Bayesian Technique for Reducing Uncertainty in Fatigue Failure Model
|
|
- Cuthbert Walsh
- 6 years ago
- Views:
Transcription
1 9IDM- Bayesian Technique or Reducing Uncertainty in Fatigue Failure Model Sriram Pattabhiraman and Nam H. Kim University o Florida, Gainesville, FL, 36 Copyright 8 SAE International ABSTRACT In this paper, Bayesian statistics is utilized to update uncertainty associated with the atigue lie relation. The distribution or atigue strain at a constant load cycle is determined using the tial uncertainty rom analytical prediction and likelihood unctions associated with data. The Bayesian technique is a good method to reduce uncertainty and at the same time provides a conservative estimate, given the distribution o analytical prediction errors and variability o data. First, the distribution o analytical atigue model error is estimated using Monte Carlo simulation with uniormly distributed parameters. Then the error distribution is progressively updated by using the variability as a likelihood unction, which is obtained rom ield data. The sensitivity o estimated distribution with respect to the tial error distribution and the selected likelihood unction is studied. The proposed method is applied to estimate the atigue lie o turbine blade. It is ound that the proposed Bayesian technique reduces the scatteredness o atigue lie by almost %, while maintang the conservative lie estimate at a given atigue strain. In addition, a good conservative estimate o atigue lie prediction has been proposed using a knockdown actor that is obtained rom the distribution o lowest data. INTRODUCTION In general, there are two dierent lie prediction models in atigue analysis: stress-lie and strain-lie models. The ormer is oten used or high-cycle atigue analysis in which the stress-strain relation is in the linear region. The latter is requently used or low- and medium-cycle atigue in which plastic deormation contributes to the atigue lie. Although the basic concept in the proposed Bayesian approach is the same, the strain-lie model will be investigated in this paper. In strain-lie atigue analysis, the total atigue strain ( t ) is decomposed by elastic strain ( e ) and plastic. For this analysis, the strain-lie curve is de- strain ( p ) ined [3] as: t s e p E b N e N c () where e is the coeicient o atigue ductility, s the coeicient o atigue strength, b the eponent o atigue strength, c the eponent o atigue ductility, and E the Young s modulus. The coeicients in the strain-lie curve are obtained using curve-itting o data. However, due to variability in and material, the results are oten scattered. In the material handbook, or eample, the standard values o the coeicients are available. However, a particular batch o material may have dierent properties. In addition, a particular machine may have dierent atigue properties due to manuacturing process used and possibility o residual stresses. Thus, an important question is how to ind more accurate lie estimate or a speciic machine when several data are available. Traditionally, saety actors have been adopted as a measure to counter variability. But, presently, there is growing interest in replacing saety actor-based determstic design with reliability-based design (e.g., Wirsching [7], SAE Aerospace Inormation Report 8 [] ). In addition, the goal o is oten to ind conservative estimate o the predicted lie. Obviously taking the lowest data can be a choice, but its variability will be high and in many cases, the lowest data will not provide enough conservativeness []. Thus, another important question is how to ind the best way o predicting conservative atigue lie o a machine. The objective o this paper is to investigate the possibility o using the Bayesian statistics in order to reduce scatteredness o the atigue lie distribution when additional data are available. In addition, a good way o conservatively estimating atigue lie is proposed using a knockdown actor a term introduced or correcting analytical predictions based on results [8] ) that is obtained rom the distribution o lowest data. The concept o Graduate student, Department o Mechanical and Aerospace Engineering, psriram8@ul.edu. Associate Proessor, Department o Mechanical and Aerospace Engineering, nkim@ul.edu.
2 knockdown actor has been adopted in aerospace structures. randomly chosen within the variability limits with the analytical value as the mean. INPUTS AND ASSUMPTIONS It is important to understand the assumptions that are used in this paper. Some o them are or convenience, and others represent the lack o knowledge. I additional inormation is available, the latter can be improved. It is irst assumed that the coeicients in Eq. () are randomly distributed and their statistical distribution parameters are known. These distributions represent the prior knowledge or analytical prediction. This inormation can be obtained by studying strain-lie data and by estimating upper- and lower-bounds o data rom the mean curve. When this inormation is not available, it is possible to assume that these parameters ( s, e, b, and c) are distributed uniormly with given bounds rom their nominal values. This will serve as a prior knowledge o the atigue ailure distribution. Even i input parameters are uniormly distributed, the atigue ailure strain will not be uniormly distributed. The conidence interval is a measure o our conidence in the analytically predicted value. It would be the lower and upper bounds o the strain-lie data. However, since only the distribution o each parameter is considered known, the bounds or lie cycle value are determined rom the distribution o all parameters. Considering cases, where only one o the parameters varies at a time, while the rest o them are at their mean values, the sensitivity o lie cycle value to each parameter has been determined, and ound to be positive or all parameters. Hence, the upper and lower bounds or lie cycle would be when all parameters are simultaneously at their algebraic maimum and mmum values, respectively. The bounds o the conidence interval are usually epressed as a percentage o analytical value. I the bounds are asymmetrically distributed about the analytical value, the maimum variation is considered. The distribution o error is the distribution o lie cycle due to the distributions o the parameters. This distribution o error is generated using the Monte Carlo Simulation (MCS). In this paper, the MCS is perormed by generating, values or each parameter, governed by its variability. These randomly generated numbers are used to calculate, values o strain lie, rom which the distribution o error can be estimated. Test variability is the scatteredness o the data. Distribution o variability is the histogram o strain-lie data at the known constant ailure atigue strain ( t ) value. However, or the want o data, the distribution o variability is assumed to be normal with same parameters as that o the distribution o error. Even i there is no limitation on the number o data, three data are assumed available through the o a speciic component. These three data are BAYESIAN UPDATE FOR FATIGUE FAILURE STRAIN NORMALIZATION: Although the raw data and tial distribution can be used or Bayesian update, it is oten more convenient to normalize all data and distributions. All the actors aecting the Bayesian update, such as the conidence interval, error distribution, variability, and results are normalized with respect to the tial value o atigue lie, N. Since the conidence interval is epressed as a percentage o analytical value, it is not aected by normalization. The parameters o variability are epressed as a raction o mean value. In the normalized distribution, the standard deviation becomes identical to the coeicient o variance (COV). LIKELIHOOD FUNCTION: The likelihood unction o a result is the probability o obtang that result, given the value o actual atigue lie and the variability. It is actually the ordinate value o probability distribution unction (PDF) o variability with the actual atigue lie as its mean, when the abscissa is equal to the result. The likelihood would be a single value, i the actual atigue lie is known. But, since only the bounds or the actual atigue lie are known, the likelihood unction varies within that conidence interval. The likelihood o the given result can be ound by considering each point within the error bounds as the actual atigue lie. The likelihood unction or a given result would be the variation o these likelihood values with the actual atigue lie values. The likelihood unction or each o the three results can be determined in a similar ashion. BAYESIAN UPDATE: The Bayesian update is based on the theory o conditional probability, which states p true p true p true () p The epression or Bayesian update is very similar, i.e. upd N N N N N de Here, N is the likelihood unction or the given result. It could also be seen as probability o obtang the result given the true value o atigue lie. N is the tial distribution o N. For updating with the irst result, this distribution is taken as the error distribution. This updated distribution is used as the tial t (3)
3 distribution or updating with second result and so on. The denominator is simply the integration o numerator. This is interpreted as the normalization o PDF such that the area under the distribution becomes one. Dierent techniques like Trapezoidal rule, Simpson s Rule, etc, can be used or this purpose. Trapezoidal rule has been used in this paper or numerical integration. Ater the tial distribution is updated using the irst upd data, N is replaced by N, and the above procedure is repeated or the net results. The mean o the distribution obtained ater updating with inal result, is called the Bayesian Lie. KNOCKDOWN FACTOR: It is common in practice to take the mmum value o the results as the actual atigue lie. Such consideration implicitly applies a knockdown actor on average atigue lie value. In this paper, an eplicit knockdown actor is calculated rom statistics and multiplied to the mean value o the updated Bayesian lie to calculate a conservative estimate o the atigue lie. It is known that the lowest o the results ollows an etreme value distribution [6]. The mean o this etreme value distribution is used or the knockdown actor. Knock down actor calculation depends on material variability only. I is the cumulative distribution unction (CDF) o material variability ater normalization, the etreme value distribution is given by, 3 3 F ( ) (4) The mean o this etreme value distribution ( F ) is the knockdown actor. [] The conservative estimate o atigue lie is the product o the Bayesian Lie and knockdown actor. NUMERICAL EXAMPLE CONSTANT CYCLE TEST As a case, the Bayesian technique is applied to steel 434 material, whose strain-lie atigue parameters are shown in Table [4]. The strain-lie curve or steel 434 material is shown as Mean curve in Figure. The uncertainty in the parameters leads to uncertainty in strain amplitude ( t ). First the sensitivity o strain amplitude with respect to each o the parameters has been determined, and ound to be positive or all parameters. The eect o the uncertainty in strain amplitude has been plotted through the Maimum and Mmum curves in Figure. These curves have been plotted considering each o the parameter at its algebraic maimum and mmum respectively, governed by its variability. 3 In the irst eample, it is assumed that the material is ailed at N =, reversals and three data are available at that reversal value. Since the crossover reversal or this material is in the order or,, the atigue strain is in the elastic region. For the material parameters in Table, the value o analytical atigue strain is.3. t Table : Strain-lie atigue parameters or steel 434 Parameter Value Elastic stiness (E) 8,9 MPa Fatigue ductility coeicient (e ).83 Fatigue ductility eponent (c) -.6 Fatigue strength coeicient (s ),73 MPa Fatigue strength eponent (b) -.9 e t N Figure : Strain-lie curve or steel Mean Mmum Maimum Figure : Histogram o atigue strain at N =, In order to ind the tial error bounds o the atigue model, all parameters aecting the atigue strain are assumed to vary uniormly % o their nominal value. When all the parameters are varying simultaneously, the value o t varies between.4 and.4. Then, the error bounds are calculated considering the maimum deviation rom the mean, i.e.,.4.3 =.3, which is about 39% o the mean. Hence, the error bounds are 39% o the mean.
4 () In addition to the error bounds, detailed distribution o t can be plotted using MCS. First,, samples o material parameters are randomly generated according to uniorm distribution. Then, the histogram o t is plotted by applying these samples to Eq. (). Figure shows the histogram o atigue strain at N =, reversals. The solid curve connects the midpoint o each bin in the histogram. The PDF o atigue strain is obtained by scaling down the curve, such that the area under the curve is unity. It turns out that the atigue strain distribution has ollowing parameters: Mean.33 SD.33 In Figure 3, the normal distribution with the same mean and standard deviation is plotted. It is clear that the histogram looks close to a normal distribution with same parameters. Although variability associated with atigue should be obtained rom more rigorous method, it is assumed that the variability is normally distributed with mean.33 and COV %. With error bounds and variability, now it is possible to perorm Bayesian update. Let us consider that three atigue s are perormed. Ater normalizing by analytical atigue strain, the three data strains are.8,., and.. These three normalized data correspond to strain values o.8,.346, and.379, respectively Normal distribution pd o total strain Figure 3: Fitting the distribution o atigue strain using normal distribution Figure 4 shows distribution o estimated atigue strain at each stage o Bayesian update. The dotted lines show the likelihood unction or each result, while the solid lines show the updated distributions. The inal updated distribution o the atigue strain has the ollowing parameters: Mean.37 SD.7 () (6) Note that the mean does not change signiicantly, while the standard deviation o the updated Bayesian distribution is about % o that o the original distribution. Thus, the three data eectively reduce the uncertainty in the atigue ailure strain. Table tabulates the variation o the parameters o the distribution o atigue ailure strain with each stage o Bayesian update. Since the atigue strain is distributed, it is better to provide a conservative estimate o the atigue strain using a knockdown actor. When the variability is normalized, the mean is shited to., while retang the COV. Hence, the knockdown actor or the normalized variability, governed by N(.,. ) is calculated to be.97, using the mean value o etreme distribution in Eq. (4). Hence, the conservative estimate o atigue ailure strain at, reversals becomes t Initial Distribution Initial with irst with second Final Bayesian stress with third Figure 4: Bayesian update history o ailure atigue strain Table : Variation o parameters with each stage o Bayesian update Mean SD Initial..4 Ater irst.9.74 Ater second Ater third..
5 () () () NUMERICAL EXAMPLE CONSTANT STRAIN TEST For the constant strain, it is assumed that the amplitude o strain applied to the machine is constant at.. For the material properties in Table, the value o analytical atigue lie is, reversals. Since the crossover reversal value or this material is 4,3 reversals, the assumed atigue strain is in the elastic region. Due to computational diiculties, the strain-lie epression is solved or y = log (N), rather than or the strain lie, N. Hence, the analytical value or y would be 4.. In order to ind the tial error bounds o the atigue model, all parameters aecting the atigue strain are assumed to vary uniormly % o their nominal value. The error bounds or y have been determined to be 6% o the mean. In addition to the error bounds, detailed distribution o y can be plotted using MCS. First,, samples o material parameters are randomly generated according to uniorm distribution. Then, the histogram o y is plotted by applying these samples to Eq. (). Figure shows the PDF o y at atigue strain, t.. It turns out that y has the ollowing distribution parameters: Mean SD.99 (7) For the want o results, the variability o the results have been assumed to a normal distribution with mean and COV.% The three additional cases or y have been assumed to at.8,. and. times the analytical value... pd o log(n) Normal Distribution Figure 6: PDF o log (N) and that o normal distribution with the same mean and standard deviation PDF o log (N).6.4. PDF o product unction Polynomial itted Figure : PDF o log (N) at ied strain t. The PDF o log (N) can be modeled as a product o PDF o a normal distribution and a polynomial. The normal distribution that has the same parameters as that o the PDF o log (N) is shown as the curve with dotted lines in Figure 6. Figure 7 plots the product unction determined rom the two curves in Figure 6. An 8th degree polynomial is itted to estimate the product unction. The dashed lines show the polynomial in Figure Figure 7: Product unction that models the dierence between PDF o log (N) and that o normal distribution Figure 8 shows distribution o estimated atigue lie at each stage o Bayesian update. The dashed lines show the likelihood unction or each result, while the solid lines show the updated distributions. The inal updated distribution o the y has the ollowing parameters: Mean 4.76 SD.4 Since the atigue lie is distributed, it is better to provide a conservative estimate o the atigue lie using knockdown actor. When the variability is normalized, the mean is shited to., while retang the COV. Hence, the (8)
6 knockdown actor or the normalized variability, governed by N(,.) is calculated to be.967. Hence, the conservative estimate o atigue ailure lie at strain amplitude o. is N = = 769 reversals. Table 3 tabulates the variation o the parameters o the distribution o atigue ailure strain with each stage o Bayesian update. The Bayesian update or the atigue ailure lie has been perormed in Eample above, considering the PDF o lie as tial distribution. The importance o prior or tial distribution could be emphasized by perorming a Bayesian update with prior as uniorm distribution between error bounds and comparing results. The Bayesian update history o ailure atigue lie with a uniorm distributed prior is shown in Figure 9. Table 4 compares the results o these two Bayesian updates. It is noted that when the actual PDF o lie is used as prior, the mean o inal distribution decreases by.3% and the standard deviation o the inal distribution reduces by 3.39%. This suggests that having a better knowledge o the prior distribution results in a better coeicient o variance or the distribution ater update. Initial Distribution Initial Initial Distribution Initial with irst with second with third 3 3 Final Bayesian strain lie with irst with second with third 3 3 Final Bayesian strain lie Figure 8: Bayesian update history o ailure atigue lie Table 3: Variation o parameters with each stage o Bayesian update Mean SD Initial.. Ater irst.936. Ater second Ater third.44.8 EFFECT OF INITIAL DISTRIBUTION Figure 9: Bayesian update history o ailure atigue lie with a uniorm distribution or prior inormation Table 4: Comparison o parameters o distribution ater Bayesian update when the prior distribution is uniorm or the actual PDF Prior Distribution Parameter Uniorm Distribution Actual Distribution Mean o inal distribution SD o inal distribution.9.8
7 EFFECT OF TEST CASES The normalized cases considered in the eample above, are.8,. and.. The Bayesian update perormed with an altogether dierent set o normalized results such as.,. and. yields an interesting result. Figure compares the distribution and mean o atigue ailure lie ater Bayesian update or the two cases o s discussed above. Case reers to the result set o [.8,.,.]. Case reers to the result set o [.,.,.]. It is noted that both the distributions are one and the same Srain lie ater Bayesian update Case Case mean Case Case mean Figure : Strain lie ater Bayesian update or two dierent set o cases considered or the update It is noted that the average o the two sets o results is same, which is.67.now, Case has two results in the etremes o the error bounds, and hence, the likelihood unction o those results are truncated. Case has all results centered on. and hence their complete likelihood unction is utilized in Bayesian update. Yet, the strain lie distribution ater Bayesian update is one and the same or both cases. Hence, it can be concluded that the distribution o atigue ailure lie ater Bayesian update will depend on the average o the normalized cases considered. The dependence o Bayesian update on the average o the three cases have been urther veriied by considering a set o identical values, [.67,.67,.67] which resulted in an identical distribution as shown in Figure. It has also been veriied that the changing the order in which the cases are considered or the update does not aect the distribution o strain lie ater Bayesian update. CONCLUSIONS Bayesian update has been demonstrated as a good method to reduce uncertainty in number o reversals (N) or constant strain amplitude case and also to reduce uncertainty in strain amplitude or constant lie case, with the knowledge o cases. It is seen that the standard deviation o the distribution obtained ater the Bayesian update, is almost hal o that o the tial error distribution. Since only the average o the three cases is the main parameter, there is no eect o having repetitive values or the cases. Also, changing the order, in which the cases are considered or the Bayesian update, doesn t aect the actual atigue lie. Having a better knowledge or the prior leads to less scatteredness in distribution obtained ater Bayesian update. REFERENCES. Jungeun An, Erdem Acar, Raphael T. Hatka, Nam H. Kim, Peter G. Iju, Theodore F. Johnson, Is the Lowest Test Data Conservative Enough?. E. Acar, J. An, R. Hatka, N. Kim, P. Iju, and T. Johnson, Options or Using Test Data to Update Failure Stress, AIAA-7-97, 48th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conerence, Honolulu, Hawaii, Apr. 3-6, 7 3. Arthur P. Boresi, Richard J. Schmidt, Advanced Mechanics o Materials Sith Edition. 4. Fracture Control Program Report 3. Society o Automotive Engineers (SAE), Integration o Probabilistic Methods into the Design Process,, Aerospace Inormation Report 8, Warrendale, PA, J.R.M. Hosking, J.R. Wallis, and E.F. Wood, Estimation o the Generalized Etreme-Value Distribution by the Method o Probability-Weighted Moments, Technometrics, Vol.7, No.3, August 98, pp Wirsching, P.H., Literature Review on Mechanical Reliability and Probabilistic Design, Probabilistic Structural Analysis Methods or Select Space Propulsion System Components (PSAM), NASA Contractor Report 899, Vol. III, Washington, D.C., Acar, E., Kale, A., and Hatka, R.T., "Comparing Eectiveness o Measures that Improve Aircrat Structural Saety," ASCE Journal o Aerospace Engineering, Vol., No.3, July 7, pp
Approximate probabilistic optimization using exact-capacity-approximate-response-distribution (ECARD)
Struct Multidisc Optim (009 38:613 66 DOI 10.1007/s00158-008-0310-z RESEARCH PAPER Approximate probabilistic optimization using exact-capacity-approximate-response-distribution (ECARD Sunil Kumar Richard
More informationFatigue verification of high loaded bolts of a rocket combustion chamber.
Fatigue veriication o high loaded bolts o a rocket combustion chamber. Marcus Lehmann 1 & Dieter Hummel 1 1 Airbus Deence and Space, Munich Zusammenassung Rocket engines withstand intense thermal and structural
More informationReliability-Based Structural Design of Aircraft Together with Future Tests
Reliability-Based Structural Design o Aircrat Together with Future Tests Erdem Acar 1 TOBB University o Economics and Technology, Söğütözü, Ankara 06560, Turkey Raphael T. Hatka 2, Nam-Ho Kim 3 University
More informationManufacturing Remaining Stresses in Truck Frame Rail's Fatigue Life Prediction
Manuacturing Remaining Stresses in Truck Frame Rail's Fatigue Lie Prediction Claudiomar C. Cunha & Carlos A. N. Dias MSX International & Department o Naval Engineering EPUSP/USP/Brazil Department o Mechanical
More informationChapter 6 Reliability-based design and code developments
Chapter 6 Reliability-based design and code developments 6. General Reliability technology has become a powerul tool or the design engineer and is widely employed in practice. Structural reliability analysis
More informationAPPLICATION OF A CONDITIONAL EXPECTATION RESPONSE SURFACE APPROACH TO PROBABILISTIC FATIGUE
9 th ASCE Specialty Conerence on Probabilistic Mechanics and Structural Reliability APPLICATION OF A CONDITIONAL EXPECTATION RESPONSE SURFACE APPROACH TO PROBABILISTIC FATIGUE Abstract F.N. Momin, H.R.
More informationStructural Safety Evaluation Using Modified Latin Hypercube Sampling Technique
International Journal o Perormability Engineering Vol. 9, No. 5, eptember 203, pp. 55-522. AM Consultants Printed in India tructural aety Evaluation Using Modiied Latin Hypercube ampling Technique P. BHATTACHAJEE,
More informationReliability Assessment with Correlated Variables using Support Vector Machines
Reliability Assessment with Correlated Variables using Support Vector Machines Peng Jiang, Anirban Basudhar, and Samy Missoum Aerospace and Mechanical Engineering Department, University o Arizona, Tucson,
More information( x) f = where P and Q are polynomials.
9.8 Graphing Rational Functions Lets begin with a deinition. Deinition: Rational Function A rational unction is a unction o the orm ( ) ( ) ( ) P where P and Q are polynomials. Q An eample o a simple rational
More informationLife Prediction Under Multiaxial Fatigue
Lie Prediction Under Multiaxial Fatigue D. Ramesh and M.M. Mayuram Department o Mechanical Engineering Indian Institute o Technology, Madras Chennai-600 036 (India) e-mail: mayuram@iitm.ac.in ABSTRACT
More informationS. Srinivasan, Technip Offshore, Inc., Houston, TX
9 th ASCE Specialty Conerence on Probabilistic Mechanics and Structural Reliability PROBABILISTIC FAILURE PREDICTION OF FILAMENT-WOUND GLASS-FIBER Abstract REINFORCED COMPOSITE TUBES UNDER BIAXIAL LOADING
More informationRATIONAL FUNCTIONS. Finding Asymptotes..347 The Domain Finding Intercepts Graphing Rational Functions
RATIONAL FUNCTIONS Finding Asymptotes..347 The Domain....350 Finding Intercepts.....35 Graphing Rational Functions... 35 345 Objectives The ollowing is a list o objectives or this section o the workbook.
More informationObjectives. By the time the student is finished with this section of the workbook, he/she should be able
FUNCTIONS Quadratic Functions......8 Absolute Value Functions.....48 Translations o Functions..57 Radical Functions...61 Eponential Functions...7 Logarithmic Functions......8 Cubic Functions......91 Piece-Wise
More informationRELIABILITY OF BURIED PIPELINES WITH CORROSION DEFECTS UNDER VARYING BOUNDARY CONDITIONS
REIABIITY OF BURIE PIPEIES WITH CORROSIO EFECTS UER VARYIG BOUARY COITIOS Ouk-Sub ee 1 and ong-hyeok Kim 1. School o Mechanical Engineering, InHa University #53, Yonghyun-ong, am-ku, Incheon, 40-751, Korea
More informationfive mechanics of materials Mechanics of Materials Mechanics of Materials Knowledge Required MECHANICS MATERIALS
RCHITECTUR STRUCTURES: FORM, BEHVIOR, ND DESIGN DR. NNE NICHOS SUMMER 2014 Mechanics o Materials MECHNICS MTERIS lecture ive mechanics o materials www.carttalk.com Mechanics o Materials 1 rchitectural
More informationFATIGUE DURABILITY OF CONCRETE EXTERNALLY STRENGTHENED WITH FRP SHEETS
FATIGUE DURABILITY OF CONCRETE EXTERNALLY STRENGTHENED WITH FRP SHEETS H. Diab () and Zhishen Wu () () Department o Urban and Civil Engineering, Ibaraki University, Japan Abstract A primary concern o the
More informationfour mechanics of materials Mechanics of Materials Mechanics of Materials Knowledge Required MECHANICS MATERIALS
EEMENTS OF RCHITECTUR STRUCTURES: FORM, BEHVIOR, ND DESIGN DR. NNE NICHOS SRING 2016 Mechanics o Materials MECHNICS MTERIS lecture our mechanics o materials www.carttalk.com Mechanics o Materials 1 S2009abn
More informationA study on the Accelerated Life Test Coupled with Computation for Life Prediction of Product According to Wear and Damage
International Journal o Mechanical & Mechatronics Engineering IJMME-IJENS Vol:15 No:03 106 A study on the Accelerated Lie Test Coupled with Computation or Lie Prediction o Product According to Wear and
More informationAXIALLY LOADED FRP CONFINED REINFORCED CONCRETE CROSS-SECTIONS
AXIALLY LOADED FRP CONFINED REINFORCED CONCRETE CROSS-SECTIONS Bernát Csuka Budapest University o Technology and Economics Department o Mechanics Materials and Structures Supervisor: László P. Kollár 1.
More informationBond strength model for interfaces between nearsurface mounted (NSM) CFRP strips and concrete
University o Wollongong Research Online Faculty o Engineering and Inormation Sciences - Papers: Part A Faculty o Engineering and Inormation Sciences 2014 Bond strength model or interaces between nearsurace
More informationUNCERTAINTY EVALUATION OF SINUSOIDAL FORCE MEASUREMENT
XXI IMEKO World Congress Measurement in Research and Industry August 30 eptember 4, 05, Prague, Czech Republic UNCERTAINTY EVALUATION OF INUOIDAL FORCE MEAUREMENT Christian chlegel, Gabriela Kiekenap,Rol
More informationAPPENDIX 1 ERROR ESTIMATION
1 APPENDIX 1 ERROR ESTIMATION Measurements are always subject to some uncertainties no matter how modern and expensive equipment is used or how careully the measurements are perormed These uncertainties
More informationReliability-Based Load and Resistance Factor Design (LRFD) Guidelines for Stiffened Panels and Grillages of Ship Structures
Reliability-Based Load and Resistance actor Design (LRD) Guidelines or Stiened Panels and Grillages o Ship Structures Ibrahim A. Assakka 1, Bilal M. Ayyub 2, Paul E. Hess, III, 3 and Khaled Atua 4 ABSTRACT
More informationKeywords: creep, damage, finite element analysis, FSRF, low-cycle fatigue, type 316 steel, weldment
--- 1 --- Application o the linear matching method to eep-atigue ailure analysis o uciorm weldment manuactured o the austenitic steel AISI type 316N(L) Yevgen Gorash and Haoeng Chen Department o Mechanical
More informationWELDED ALUMINUM ALLOY PLATE GIRDERS SUBJECTED TO SHEAR FORCE
Advanced Steel Construction Vol. 8, No. 1, pp. 71-94 (2012) 71 WELDED ALUMINUM ALLOY PLATE GIRDERS SUBJECTED TO SHEAR FORCE Feng Zhou 1a, 1b, Ben Young 2,* and Hin-Chung Lam 3 1a Department o Building
More informationAssessment of Fatigue Damage Features in a Piping System Using Signal Processing Approach
PROCESSING (SIP8), Istanbul, Turkey, May 27-3, 28 Assessment o Fatigue Damage Features in a Piping System Using Signal Processing Approach 1 S. ABDULLAH, 2 M. LOMAN, 3 N. JAMALUDDIN, 4 A. ARIFIN, 5 Z.
More informationDETC A GENERALIZED MAX-MIN SAMPLE FOR RELIABILITY ASSESSMENT WITH DEPENDENT VARIABLES
Proceedings o the ASME International Design Engineering Technical Conerences & Computers and Inormation in Engineering Conerence IDETC/CIE August 7-,, Bualo, USA DETC- A GENERALIZED MAX-MIN SAMPLE FOR
More information8.3 Design of Base Plate for Thickness
8.3 Design o Base Plate or Thickness 8.3.1 Design o base plate or thickness (Elastic Design) Upto this point, the chie concern has been about the concrete oundation, and methods o design have been proposed
More informationThe achievable limits of operational modal analysis. * Siu-Kui Au 1)
The achievable limits o operational modal analysis * Siu-Kui Au 1) 1) Center or Engineering Dynamics and Institute or Risk and Uncertainty, University o Liverpool, Liverpool L69 3GH, United Kingdom 1)
More informationReliability of Axially Loaded Fiber-Reinforced-Polymer Confined Reinforced Concrete Circular Columns
American J. o Engineering and Applied Sciences (1): 31-38, 009 ISSN 1941-700 009 Science Publications Reliability o Axially Loaded Fiber-Reinorced-Polymer Conined Reinorced Concrete Circular Columns Venkatarman
More informationRESOLUTION MSC.362(92) (Adopted on 14 June 2013) REVISED RECOMMENDATION ON A STANDARD METHOD FOR EVALUATING CROSS-FLOODING ARRANGEMENTS
(Adopted on 4 June 203) (Adopted on 4 June 203) ANNEX 8 (Adopted on 4 June 203) MSC 92/26/Add. Annex 8, page THE MARITIME SAFETY COMMITTEE, RECALLING Article 28(b) o the Convention on the International
More information3. Several Random Variables
. Several Random Variables. Two Random Variables. Conditional Probabilit--Revisited. Statistical Independence.4 Correlation between Random Variables. Densit unction o the Sum o Two Random Variables. Probabilit
More informationA fatigue driving energy approach to high-cycle fatigue life estimation under variable amplitude loading
ORIGINL CONTRIBUTION doi: 0./e.2347 atigue driving energy approach to high-cycle atigue lie estimation under variable amplitude loading Z. PENG, H-Z. HUNG, S-P. ZHU, H. GO and Z. LV Institute o Reliability
More informationApplication of Mathematica Software for Estimate the Fatigue Life Time Duration of Mechanical System
ANALELE UNIVERSITĂłII EFTIMIE MURGU REŞIłA ANUL XVII, NR. 2, 2010, ISSN 1453-7397 Petru Florin Minda, Ana Maria Budai Application o Mathematica Sotware or Estimate the Fatigue Lie Time Duration o Mechanical
More informationFinite Element Modeling of Residual Thermal Stresses in Fiber-Reinforced Composites Using Different Representative Volume Elements
Proceedings o the World Congress on Engineering 21 Vol II WCE 21, June 3 - July 2, 21, London, U.K. Finite Element Modeling o Residual Thermal Stresses in Fiber-Reinorced Composites Using Dierent Representative
More informationTechniques for Estimating Uncertainty Propagation in Probabilistic Design of Multilevel Systems
0th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conerence 0 August - September 004, Albany, New Yor AIAA 004-4470 Techniques or Estimating Uncertainty Propagation in Probabilistic Design o Multilevel
More informationEx x xf xdx. Ex+ a = x+ a f x dx= xf x dx+ a f xdx= xˆ. E H x H x H x f x dx ˆ ( ) ( ) ( ) μ is actually the first moment of the random ( )
Fall 03 Analysis o Eperimental Measurements B Eisenstein/rev S Errede The Epectation Value o a Random Variable: The epectation value E[ ] o a random variable is the mean value o, ie ˆ (aa μ ) For discrete
More informationReliability assessment on maximum crack width of GFRPreinforced
Fourth International Conerence on FRP Composites in Civil Engineering (CICE2008) 22-24July 2008, Zurich, Switzerland Reliability assessment on maximum crack width o GFRPreinorced concrete beams Z. He and
More informationMODULE 6 LECTURE NOTES 1 REVIEW OF PROBABILITY THEORY. Most water resources decision problems face the risk of uncertainty mainly because of the
MODULE 6 LECTURE NOTES REVIEW OF PROBABILITY THEORY INTRODUCTION Most water resources decision problems ace the risk o uncertainty mainly because o the randomness o the variables that inluence the perormance
More information«Develop a better understanding on Partial fractions»
«Develop a better understanding on Partial ractions» ackground inormation: The topic on Partial ractions or decomposing actions is irst introduced in O level dditional Mathematics with its applications
More information6.1 The Linear Elastic Model
Linear lasticit The simplest constitutive law or solid materials is the linear elastic law, which assumes a linear relationship between stress and engineering strain. This assumption turns out to be an
More informationProbabilistic Analysis of Multi-layered Soil Effects on Shallow Foundation Settlement
Probabilistic Analysis o Multi-layered Soil ects on Shallow Foundation Settlement 54 Y L Kuo B Postgraduate Student, School o Civil and nvironmental ngineering, University o Adelaide, Australia M B Jaksa
More informationIMPACT BEHAVIOR OF COMPOSITE MATERIALS USED FOR AUTOMOTIVE INTERIOR PARTS
0 th HSTAM International Congress on Mechanics Chania, Crete, Greece, 5 7 May, 03 IMPACT BEHAVIOR OF COMPOSITE MATERIALS USED FOR AUTOMOTIVE INTERIOR PARTS Mariana D. Stanciu, Ioan Curtu and Ovidiu M.
More informationCurve Sketching. The process of curve sketching can be performed in the following steps:
Curve Sketching So ar you have learned how to ind st and nd derivatives o unctions and use these derivatives to determine where a unction is:. Increasing/decreasing. Relative extrema 3. Concavity 4. Points
More informationExample 1. Stress amplitude (MPa) 130 1x10 7 (no failure)
Example 1 For the ollowing R=-1 AISI 1090 steel test data, plot two S-N curves, one using loglinear coordinates and the other using log-log coordinates. a) Use linear regression to estimate the best it
More informationProfessor, Institute of Engineering Mechanics, Harbin. China 2. Ph.D Student, Institute of Engineering Mechanics, Harbin. China 3
The 14 th World Conerence on Earthquake Engineering COMPARISON OF FRP-RETROFITTING STRATEGIES IN CHINESE AND ITALIAN CODES J. W. DAI 1, Y.R. WANG 2, B. JIN 1, 3, D.F.ZU 4, Silvia Alessandri 5, Giorgio
More informationQuality control of risk measures: backtesting VAR models
De la Pena Q 9/2/06 :57 pm Page 39 Journal o Risk (39 54 Volume 9/Number 2, Winter 2006/07 Quality control o risk measures: backtesting VAR models Victor H. de la Pena* Department o Statistics, Columbia
More informationMICROMECHANICAL FAILURE ANALYSIS OF UNIDIRECTIONAL FIBER-REINFORCED COMPOSITES UNDER IN-PLANE AND TRANSVERSE SHEAR
THE 19 TH INTERNATIONAL CONFERENCE ON COMPOSITE MATERIALS MICROMECHANICAL FAILURE ANALYSIS OF UNIDIRECTIONAL FIBER-REINFORCED COMPOSITES UNDER IN-PLANE AND TRANSVERSE SHEAR Lei Yang*, Ying Yan, Zhiguo
More informationNUMERICAL ASSESSMENT OF REINFORCED CONCRETE MEMBERS RETROFITTED WITH FIBER REINFORCED POLYMER FOR RESISTING BLAST LOADING
NUMERICAL ASSESSMENT OF REINFORCED CONCRETE MEMBERS RETROFITTED WITH FIBER REINFORCED POLYMER FOR RESISTING BLAST LOADING By GRAHAM LONG A THESIS PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA
More informationBolted Joints Analysis Methods and Evaluation
International OPEN ACCESS Journal O Modern Engineering Research (IJMER) Bolted Joints Analysis Methods and Evaluation G. Chaitanya 1, M. Kumara Swamy 2 1 Mechanical engineering, UCEK (A)/Jawaharlal Nehru
More informationHYDROELASTIC TAILORING AND OPTIMIZATION OF A COMPOSITE MARINE PROPELLER
HYDROELASTIC TAILORING AND OPTIMIZATION OF A COMPOSITE MARINE PROPELLER José P. Blasques, Christian Berggreen and Poul Andersen Department o Mechanical Engineering, Technical University o Denmark Nils
More informationAnalysis of aircraft trajectory uncertainty using Ensemble Weather Forecasts
DOI: 10.13009/EUCASS017-59 7 TH EUROPEAN CONERENCE OR AERONAUTICS AND SPACE SCIENCES (EUCASS Analysis o aircrat traectory uncertainty using Ensemble Weather orecasts Damián Rivas, Antonio ranco, and Alonso
More informationProbabilistic Model of Error in Fixed-Point Arithmetic Gaussian Pyramid
Probabilistic Model o Error in Fixed-Point Arithmetic Gaussian Pyramid Antoine Méler John A. Ruiz-Hernandez James L. Crowley INRIA Grenoble - Rhône-Alpes 655 avenue de l Europe 38 334 Saint Ismier Cedex
More informationReliability assessment using probabilistic support vector machines. Anirban Basudhar and Samy Missoum*
156 Int. J. Reliability and Saety, Vol. 7, o. 2, 2013 Reliability assessment using probabilistic support vector machines Anirban Basudhar and Samy Missoum* Aerospace and Mechanical Engineering Department,
More informationSyllabus Objective: 2.9 The student will sketch the graph of a polynomial, radical, or rational function.
Precalculus Notes: Unit Polynomial Functions Syllabus Objective:.9 The student will sketch the graph o a polynomial, radical, or rational unction. Polynomial Function: a unction that can be written in
More informationSOME RESEARCH ON FINITE ELEMENT ANALYSIS OF COMPOSITE MATERIALS
The 3 rd International Conerence on DIAGNOSIS AND PREDICTION IN MECHANICAL ENGINEERING SYSTEMS DIPRE 12 SOME RESEARCH ON FINITE ELEMENT ANALYSIS OF Valeriu DULGHERU, Viorel BOSTAN, Marin GUŢU Technical
More informationLecture 8 Optimization
4/9/015 Lecture 8 Optimization EE 4386/5301 Computational Methods in EE Spring 015 Optimization 1 Outline Introduction 1D Optimization Parabolic interpolation Golden section search Newton s method Multidimensional
More informationUsing ABAQUS for reliability analysis by directional simulation
Visit the SIMULIA Resource Center or more customer examples. Using ABAQUS or reliability analysis by directional simulation I. R. Iversen and R. C. Bell Prospect, www.prospect-s.com Abstract: Monte Carlo
More informationSafety Envelope for Load Tolerance and Its Application to Fatigue Reliability Design
Safety Envelope for Load Tolerance and Its Application to Fatigue Reliability Design Haoyu Wang * and Nam H. Kim University of Florida, Gainesville, FL 32611 Yoon-Jun Kim Caterpillar Inc., Peoria, IL 61656
More informationProbabilistic Engineering Mechanics
Probabilistic Engineering Mechanics 6 (11) 174 181 Contents lists available at ScienceDirect Probabilistic Engineering Mechanics journal homepage: www.elsevier.com/locate/probengmech Variability response
More informationLeast-Squares Spectral Analysis Theory Summary
Least-Squares Spectral Analysis Theory Summary Reerence: Mtamakaya, J. D. (2012). Assessment o Atmospheric Pressure Loading on the International GNSS REPRO1 Solutions Periodic Signatures. Ph.D. dissertation,
More informationMath-3 Lesson 8-5. Unit 4 review: a) Compositions of functions. b) Linear combinations of functions. c) Inverse Functions. d) Quadratic Inequalities
Math- Lesson 8-5 Unit 4 review: a) Compositions o unctions b) Linear combinations o unctions c) Inverse Functions d) Quadratic Inequalities e) Rational Inequalities 1. Is the ollowing relation a unction
More informationScattered Data Approximation of Noisy Data via Iterated Moving Least Squares
Scattered Data Approximation o Noisy Data via Iterated Moving Least Squares Gregory E. Fasshauer and Jack G. Zhang Abstract. In this paper we ocus on two methods or multivariate approximation problems
More informationQuadratic Functions. The graph of the function shifts right 3. The graph of the function shifts left 3.
Quadratic Functions The translation o a unction is simpl the shiting o a unction. In this section, or the most part, we will be graphing various unctions b means o shiting the parent unction. We will go
More informationThe Application of Reliability Methods in the Design of Tophat Stiffened
The Application o Reliability Methods in the Design o Tophat Stiened Composite Panels under In-plane Loading Yang N. (1)() & Das P. K., () (1) Harbin Engineering University, China ()University o Strathclyde,
More informationFiber / Toughened Epoxy Composites under
Fatigue Behavior o Impact-Damaged Carbon Fiber / Toughened Epoxy Composites under Compressive loading Toshio Ogasawara, Hisaya Katoh, unao ugimoto, and Takashi Ishikawa Advanced d Composite Technology
More informationAnalysis of Friction-Induced Vibration Leading to Eek Noise in a Dry Friction Clutch. Abstract
The 22 International Congress and Exposition on Noise Control Engineering Dearborn, MI, USA. August 19-21, 22 Analysis o Friction-Induced Vibration Leading to Eek Noise in a Dry Friction Clutch P. Wickramarachi
More informationFinite element modeling incorporating nonlinearity of material behavior based on the fib Model Code 2010
Peer-reviewed & Open access journal www.academicpublishingplatorms.com Finite element modeling incorporating non-linearity o material behavior ATI - Applied Technologies & Innovations Volume 5 Issue November
More informationEstimation of Sample Reactivity Worth with Differential Operator Sampling Method
Progress in NUCLEAR SCIENCE and TECHNOLOGY, Vol. 2, pp.842-850 (2011) ARTICLE Estimation o Sample Reactivity Worth with Dierential Operator Sampling Method Yasunobu NAGAYA and Takamasa MORI Japan Atomic
More information9.1 The Square Root Function
Section 9.1 The Square Root Function 869 9.1 The Square Root Function In this section we turn our attention to the square root unction, the unction deined b the equation () =. (1) We begin the section
More informationANALYSIS OF FAILURE ASSESSMENT FOR SPHERICAL PRESSURE VESSELS
(ISSN 78 664) VOLUME-5, ISSUE-, March 6 ANALYSIS OF FAILURE ASSESSMENT FOR SPHERICAL PRESSURE VESSELS Sumit Goel, Anil Kumar, Abhishek Kr. Goel M.Tech. Scholar, Department o Mechanical Engineering, Subharti
More informationThis is an author-deposited version published in : Eprints ID : 11904
Open Archive TOULOUSE Archive Ouverte (OATAO) OATAO is an open access repository that collects the work o Toulouse researchers and makes it reely available over the web where possible. This is an author-deposited
More informationMath-3 Lesson 1-4. Review: Cube, Cube Root, and Exponential Functions
Math- Lesson -4 Review: Cube, Cube Root, and Eponential Functions Quiz - Graph (no calculator):. y. y ( ) 4. y What is a power? vocabulary Power: An epression ormed by repeated Multiplication o the same
More informationEffects of Error, Variability, Testing and Safety Factors on Aircraft Safety
Effects of Error, Variability, Testing and Safety Factors on Aircraft Safety E. Acar *, A. Kale ** and R.T. Haftka Department of Mechanical and Aerospace Engineering University of Florida, Gainesville,
More informationarxiv:quant-ph/ v2 12 Jan 2006
Quantum Inormation and Computation, Vol., No. (25) c Rinton Press A low-map model or analyzing pseudothresholds in ault-tolerant quantum computing arxiv:quant-ph/58176v2 12 Jan 26 Krysta M. Svore Columbia
More informationdesign variable x1
Multipoint linear approximations or stochastic chance constrained optimization problems with integer design variables L.F.P. Etman, S.J. Abspoel, J. Vervoort, R.A. van Rooij, J.J.M Rijpkema and J.E. Rooda
More informationRobust Residual Selection for Fault Detection
Robust Residual Selection or Fault Detection Hamed Khorasgani*, Daniel E Jung**, Gautam Biswas*, Erik Frisk**, and Mattias Krysander** Abstract A number o residual generation methods have been developed
More informationProbability & Statistics: Infinite Statistics. Robert Leishman Mark Colton ME 363 Spring 2011
Probability & Statistics: Infinite Statistics Robert Leishman Mark Colton ME 363 Spring 0 Large Data Sets What happens to a histogram as N becomes large (N )? Number of bins becomes large (K ) Width of
More informationSupplement To: Search for Tensor, Vector, and Scalar Polarizations in the Stochastic Gravitational-Wave Background
Supplement To: Search or Tensor, Vector, and Scalar Polarizations in the Stochastic GravitationalWave Background B. P. Abbott et al. (LIGO Scientiic Collaboration & Virgo Collaboration) This documents
More informationBuckling of Double-walled Carbon Nanotubes
Buckling o Double-walled Carbon anotubes Y. H. Teo Engineering Science Programme ational University o Singapore Kent idge Singapore 960 Abstract This paper is concerned with the buckling o double-walled
More informationNumerical Methods - Lecture 2. Numerical Methods. Lecture 2. Analysis of errors in numerical methods
Numerical Methods - Lecture 1 Numerical Methods Lecture. Analysis o errors in numerical methods Numerical Methods - Lecture Why represent numbers in loating point ormat? Eample 1. How a number 56.78 can
More informationProducts and Convolutions of Gaussian Probability Density Functions
Tina Memo No. 003-003 Internal Report Products and Convolutions o Gaussian Probability Density Functions P.A. Bromiley Last updated / 9 / 03 Imaging Science and Biomedical Engineering Division, Medical
More informationOBSERVER/KALMAN AND SUBSPACE IDENTIFICATION OF THE UBC BENCHMARK STRUCTURAL MODEL
OBSERVER/KALMAN AND SUBSPACE IDENTIFICATION OF THE UBC BENCHMARK STRUCTURAL MODEL Dionisio Bernal, Burcu Gunes Associate Proessor, Graduate Student Department o Civil and Environmental Engineering, 7 Snell
More informationOptimal Control of process
VYSOKÁ ŠKOLA BÁŇSKÁ TECHNICKÁ UNIVERZITA OSTRAVA FAKULTA METALURGIE A MATERIÁLOVÉHO INŽENÝRSTVÍ Optimal Control o process Study Support Milan Heger Ostrava 8 Title: Optimal Control o process Code: Author:
More informationOPTIMAL PLACEMENT AND UTILIZATION OF PHASOR MEASUREMENTS FOR STATE ESTIMATION
OPTIMAL PLACEMENT AND UTILIZATION OF PHASOR MEASUREMENTS FOR STATE ESTIMATION Xu Bei, Yeo Jun Yoon and Ali Abur Teas A&M University College Station, Teas, U.S.A. abur@ee.tamu.edu Abstract This paper presents
More informationCHAPTER 8 ANALYSIS OF AVERAGE SQUARED DIFFERENCE SURFACES
CAPTER 8 ANALYSS O AVERAGE SQUARED DERENCE SURACES n Chapters 5, 6, and 7, the Spectral it algorithm was used to estimate both scatterer size and total attenuation rom the backscattered waveorms by minimizing
More informationContribution of Building-Block Test to Discover Unexpected Failure Modes
Contribution of Building-Block Test to Discover Unexpected Failure Modes Taiki Matsumura 1, Raphael T. Haftka 2 and Nam H. Kim 3 University of Florida, Gainesville, FL, 32611 While the accident rate of
More informationINPUT GROUND MOTION SELECTION FOR XIAOWAN HIGH ARCH DAM
3 th World Conerence on Earthquake Engineering Vancouver, B.C., Canada August -6, 24 Paper No. 2633 INPUT GROUND MOTION LECTION FOR XIAOWAN HIGH ARCH DAM CHEN HOUQUN, LI MIN 2, ZHANG BAIYAN 3 SUMMARY In
More informationAcoustic forcing of flexural waves and acoustic fields for a thin plate in a fluid
Acoustic orcing o leural waves and acoustic ields or a thin plate in a luid Darryl MCMAHON Maritime Division, Deence Science and Technology Organisation, HMAS Stirling, WA Australia ABSTACT Consistency
More informationAUGMENTED POLYNOMIAL GUIDANCE FOR TERMINAL VELOCITY CONSTRAINTS
AUGMENTED POLYNOMIAL GUIDANCE FOR TERMINAL VELOCITY CONSTRAINTS Gun-Hee Moon*, Sang-Woo Shim*, and Min-Jea Tah* *Korea Advanced Institute Science and Technology Keywords: Polynomial guidance, terminal
More informationCalibration of Bond Coefficient for Deflection Control of FRP RC Members
Fourth International Conerence on FRP Composites in Civil Engineering (CICE008) -4July 008, Zurich, Switzerland Calibration o Bond Coeicient or Delection Control o FRP RC Members R. Fico, A. Prota & G.
More informationGuidelines for Nonlinear Finite Element Analysis of Concrete Structures
P rd /P exp [%] Rijkswaterstaat Technical Document (RTD) Guidelines or Nonlinear Finite Element Analysis o Concrete Structures Doc.nr.: RTD 1016-1:2017 Version: 2.1 Status: Final Date: 15 June 2017 100
More informationInternal thermal noise in the LIGO test masses: A direct approach
PHYSICAL EVIEW D VOLUME 57, NUMBE 2 15 JANUAY 1998 Internal thermal noise in the LIGO test masses: A direct approach Yu. Levin Theoretical Astrophysics, Caliornia Institute o Technology, Pasadena, Caliornia
More informationStrain and Stress Measurements with a Two-Dimensional Detector
Copyright ISSN (C) 97-, JCPDS-International Advances in X-ray Centre Analysis, or Volume Diraction 4 Data 999 5 Strain and Stress Measurements with a Two-Dimensional Detector Baoping Bob He and Kingsley
More informationIntroduction. Methods of vibration control
ISSN: 394-3696 VOLUME 1, ISSUE DEC-014 Identiication o coulomb, viscous and particle damping parameters rom the response o SDOF harmonically orced linear oscillator Mr.U.L.Anuse. Department o Mechanical
More informationA STUDY OF 0 -FIBRE MICROBUCKLING IN MULTIDIRECTIONAL COMPOSITE LAMINATES
A STUDY OF -FIBRE MICROBUCKLING IN MULTIDIRECTIONAL COMPOSITE LAMINATES P. Berbinau and C. Soutis Department o Aeronautics, Imperial College o Science, Technology & Medicine Prince Consort Rd, London SW7
More informationMaterials Science and Engineering A
Materials Science and Engineering A 528 (211) 48 485 Contents lists availale at ScienceDirect Materials Science and Engineering A journal homepage: www.elsevier.com/locate/msea Study o strength and its
More informationBurst strength behaviour of an aging subsea gas pipeline elbow in different external and internal corrosion-damaged positions
csnak, 2015 Int. J. Nav. Archit. Ocean Eng. (2015) 7:435~451 http://dx.doi.org/10.1515/ijnaoe-2015-0031 pissn: 2092-6782, eissn: 2092-6790 Burst strength behaviour o an aging subsea gas pipeline elbow
More informationThe Deutsch-Jozsa Problem: De-quantization and entanglement
The Deutsch-Jozsa Problem: De-quantization and entanglement Alastair A. Abbott Department o Computer Science University o Auckland, New Zealand May 31, 009 Abstract The Deustch-Jozsa problem is one o the
More informationNotched Strength Estimation of Graphite/Epoxy Laminated Composite with Central Crack under Uniaxial Tensile Loading
International Journal o Composite Materials 5, 5(6): 77-8 DOI:.593/j.cmaterials.556.6 Notched Strength Estimation o Graphite/Epoxy Laminated Composite with Central Crack under Uniaxial Tensile Loading
More information