of the blade. Single sensor hot-wire measurements were made within the tip clearance on the suction side of the blade 1mm from the tip gap exit. These measurements show that the mass flux through the tip clearance is closely related to the pressure difference across the tip gap.
Master of Science

Multiple high-fidelity, time-accurate computational fluid dynamics simulations were performed to investigate the effects of upstream stator loading and rotor shock strength on vortex shedding characteristics in a single stage transonic compressor. Various configurations of a transonic axial compressor stage, including three stator/rotor axial spacings of close, mid, and far in conjunction with three stator loadings of decreased, nominal, and increased were simulated in order to understand the flow physics of transonic blade-row interactions. Low-speed compressors typically have reduced stator/rotor axial spacing in order to decrease engine weight, and also because there is an increase in efficiency with reduced axial spacing. The presence of a rotor bow shock in high-speed compressors causes additional losses as the shock interacts with the upstream stator trailing edge. This research analyzes the strength of shock-induced vortices due to these unsteady blade-row interactions. The time-accurate URANS code, TURBO, was used to generate periodic, quarter annulus simulations of the Blade Row Interaction compressor rig. Both time-averaged and time-accurate results compare well with experimentally-observed trends. It was observed that vortex shedding was synchronized to the passing of a rotor bow shock. Normal and large shock-induced vortices formed on the stator trailing edge immediately after the shock passing, but the large vortices were strengthened at the trailing edge due to a low-velocity region on the suction surface. This low velocity region was generated upstream of mid-chord on the suction surface from a shock-induced thickening of the boundary layer or separation bubble, due to the rotor bow shock reflecting off the stator trailing edge and propagating upstream. The circulation of the shock-induced vortices increased with shock strength (decreased axial spacing) and stator loading. Most design tools do not directly account for unsteady effects such as blade-row interactions, so a model is developed to help designers account for shock-induced vortex strength with varying shock strength and stator loading. An understanding of the unsteady interactions associated with blade loading and rotor shock strength in transonic stages will help compressor designers account for unsteady flow physics early in the design process.

The tandem airfoil has potential to do more work as a compressor blade than a single airfoil without incurring significantly higher losses. Although tandem blades are sometimes employed as stators, they have not been used in any known commercial rotors. The goal of this work is to evaluate the aerodynamic feasibility of using a tandem rotor in the rear stages of a core compressor. As such, the results are constrained to shock-free, fully turbulent flow. The work is divided into 2-D and 3-D simulations. The 3-D results are subject to an additional constraint: thick endwall boundary layers at the inlet. Existing literature data on tandem airfoils in 2-D rectilinear cascades have been compiled and presented in a Lieblein loss versus loading correlation. Large scatter in the data gave motivation to conduct an extensive 2-D CFD study evaluating the overall performance as a function of the relative positions of the forward and aft airfoils. CFD results were consistent with trends in the open literature, both of which indicate that a properly designed tandem airfoil can outperform a comparable single airfoil on- and off-design. The general agreement of the CFD and literature data serves as a validation for the computational approach. A high hub-to-tip ratio 3-D blade geometry was developed based upon the best-case tandem airfoil configuration from the 2-D study. The 3-D tandem rotor was simulated in isolation in order to scrutinize the fluid mechanisms of the rotor, which had not previously been well documented. A geometrically similar single blade rotor was also simulated under the same conditions for a baseline comparison. The tandem rotor was found to outperform its single blade counterpart by attaining a higher work coefficient, polytropic efficiency and numerical stall margin. An examination of the tandem rotor fluid mechanics revealed that the forward blade acts in a similar manner to a conventional rotor. The aft blade is strongly dependent upon the flow it receives from the forward blade, and tends to be more three-dimensional and non-uniform than the forward blade.
Ph. D.

Horizontal Axis Tidal Turbines (HATTs) can experience amplified, time varying hydrodynamic loads during operation due to dynamic stall. Elevated hydrodynamic loads impose high structural loads on turbine blades, thus appreciably shortening machine service life. An improved characterization of the unsteady hydrodynamic loads on tidal turbine blades is therefore necessary to enable more reliable predictions of their fatigue life and to avoid premature failures. This thesis reports on a Computational Fluid Dynamics (CFD) analysis of the unsteady blade loading of a scale-model HATT taking dynamic stall into account. Numerical simulations are performed both in two-dimensional (2-D) and three-dimensional (3-D) using the commercial CFD solver ANSYS Fluent. After a brief description of the theories and methods involved, the behaviour of flow at low Reynolds number around a NACA-0012 aerofoil pitching in a sinusoidal pattern that induces dynamic stall is studied firstly to validate the numerical method and the choice of turbulence models. Then full 3-D computations of a rotating scale-model HATT rotor are presented for steady and periodic unsteady inflow situations, respectively. The reliability of the 3-D numerical method is evaluated by comparing the blade loads, especially the out-of-plane blade-root bending moment (defined as being about an axis normal to the rotor axis), with measurement data obtained from experimental tests conducted at the University of Strathclyde’s Kelvin Hydrodynamics Laboratory towing tank. Analyses in the steady velocity study are documented for a broad range of rotor speeds and flow velocities. Furthermore, investigations of 3-D flow separation and scale effects on blade loads are also performed. The periodic unsteady velocity study aims to examine the out-of-plane blade-root bending moment response to harmonic axial motion, deemed representative of the free-stream velocity perturbations induced by the unsteady flow. Parametric tests on oscillatory frequencies and amplitudes are carried out in order to analyse the HATT blade hydrodynamic behaviour under different flow patterns. Detailed flow field data is analysed to understand 3-D dynamic stall from a modelling perspective. It is concluded that the results by the present study provide significant insights into the flow physics occurring around the HATT rotor blades under various flow conditions. The CFD method can be used for designing more advanced HATT rotors, it also can be used to fine tune the computationally faster lower order Blade Element Momentum (BEM) methods for parametric design studies where experimental data is not available, particularly at the challenging rotor operating conditions involving flow separation and dynamically varying hydrodynamic behaviours.

A probabilistic methodology for the reliability analysis of composite rotor blades at the ply level was developed. The proposed methodology involves (i) the quantification of the uncertainties (physical, statistical and model) related to the material properties and the extreme aero-elastic loads based on experimental data as well as on 10 min load simulations respectively, (ii) the identification of the critical failure modes of the composite structure in terms of limit state functions and (iii) the selection of an appropriate reliability method to perform the analysis. It is pointed out that the reliability method should be able to handle the considerably large number of limit state function introduced by the ply level reliability approach and estimate the failure probability of the structure. To efficiently deal with the problem, an appropriate implementation of the Response Surface Method combined with crude Monte Carlo simulation was proposed. The methodology was implemented for two real rotor blade designs, namely a 30m Glass/Polyester and the 65m UPWIND reference rotor baled. Initially, calculations were performed for the first case study using a 3D shell FE formulation in a commercial probabilistic code. An efficient procedure was introduced to define the stochastic character of the concentrated loads acting on the 3D FE model starting from load time series of sectional stress resultants from aero-elastic beam simulations. For the first time such a detailed model was analyzed and assessed in a probabilistic base. Nevertheless, a considerable CPU time was in need for the performance of such a reliability analysis. The development of an efficient probabilistic tool capable to perform consecutive reliability analyses at the ply level of the composite rotor blade structure and prove valuable for the probabilistic design was carried out. To demonstrate the efficiency of the developed tool, the impact of various probabilistic modelling assumptions directly on the β-index value of a rotor blade design was studied.
Στην παρούσα διατριβή αναπτύχθηκε στοχαστική μεθοδολογία για την αποτίμηση αξιοπιστίας πτερυγίων ανεμογεννητριών από σύνθετα υλικά, στο επίπεδο της στρώσης, υπό ακραία στατική φόρτιση. Η προτεινόμενη μεθοδολογία περιλαμβάνει (i) την ποσοτικοποίηση αβεβαιοτήτων (φυσική, στατιστική και αβεβαιότητα μοντέλου) που σχετίζονται με τις βασικές παραμέτρους του πτερυγίου (υλικά και φορτία) στηριζόμενη σε ένα μεγάλο αριθμό πειραμάτων για τον προσδιορισμό των μηχανικών ιδιοτήτων του συνθέτου υλικού καθώς και 10-λεπτες αεροελαστικές χρονοσειρές για την ακραία στατική φόρτιση (ii) την αναγνώριση όλων των σημαντικών μηχανισμών αστοχίας της κατασκευής και την έκφρασή τους στη μορφή οριακών συναρτήσεων αστοχίας και (iii) την επιλογή μίας κατάλληλης μεθόδου αξιοπιστίας. Σημειώνεται ότι η μέθοδος αξιοπιστίας θα πρέπει να είναι ικανή να διαχειρίζεται ένα πολύ μεγάλο αριθμό οριακών συναρτήσεων αστοχίας όπως επιβάλει η ανάλυση αξιοπιστίας στο επίπεδο της στρώσης της κατασκευής. Για το σκοπό αυτό προτάθηκε μια κατάλληλη τροποποίηση της Response Surface Method τεχνικής η οποία συνδυάστηκε με την μέθοδο προσομοίωσης crude Monte Carlo. Η προτεινόμενη στοχαστική μεθοδολογία εφαρμόστηκε για την περίπτωση δυο πραγματικών πτερυγίων: ενός 30 m Glass/Polyester και του 65 m Glass/Epoxy (UPWIND) πτερυγίου. Η ανάλυση αρχικά πραγματοποιήθηκε σε γενικού σκοπού στοχαστικά εργαλεία κάνοντας χρήση τρισδιάστατου μοντέλου πεπερασμένων στοιχείων. Σημειώνεται ότι ο υπολογισμός των φορτίων από αεροελαστικούς κώδικες υλοποιείται πάντα στη βάση στοιχείων δοκού. Προτάθηκε επομένως διαδικασία για την στοχαστική αναπαράσταση των συγκεντρωμένων δυνάμεων που επιβάλλονται στο τρισδιάστατο μοντέλο πεπερασμένων στοιχείων του πτερυγίου στηριζόμενη σε χρονοσειρές εσωτερικών αντιδράσεων στη διατομή όπως εξάγονται από αεροελαστικους υπολογισμούς. Για πρώτη φορά σε αυτή την εργασία, πραγματοποιήθηκε η στοχαστική ανάλυση ενός τόσο λεπτομερειακού μοντέλου. Ωστόσο η παραπάνω προσέγγιση αποδείχτηκε αρκετά χρονοβόρα. Για το σκοπό αυτό αναπτύχθηκε υπολογιστικό εργαλείο ικανό να εκτελεί ένα μεγάλο αριθμό επαναλήψεων της προαναφερθείσας μεθοδολογίας και να φανεί χρήσιμο στο σχεδιασμό πτερυγίων με προκαθορισμένο επίπεδο αξιοπιστίας. Εξαιτίας της απλότητας της προετοιμασίας των δεδομένων εισόδου και της ταχύτητας επίλυσης, το νέο εργαλείο έδωσε τη δυνατότητα για τη μελέτη διαφόρων στατιστικών υποθέσεων που αφορούσαν τη δομική αξιοπιστία του πτερυγίου εξετάζοντας απευθείας τον δείκτη αξιοπιστίας β της κατασκευής.