PSI - Issue 6

First page Table of contents 1 Next page Last page

XXVII International Conference «Mathematical and Computer Simulation in Mechanics of Solids and Structures. Fundamentals of static and dynamic fracture»,MCM 2017,25-27 September 2017, Saint-Petersburg, Russia

Volume 6 • 2017

ISSN 2452-3216

ELSEVIER

Guest Editors: Y uri P etrov Vadim Sil b erschmidt

Available online al www.sciencedirect.com ScienceDirect

ScienceDirect Available online at www.sciencedirect.com Av ilable o line at ww.sciencedire t.com ienceDirect Structural Integrity Procedia 00 (2016) 000 – 000 Procedia S ructural Int grity 6 ( 7) 1–4 Available online at www.sciencedirect.com ScienceDirect StructuralIntegrity Procedia 00 (2017) 000 – 000

www.elsevier.com/locate/procedia

* Corresponding author. E-mail address: yp@YP1004.spb.edu

* Corresponding author. Tel.: +351 218419991. E-mail address: amd@tecnico.ulisboa.pt 2452-3216 © 201 7 The Authors. Published by Elsevier B.V. Peer-review under responsibility of the MCM 2017 organizers.

2452-3216 Copyright  2017 The Authors. Published by Elsevier B.V. Peer-review under responsibility of the MCM 2017 organizers. 10.1016/j.prostr.2017.11.001

Vadim Silberschmidt et al. / Procedia Structural Integrity 6 (2017) 1–4 Author name / StructuralIntegrity Procedia 00 (2017) 000 – 000

Mechanics of composites;

•

• Nanomechanics and problems of strength enhancement of materials; • Information technologies and software for structural modelling; • Extreme conditions and seismic resistance

The The success of the conference is primarily thanks to a strong and enthusiastic support of participants from all around the world, hard work of the conference organizers and generous support provided by ESIS . The conference received more than 212 abstracts, 169 papers were accepted for presentation, 138 papers were presented at the conference and 105 papers were selected for publication in the conference proceedings. The growing numbers and increasing quality of conference papers indicate the rising significance of the conference topics as well as importance of ESIS TC5 activities. This issue comprises a part of MCM-2017 papers selected for publication in Procedia Structural Integrity . We hope the reader will judge the excellence of the conference from the quality and novelty of the presented research. We also hope that the next MCM-2019 conference ( MCM is a biannual conference held every odd year) will find new participants among the readers of this issue.

Conference Chairs

Yuri Petrov, Saint Petersburg, Russia Vadim Silberschmidt, Loughborough, UK

Vadim Silberschmidt et al. / Procedia Structural Integrity 6 (2017) 1–4 Author name / Structural Integrity Procedia 00 (2017) 000 – 000

Committees Co-Chairmen: Yuri Petrov and Vadim Silberschmidt International Scientific Committee members N. Morozov B. Karihaloo A. Belyaev

R. Arutyunyan A. Belostotsky N. Vatin R. Goldshtein L. Igumnov D. Indeitsev G. Kadisov G. Kashevarova R. Kayumov S. Klovanich A. Krivtsov E. Lomakin A. Maslennikov I. Ovidko A. Perelmuter S. Petinov A. Rodionov L. Rozin N. Taranukha V. Travush V. Chirkov F. Shklyarchuk J. Kaplunov D. Prikazchikov Ya-Pu Zhao I. Hussainova N. Gupta A. Iqbal J. Džugan D. Rittel D. Sherman M. Wiercigroch A. Pandolfi E. Simbort Wen Zhu Shao A. Borovkov V. Shlyannikov G. Mushuris

Vadim Silberschmidt et al. / Procedia Structural Integrity 6 (2017) 1–4 Author name / StructuralIntegrity Procedia 00 (2017) 000 – 000

Local Organizing and Scientific Committee Yuri Rutman Svetlana Atroshenko Vladimir Smirnov V. Bakulin D. Bondarev

A. Bragov V. Bratov G. Fedorovsky

A. Frumen S. Galileev A. Gruzdkov A. Ivanov L. Kagan-Rozentsveig N. Kazarinov L. Kondratyeva V. Lalin V. Meleshko B. Melnikov N. Ostrovskaya N. Selyutina A. Uzdin G. Volkov Editorial team: Yuri Petrov Vadim Silberschmidt Svetlana Atroshenko Yuri Rutman

ScienceDirect Available online at www.sciencedirect.com Av ilable o line at www.sciencedire t.com ScienceDirect Structural Integrity Procedia 00 (2016) 000 – 000 P o edi Structural Integr ty 6 (2017) 69–76 Available online at www.sciencedirect.com ScienceDirect Structural I tegrity Procedia 00 (2017) 000 – 000 Available online at www.sciencedirect.com ScienceDirect Structural Integrity Procedia 00 (2017) 000 – 000

www.elsevier.com/locate/procedia www.elsevier.com/locate/procedia

www.elsevier.com/locate/procedia

XV Portuguese Conference on Fracture, PCF 2016, 10-12 February 2016, Paço de Arcos, Portugal Thermo-mechanical modeling of a high pressure turbine blade of an airplane gas turbine engine P. Brandão a , V. Infante b , A.M. Deus c * a Department of Mechanical Engineering, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais, 1, 1049-001 Lisboa, Portugal b IDMEC, Department of Mechanical Engineering, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais, 1, 1049-001 Lisboa, Portugal c CeFEMA, Department of Mechanical Engineering, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais, 1, 1049-001 Lisboa, Portugal Abstract During their operation, modern aircraft engine components are subjected to increasingly demanding operating conditions, especially the high pressure turbine (HPT) blades. Such conditions cause these parts to undergo different types of time-dependent degradation, one of which is creep. A model using the finite element method (FEM) was developed, in order to be able to predict the creep behaviour of HPT blades. Flight data records (FDR) for a specific aircraft, provided by a commercial aviation company, were used to obtain thermal and mechanical data for three different flight cycles. In order to create the 3D model needed for the FEM analysis, a HPT blade scrap was scanned, and its chemical composition and material properties were obtained. The data that was gathered was fed into the FEM model and different simulations were run, first with a simplified 3D rectangular block shape, in order to better establish the model, and then with the real 3D mesh obtained from the blade scrap. The overall expected behaviour in terms of displacement was observed, in particular at the trailing edge of the blade. Therefore such a model can be useful in the goal of predicting turbine blade life, given a set of FDR data. Copyright © 2017 The Authors. ublishe by E sevier B.V. Peer-review und responsibility of the MCM 2017 organizers. XXVII International Conference “Mathematical and Computer Simulations in Mechanics of Solids and Structures”. Fundamentals of Static and Dynamic Fracture (MCM 2017) A Bayesian approach for controlling structural displacements Maria Grazia D’Urso a, *, Antonella Gargiulo a , Salvatore Sessa b a DICeM – Department of Civil and Mechanical Engineering, Università degli Studi di Cassino e del Lazio Meridionale, Via G. Di Biasio 43, 03043, Cassino (RM), Italy b Department of Structures for Engineering and Architecture, University of Naples Federico II, Via Claudio 21, 80125 Napoli, Italy Abstract Bayesian Networks represent one of the most powerful and effective tools for knowledge acquisition in the observation of physical phenomena affected by randomness a d uncertainties. The methodology is the result of several developments concerning the Bayesian statistical theory and permits, by inference, to update the statistics describing physical variables by the observation of experimental evidences. In general, Bayesian Networks have become a very popular and versatile approach in problem solving strategies because of their capability in enhancing the status of knowledge of a physical problem domain and to characterize expected outcomes. In particular, this work presents a strategy performing the Bayesian updating of the mechanical and geometrical properties of a steel structure. Based on high-precision topographical measurements, such a strategy has the purpose of accurately estimating the structural displacements expected during the structural life-cycle. © 2017 The Authors. Published by Elsevier B.V. Peer-review under responsibility of the MCM 2017 organizers. Keywords: Bayesian Network; displacements; conditional probability; probabilistic inference observation; error model. 1. Introduction Monitoring of displacem nts, deflections and ground settlements of civil infrastructures can be performed by periodically performing topographical surveys detecting the coordinates and mutual locations of a set of control XXVII International Conference “Mathematical and Computer Simulations in echanics of Solids and Structures”. Fundamentals of Static and Dynamic Fracture (MCM 2017) A Bayesian approach for controlling structural displacements Maria Grazia D’Urso a, *, Ant nella Gargiulo a , Salvatore Sessa b a DICeM – Department of Civil and Mechanical Engineering, Univer tà degli Studi di Cassino e del Lazio Meridionale, Via G. Di Biasio 43, 03043, Cass no (RM), It ly b Department of Structures for Engineering and Architecture, University of Naples Federico II, Via Claudio 21, 80125 Napoli, Italy Abstract Bayesian N tworks repr sent one of the most powerful and effective tools for knowledge acquisiti n in the observation of physical phenomena ffected by random ess and uncertainties. The me hodology is th result of several developments concerning the Bayesian st tistical th ory and permits, by inference, to update the statistics describing physical vari bles by the observation of experimental evid nces. In general, Bay sian Network have become a v ry popular nd versatile appro ch in problem solving strategies because of their capability in enhancing the status of knowledg of a physical problem do ain d to characterize expected outcomes. In partic lar, this work presents a strategy performing the Bayesian updating of he mec nical and geometri al properties of a st el structure. Based o high-precision topographi al measurements, such a strategy has the purpose of accurately estimating the structural displacements expected during the structural life-cycle. © 2017 The Autho s. Publ shed by Elsevier B.V. Peer-review under responsibility of the MCM 2017 organizers. Keywords: Bayesian Network; displacements; conditional probability; probabilistic inference observation; error model. 1. Introduction Monitoring of displacements, defle tions an grou d settlements of civil infrastructures can be performed by periodically performing topographical surveys detecting the coordinates and mutual locations of a set of control © 2016 The Authors. Published by Elsevier B.V. Peer-review under responsibility of the Scientific Committee of PCF 2016.

Keywords: High Pressure Turbine Blade; Creep; Finite Element Method; 3D Model; Simulation.

* Corresponding author. Tel.: +39-0776-299-4309. E-mail address: durso@unicas.it * Correspon ing author. Tel.: +39-0776-299-4309. E-mail address: durso@unicas.it

* Corresponding author. Tel.: +351 218419991. E-mail address: amd@tecnico.ulisboa.pt 2452 3216 © 2017 Th Authors. Published by Elsevier B.V. Peer-review under responsibility of the MCM 2017 organizers. 2452-3216 © 2017 The Authors. Published by Elsevier B.V. Peer-review under responsibility of the MCM 2017 organizers.

2452-3216 Copyright  2017 The Authors. Published by Elsevier B.V. Peer-review under responsibility of the MCM 2017 organizers. 10.1016/j.prostr.2017.11.011

Maria Grazia D’Urso et al. / Procedia Structural Integrity 6 (2017) 69–76 Author name / Structural Integrity Procedia 00 (2017) 000 – 000

70 2

points. Moreover, the interpretation of survey measurements is usually performed by adopting statistical strategies in order to account for instrumental errors and estimating confidence intervals of the results. An appealing benefit of Bayesian Networks is their capability in accounting for a priori statistical characterization of the structural parameters which is updated by survey observations and, subsequently, can predict future structural responses. In this sense, differently from traditional statistical approaches, Bayesian updating can forecast anomalous behaviors before their occurrencies. In fact, it is well known that the accuracy of survey results obtained by least squares approaches is significantly influenced by the adopted stochastic model. On the contrary, use of the Bayesian approach requires far less observations to get a desired accuracy of the displacement measurement. Bayesian Networks, implemented in conjunction with Markov Chains and Monte Carlo Simulations, permit to determine an efficient relationship between the prior knowledge of the structural model and the survey observations. In this respect, an effective and accurate characterization of the prior statistics of the structural domain represents an essential aspect of the identification process, especially in presence of limited observations or when their detection involves expensive activities, since it permits to forecast structural responses, although with limited confidence, even in absence of experimental evidences. The application of Bayesian updating to structural models concerns mainly two different aspects: parameter learning is focused on the characterization of the marginal probabilities of the adopted structural parameters while structure learning concerns the relationships between different parameters and their conditional probabilities. Both these tasks are performed in machine learning methodologies in which optimization algorithms, analyzing experimental outcomes, determine the mutual dependency of parameters and responses. Moreover, observations permit to update the prior statistics of the structural parameters by an inference process. Finally, the updated parameters can be used to forecast future structural responses by performing reliability analysis algorithms. The present research analyzes the outcomes of a structural survey of a steel truss vault in order to characterize its constitutive parameters and to detect possible anomalies. In particular, the vertical displacements of the structural nodes have been detected by a total station; subsequently, the recorded data have been interpreted by a Bayesian network characterizing the relationships between displacements and mechanical parameters. It is worth to be emphasized that the inference procedure accounts for the whole set of observed displacements and their correlation so that parameters’ updating assumes the capabilities of a multi -objective identification process.

Fig. 1.(a) Example of Bayesian Network nodes and connections; (b) Case-study: a steel truss barrel vault.

2. Probabilistic Inference updating

Bayesian Networks are defined by means of random variables (nodes) mutually connected, see, e.g., Fig. 1(a). Variables not depending upon different nodes (namely parent variables) are characterized by marginal Probability Density Functions (PDFs) while variables influenced by different nodes of the network (defined as child variables) are characterized by PDFs conditioned by the value of their parents. Use of conditional probability to establish co nnections between parent and child nodes is particularly feasible to represent the modularity of random systems constituted by redundant components; moreover, implemented frameworks available in the literature that perform

Maria Grazia D’Urso et al. / Procedia Structural Integrity 6 (2017) 69–76 Author name / Structural Integrity Procedia 00 (2017) 000 – 000

both parameters and structure learning and graphically represent variables and connections, make their use particularly intuitive in common practice. Observation of experimental data permits to set the actual value of some variables, defined as evidences , for which a deterministic characterization is assumed. Purpose of the Bayesian Network consists in assessing, by statistical inference, the updated , or posterior, probabilistic distributions of the remaining nodes representing the global statistical characterization of an event or scenario . In brief, probabilistic inference, representing the pivotal phase of the machine learning process, determines the probability distributions P[X i |E] of the random variable X i for an observed event E which characterize the probabilistic behavior of the analyzed system. To fix ideas, starting from the nodes set as evidences, conditioned probability distributions are updated by inference, intuitively performed by the application of the Bayes’ Theorem, so that the evidence propagates among the network , as shown in Casaca et al. (2008) and Straub (2010). Conditional probabilities have been defined by assuming discrete descriptions of the random variables by Conditional Probability Tables (CPT). Bayesian inference updating consists in computing, by means of optimization algorithms, the posterior values of the CPT, and subsequently the discrete probability distribution of each node, relevant to one or more evidences introduced in the network. Computations have been performed by the freeware Genie which provides an exhaustive framework for Bayesian Network analysis.

Fig. 2. (a) Workflow of a topographical survey session; (b) workflow of the Bayesian Updating procedure

3. The case-study Bayesian Network

The case-study analyzed in this research consists in a steel truss barrel vault, shown in Figure 1(b), which was monitored during its construction phases by two topographical surveys, detecting the structural displacements, performed on February 28 th and March 22 nd 2015, respectively. The survey campaign aimed to detect possible anomalous behaviors. In particular, while classical procedures for the statistical assessment of survey data analyse the evolving values of displacements and can identify anomalously large values only after that they have occurred, the Bayesian updating workflow, reported in Figure 2(a), is capable of interpreting the values-in-time of the responses, update the statistics of the structural parameters and forecast the expected maximum values of the response which are compared with the values determined by the structural design. It is worth to be emphasized that the updated statistics of the network variables is highly influenced by the definition of the assumed prior distributions which, subsequently, must be properly computed by simulations consistent with the physical behaviour of the model. Main phases of the procedure for the Bayesian Network characterization and of the parameters updating are reported in Figure 2(b).

4. Geometrical scheme of the survey net

The monitored sail-shaped vault consists in a net of steel columns and beams and presents a 40x50 m rectangular plan. Main beams consist in 9 frames made of square-piped elements and vertical molded plate columns and are connected by pin joints to 13 secondary beams presenting square cross sections.

Maria Grazia D’Urso et al. / Procedia Structural Integrity 6 (2017) 69–76 Author name / Structural Integrity Procedia 00 (2017) 000 – 000

Fig. 3. (a) Axonometric representation of the net adopted in the topographical survey; (b) Joint targets monitored by the topographical survey.

Fig. 4. Monitored points included in the Bayesian Network.

Surveys have been performed at the end of the steel frames realization in order to control the displacements generated by the dead loads and investigate the correct installation of the structural elements. To this end, the monitored joints, whose numbering is shown in Figure 3(a), have been equipped with 94 targets, shown in Figure 3(b), so that measurements concern the mutual distances between consecutive targets, azimuthal and zenithal angles. In order to reduce the computational effort of the updating procedure, the responses included in the Bayesian network, shown by red bullets in Figure 4, are relevant to 14 joints located on the vault boundary and 4 nodes located at the top beams. Measurements have been performed by using a high precision total station type Leica TPR 30 equipped with innovative optical and digital technologies. Table 1 shows the detected relative vertical altitudes Δz mar . and Δz feb , measured in the February 2015 and March 2015 survey sessions, respectively, and the relative vertical displacements Δu computed as Δu= Δz mar .- Δz feb . 5. Structure of the Bayesian Network The Bayesian Network used in this research has been defined by prior PDFs of the structural parameters of interest and by conditional PDFs between those parameters and the esteemed responses. A schematized representation of the adopted network is reported in Figure 5(a). It is worth to be emphasized that some variables of interest, which are described below, are directly involved in the updating procedure as evidences or target parameters. Different parameters, although included in the computational definition of the network, are not represented for brevity. To illustrate the physical meaning of all the involved random variables, the network nodes are arranged by different typologies. In particular, the parent variables are: 1. Structural parameters : represented in black, consist in the parameters characterizing the structural model, such as the Young’s modulus, see, e.g., Fig. 6(a), loads, joint performance coefficients etc.

Maria Grazia D’Urso et al. / Procedia Structural Integrity 6 (2017) 69–76 Author name / Structural Integrity Procedia 00 (2017) 000 – 000

2. Model error ε fem : represented in light blue, it models the inaccuracies related to the finite element model. The node has unitary-mean Gaussian distribution, shown in Fig. 6(b), with coefficient of variation (c.o.v.) of 30%. Survey measurement error ε l : represented in violet, it is related to the instrumental error of the survey sessions. It is characterized by a unitary-mean Gaussian distribution, shown in Fig. 6(c), with 5% c.o.v. Child variables can be summarized as: 1. Theoretical displacements u fem,i : represented in blue, consists in the absolute displacements of the monitored nodes computed by a finite element analysis. Progressive index i denotes the node of the survey net for which the displacement is computed. 2. Real displacements u i : reported in red, denote the real, physical displacement of each node. Their outcomes are esteemed as u i = u fem,i ε fem . 3. Detected relative displacements  ij : represented in green will be adopted as evidences of the network. Such quantities represent the relative displacement detected between two consecutive nodes corrected by the instrumental error:  ij = (u i – u j ) ε l . In conclusion, the model is made of 53 nodes, related by 59 dependencies. The probability distributions of all the random variables have been discretized in order to implement and analyze the network by Genie 2.0, a freeware framework for scientific research purposes. A part of the network implemented in Genie is shown in Figure 5(b) in which parent variables are represented in violet, child nodes are depicted in light blue and dependencies are represented as arrows.

Table 1. Target nodes vertical displacements and altitudes.

Some parent nodes PDFs are represented in, 6(b) and 6(c). Probabilistic dependencies, numerically defined by conditional PDFs, characterize the likelihood that a child variable assumes a specific value as function of all possible states of its parent variables. Such a dependency has been determined by theoretical considerations, simplified models available in the literature and a Finite Element-based Monte Carlo simulation. Since the software needs the definition of a finite number of variable states, PDFs have been suitably discretized. The generation of the conditional PDFs of the child variables has been performed by the following steps: 1. Random generation of m occurrences of the parent variables; 2. Computation of m corresponding finite element responses; 3. Computation of the absolute displacement occurrences by applying the model error; 4. Determination of the relative displacements occurrences by combining absolute displacements and survey error;

Maria Grazia D’Urso et al. / Procedia Structural Integrity 6 (2017) 69–76 Author name / Structural Integrity Procedia 00 (2017) 000 – 000

74 6

5. Definition of n intervals (states) for each variable; 6. Determination of the conditional PDFs by statistical analysis of the generated occurrences performed by an ad-hoc algorithm implemented in Matlab. Obviously, the occurrences of the finite element displacements depend on the realizations of the structural parameters generated by the Monte Carlo procedure. It is worth to be emphasized that, because of the Markov hypothesis, conditional probabilities of each child variable depend exclusively on the state of their directly connected parent variables. Two examples of the PDF entries relevant to the U fem,i and U i displacements, discretized as matrices, are reported in Figures 7 and 8. Note that each variable depends on the states of the corresponding parent nodes so that the FEM displacements depends on the outcome of the Young’s modulus while displacement U i , in Fig. 8, depends on the states of U fem,i and ε fem .

Fig. 5. (a) Scheme of the adopted Bayesian Network; (b) Outline of the Bayesian Network modeled in Genie 2.0.

Fig. 6. (a) Young’s modulus PDF; (b) FEM error PDF; (c) Survey error PDF.

6. Discussion of the Bayesian Updating results Bayesian updating of the node PDFs can be performed as the values of variables D ij are set, as evidence, equal to the survey measurements. Subsequently, the software computes by inference the posterior PDFs of each node. The quantities of interest for this survey are the real displacements U i whose updated PDFs represent the probability distributions of the real displacements attained by the structure. Expected values of the displacement of each monitored node are reported in Figure 9(a) where anomalously high values are boxed in red and represented as red bullets in Figure 9(b). In particular, nodes belonging to the top beam (n. 21) and to the edge beam (n. 48 and 50) are expected to attain at displacement greater than one centimetre with probability values of, respectively, 46.3%,

Maria Grazia D’Urso et al. / Procedia Structural Integrity 6 (2017) 69–76 Author name / Structural Integrity Procedia 00 (2017) 000 – 000

75 7

64% and 65.6%. The latter two nodes are located on a doubled beam in proximity of some joints with columns and the high associated probability indicates a high risk that the region nearby such nodes can present significant damage. It is worth to be emphasized that a structural inspection, subsequent to the survey, has proved that some connections located nearby the two anomalous nodes were affected by manufacturing defects.

Fig. 7. Conditional PDF values of a displacement U fem,i .

Fig. 8. Conditional PDF values of a displacement U i .

Fig. 9. (a) Expected values of the structural displacements; (b) Nodes with anomalous displacements.

7. Conclusions A Bayesian Network conceived for the survey of a steel vault, aiming to update the structural parameters and forecast expected displacements and anomalous behaviours, has been presented. This was motivated by the fact that even the rough analysis of a preliminary survey, when the structure was subject to its self-weight only, indicated unexpectedly large displacements at the top of the vault and nearby the edge beam. Eventually, the Bayesian updating analysis described in this research confirmed such an anomalous behaviour which was caused by handcrafting defects of some steel joints between beam and column elements. The main advantage of the proposed network consists in the fact that the updating analysis forecasts expected values of the displacements (namely displacements of nodes 21, 48 and 50, all resulting about 1.22 cm), which can

Maria Grazia D’Urso et al. / Procedia Structural Integrity 6 (2017) 69–76 Author name / Structural Integrity Procedia 00 (2017) 000 – 000

76 8

be compared with the corresponding design values, before that they actually occur inducing significant damage. Moreover, the computed expected values are characterized by a probability distribution which determines the likelihood of the outcomes and the confidence of the results. Despite of their efficiency, Bayesian Networks often present a strong mutual dependency of the considered variables resulting in significant computational effort. Moreover, such a demand increment tends to sensibly increase as the set of variables of the model is enriched in order to characterize more accurate responses. For this reason, future work will investigate alternative strategies such as algorithms based on the likelihood principle or, especially, strategies focused on different formulation of the network dependencies in order to reduce the mutual dependencies and to obtain almost-Markovian structures. Nevertheless, Bayesian Networks represent a very effective approach defining a reliable computational tool, although its efficiency depends on suitable updating procedures of the statistical characterization, which results particularly suitable for multidisciplinary activities and for data exchange with different technologies such as spatio temporal GIS systems. Acknowledgments Financial support from the Italian Ministry of Education, University and Research (MIUR) in the framework of the Project PRIN code 2015HJLS7E – is gratefully acknowledged. Bensi M., Der Kiureghian A., Straub D. - Bayesian network modeling of correlated random variables drawn from a Gaussian random field - Structural Safety, 2011. Cárdenas I.C., Al-jibouri S.S., Halman J.I. – A Bayesian Belief Networks Approach to Risk Control in Construction Projects – University of Twente, The Netherlands, 2012. Casaca J., Mateus P., Coelho J. – Bayesian Estimation in Dam Monitoring Networks – 4th IAG Symposium on Geodesy for Geotechnical and Structural Engineering, Lisbon 2008. Chizhova M., Korovin D., Gurianov A., Brodovskii M., Brunn A., Stilla U., Luhmann T. – Probabilistic reconstruction of the orthodox churches from precision point clouds using Bayesian network and cellular automata – The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Volume XLII-2/W3, 2017 - 3D Virtual Reconstruction and Visualization of Complex Architectures, Nafplio, Greece, 1 – 3 March 2017. D’Urso M.G., Russo P., Sessa S. – Sull’impiego del monitoraggio geomatico per la stima dei parametri nei modelli di calcolo degli spostamenti strutturali – Atti della 16a Conferenza Nazionale ASITA, Vicenza, vol. I, 523-530, 2012. Growe S., Schroder T., Liedtke C.-E. – Use of Bayesian networks as judgement calculus in a knowledge based image interpretation system – International Archives of Photogrammetry and Remote Sensing, Vol. XXXIII, Part B3 – Amsterdam 2000. Horney M. – Bayesian Networks – Technical Report n. 5 – Boston University – 2014 Jensen F.V., Nielsen T.D. – Bayesian Networks and Decision Graphs second edition – Springer Science + Business Media LLC, 2007 - ISBN-10: 0-387-68281-3 Niculita O., Skaf Z., Jennions I.K. - The Application of Bayesian Change Point Detection in UAV Fuel Systems – ScienceDirect, Procedia CIRP 22, 115-121, 2014. Russell S.J., Norvig P. - Artificial intelligence: a modern approach. 2nd edition, Prentice-Hall, Englewood Cliffs, N.J., 2003. Sansò F., De Lacy M.C. – The Bayesian Approach Applied to Significant Deformation Identification - Geodetic Deformation Monitoring From Geophysical to Engineering Roles, Springer – International Association of Geodesy Symposia Vol. 131,19-29 – March 17-19, 2005. Sessa S., D’Urso M.G. - Employment of Bayesian networks for risk assessment of excavation processes in dense urban areas - Safety, Reliability, Risk and Life-Cycle Performance of Structures & Infrastructures - Eds: Deodatis, Ellingwood & Frangopol, 2013 Taylor & Francis Group, London, ISBN 978-1-138-00086-5; 3163-3169 Straub D. – Part I Bayesian Networks – Lecture Notes on Engineering Risk Analysis - Technische Universität München, Summer schools, 2010. Straub D. – Part J Modeling with Bayesian Networks – Lecture Notes on Engineering Risk Analysis - Technische Universität München, Summer schools, 2010. Tanir E., Felsenstein K., Yalcinkaya M. – Using Bayesian methods for the parameter estimation of deformation monitoring networks – Natural Hazards and Earth System Sciences, 8, 335-347, 2008. Yu Xin,Wen Zongyong, Zhu Zhaorong, Xia Qiang, Shun Lan – Remote sensing image classification applied to the first national geographical information census of China – The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Volume XLI-B7, 2016 - XXIII ISPRS Congress, Prague, Czech Republic 12 – 19 July 2016. Zhu J., Santerre R., Chang X.W. – A Bayesian method for linear, inequality – constrained adjustment and its application to GPS positioning – Journal of Geodesy 78, 528-534, Springer-Verlag, 2005 DOI 10.1007/s00190-004-0425-y. References

ScienceDirect Available online at www.sciencedirect.com Av ilable o line at ww.sciencedire t.com ScienceDirect Structural Integrity Procedia 00 (2016) 000 – 000 Procedia Structu al Integrity 6 (2017) 236–243 Available online at www.sciencedirect.com Structural Integrity Procedia 00 (2017) 000–000 Available online at www.sciencedirect.com Structural Integrity Procedia 0 (2017) 0– 0

www.elsevier.com/locate/procedia www.elsevier.com / locate / procedia www.elsevier.com / locate / procedia

XV Portuguese Conference on Fracture, PCF 2016, 10-12 February 2016, Paço de Arcos, Portugal Thermo-mechanical modeling of a high pressure turbine blade of an airplane gas turbine engine P. Brandão a , V. Infante b , A.M. Deus c * a Department of Mechanical Engineering, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais, 1, 1049-001 Lisboa, Portugal b IDMEC, Department of Mechanical Engineering, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais, 1, 1049-001 Lisboa, Portugal c CeFEMA, Department of Mechanical Engineering, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais, 1, 1049-001 Lisboa, Portugal Abstract During their operation, modern aircraft engine components are subjected to increasingly demanding operating conditions, especially the high pressure turbine (HPT) blades. Such conditions cause these parts to undergo different types of time-dependent degradation, one of which is creep. A model using the finite element method (FEM) was developed, in order to be able to predict the creep behaviour of HPT blades. Flight data records (FDR) for a specific aircraft, provided by a commercial aviation company, were used to obtain thermal and mechanical data for three different flight cycles. In order to create the 3D model needed for the FEM analysis, a HPT blade scrap was scanned, and its chemical composition and material properties were obtained. The data that was gathered was fed into the FEM model and different simulations were run, first with a simplified 3D rectangular block shape, in order to better establish the model, and then with the real 3D mesh obtained from the blade scrap. The overall expected behaviour in terms of displacement was observed, in particular at the trailing edge of the blade. Therefore such a model can be useful in the goal of predicting turbine blade life, given a set of FDR data. Copyright © 2017 The Authors. Published by Elsevier B.V. Peer-review under responsibility of the MCM 2017 organizers. XXVII International Conference “Mathematical and Computer Simulations in Mechanics of Solids and Structures”. Fundamentals of Static and Dynamic Fracture (MCM 2017) Analytical solution of elastic fields induced by a 2D inclusion of arbitrary polygonal shape Giulio Zuccaro a,b, ∗ , Salvatore Trotta a , Salvatore Sessa a , Francesco Marmo a , Luciano Rosati a,b a University of Naples Federico II, Department of Structures for Engineering and Architecture, Via Claudio 21, 80125 Naples, Italy b LUPT-PLINIVS Study Centre, Via Toledo 402, 80134 Naples, Italy Abstract We generalize a recent application of the equivalent inclusion method, Jin et al. (2011), to derive the elastic field induced by a constant eigenstrain applied to an elliptic inclusion whose boundary is approximated by a polygon, the number of sides being assigned so as to recover the analytical values of the entries of the Eshelby tensor. The generalization consists in the fact that displacements, strains, stresses and the Eshelby tensor can be given a unique expression, holding inside and outside the inclusion, thus avoiding the recourse to the derivation of distinct expressions, based upon di ff erent approaches, for the elastic fields. The proposed approach has been successfully applied to evaluate the elastic fields induced by an elliptical cavity in a linear isotropic infinite plate subjected to a remote loading by recovering the cla sical olutions by Inglis (1913) and Maugis (1992). Furthermore it can easily be applied to elliptical holes arbitrarily oriented with respect to t loading direction. c 2017 The Authors. Published by Elsevier B.V. r-review under responsibility of the CM 2017 organizers. Keywords: Nano-struc ures, Micro-m chanics, Inhomogeneity, shelby tensor, Equ valent inclusion method. XXVII International Conference “Mathematical and Computer Simulations in Mechanics of Solids and Structures”. Fundamentals of Static and Dynamic Fracture (MCM 2017) nalytical solution of elastic fields induced by a 2D inclusion of arbitrary polygonal shape Giulio Zuccaro a,b, ∗ , Salvatore Trotta a , Salvatore Sessa a , Francesco Marmo a , Luciano Rosati a,b a University of Naples Federico II, Department of Structures for Engineering and Architecture, Via Claudio 21, 80125 Naples, Italy b LUPT-PLINIVS Study Centre, Via Toledo 402, 80134 Naples, Italy Abstract We generalize a recent application of the equivalent inclusion method, Jin et al. (2011), to derive the elastic field induced by a constant eigenstrain applied to an elliptic inclusion whose boundary is approximated by a polygon, the number of sides being assigned so as to recover the analytical values of the entries of the Eshelby tensor. The generalization consists in the fact that displacements, strains, stresses and the Eshelby tensor can be given a unique expression, holding inside and outside the inclusion, thus avoiding the recourse to the derivation of distinct expressions, based upon di ff erent approaches, for the elastic fields. The proposed approach has been successfully applied to evaluate the elastic fields induced by an elliptical cavity in a linear isotropic infinite plate subjected to a remote loading by recovering the classical solutions by Inglis (1913) and Maugis (1992). Furthermore it can easily be applied to elliptical holes arbitrarily oriented with respect to the loading direction. c 2017 The Author . Published by Elsevier B.V. Peer-review und r responsibility of the MCM 2017 organizers. Keywords: Nano-structures, Micro-mechanics, Inhomogeneity, Eshelby tensor, Equivalent inclusion method. Keywords: High Pressure Turbine Blade; Creep; Finite Element Method; 3D Model; Simulation. In a celebrated pap r on the ellipsoidal inclusion, Eshelby (1957) considered an infinitely extended elastic medium containing an ellipsoidal subdomain subjected to a uniformly distributed stress-free transformation strain and proved that the resulting total strains and stresses inside the ellipsoidal inclusion were also uniform. The question of determining elastic fields outside an inclusion was addressed in a subsequent paper Eshelby (1959) in which Eshelby pointed out that the solution for the exterior elastic fields was more complicated and the correspond ing formulation tedious. In particular Eshelby pointed out that the displacements were continuous across the boundary of the inclusion while strain, stresses and the so-called Eshelby tensor were not. In a celebrated paper on the ellipsoidal inclusion, Eshelby (1957) considered an infinitely extended elastic medium containing an ellipsoidal subdomain subjected to a uniformly distributed stress-free transformation strain and proved that the resulting total strains and stresses inside the ellipsoidal inclusion were also uniform. The question of determining elastic fields outside an inclusion was addressed in a subsequent paper Eshelby (1959) in which Eshelby pointed out that the solution for the exterior elastic fields was more complicated and the correspond ing formulation tedious. In particular Eshelby pointed out that the displacements were continuous across the boundary of the inclusion while strain, stresses and the so-called Eshelby tensor were not. © 2016 The Authors. Published by Elsevier B.V. Peer-review under responsibility of the Scientific Committee of PCF 2016. 1. Introduction 1. Introduction

* Corresponding author. Tel.: +351 218419991. E-mail address: amd@tecnico.ulisboa.pt ∗ Corresponding author. Tel.: + 39-081-253-8925. E-mail address: zuccaro@unina.it ∗ Corresponding author. Tel.: + 39-081-253-8925. E-mail address: zuccaro@unina.it

2452-3216 © 2016 The Authors. Published by Elsevier B.V. Peer-review under responsibility of the Scientific Committee of PCF 2016. 2210-7843 c 2017 The Authors. Published by Elsevier B.V. Peer-review under responsibility of the MCM 2017 organizers. 2210-7843 c 2017 The Author . Published by Elsevier B.V. Peer-review under responsibility of the MCM 2017 organizers. 2452-3216 Copyright  2017 The Authors. Published by Elsevier B.V. Peer-review under responsibility of the MCM 2017 organizers. 10.1016/j.prostr.2017.11.036

Giulio Zuccaro et al. / Procedia Structural Integrity 6 (2017) 236–243 Author name / Structural Integrity Procedia 00 (2017) 000–000

237

Subsequently Mura (1982) coined the alternative terminology “eigenstrain” to represent a broad range of inelastic strains such as thermal strains, plastic strains, phase transformation, and misfit strains. According to Eshelby (1957) and Mura (1982), the subdomain containing the eigenstrain is called an inclusion to distinguish it from the term inhomogeneity which refers to a subdomain with a di ff erent material. As it is well known the Eshelby inclusion model and the related solutions represent the cornerstone of modern micromechanics thanks to which several advancements have been achieved in modern science and technology, Li and Wang (2008). To actually compute the elastic fields inside and outside the inclusion Eshelby evaluated the analytical expression of two potentials, namely an harmonic and a biharmonic one. This was possible only for inclusions of ellipsoidal (elliptical) shape though the expressions of the potentials were sensibly di ff erent inside and outside the inclusion. Although there have been extensive studies Zhou et al. (2013) related to the Eshelby inclusions, closed-form solu tions exist only for a limited number of cases, even for the two-dimensional (2D) inclusion in plane elasticity. Chiu (1980) obtained closed form solution of stress field in an elastic layer caused by a rectangular inclusion subjected to a uniform eigenstrain. Nozaki and Taya (2001) presented an exact solution to the stress field produced by a polygonal inclusion with uniform eigenstrain. Based on the complex variable method, Muskhelishvili (1953), Ru (1999) derived analytic solutions for an inclusion in a plane or half-plane while extensive references to the case of 3D inclusions can be found in Rodin (1996), Huang et al. (2011), Zhou et al. (2013), Trotta et al. (2017b). Two recent approaches to the evaluation of the Eshelby tensor and of the fields induced by a constant eigenstrain have been proposed in Trotta et al. (2016, 2017a) for the 2D case, and in Trotta et al. (2017b), for the 3D case. Remarkably all quantities of interest are obtained as algebraic sums whose scalar coe ffi cients depend upon the position vectors defining the polygonal (polyhedral) approximation of the inclusion boundary. In particular, displacements, strains, stresses and the Eshelby tensor are given by a unique expression inside and outside the inclusion, though recovering the correct jumps across its boundary, so that the derivation of distinct formu las for the elastic fields by di ff erent approaches exploited inside and outside the inclusion, can be completely avoided. This is in contrast with the previous contributions on the topic (see, e.g., Mura (1982), Ju and Sun (1999), Kim and Lee (2010), Jin et al. (2011), Jin et al. (2014), Jin et al. (2016) and Jin et al. (2017)). In particular, Jin et al. (2011) extended the analytical formulation developed in Ju and Sun (1999) and derived a novel expression of the Eshelby tensor correcting a previous one contributed in Kim and Lee (2010). The novel expression has been applied in Jin et al. (2014) to elegantly solve a classical problem in elasticity, namely stress concentration around elliptical holes in an infinite isotropic elastic plane, by the equivalent inclusion method. Subsequently, Jin et al. (2016) have developed explicit analytical solutions for displacements, displacement gra dients, strains and stresses, for both the interior and exterior fields, of an ellipsoidal inclusion. The specialization of their findings to plane strain has been reported in Jin et al. (2017) with reference to the elastic fields produced by a 2D elliptic cylindrical inclusion in a full plane with uniform eigenstrains. On the contrary we show that the same solution can be obtained by our formulation once the boundary of the elliptical inclusion has been approximated by a polygon having a number of sides, to be determined numerically, able to guarantee that the “numerical” Eshelby tensor does coincide with the exact one. Besides being more compact and recovering the classical solutions by Inglis (1913) and Maugis (1992), as in the quoted papers by Jin et al., the proposed approach can be successfully exploited to evaluate the elastic fields for problems in which the elliptical cavity is arbitrarily oriented with respect to non-uniform remote loadings. Let us consider an infinite, homogeneous and isotropic matrix containing an infinetely long cylindrical inclusion with uniform eigenstrain ε ∗ . We adopt a Cartesian reference frame of origin O and axis x 1 , x 2 orthogonal to the axis of the inclusion, see, e.g., Fig. 1 in Trotta et al. (2017a). We further denote by Ω the intersection of the cylindrical inclusion with the x 1 , x 2 plane and we assume that Ω has an arbitrary polygonal shape. The Eshelby tensor S is defined as the fourth-order tensor providing the strain tensor ε at an arbitrary poin P of the elastic medium through the relation ε ( ρ ) = S ε ∗ ( ρ ). In particular the Eshelby tensor is known to be constant if and only if the inclusion has an elliptical shape. Hence, under this assumption the elastic strain induced by ε ∗ is constant within the inclusion and depends upon the generic point within the host material (matrix) since the same happens for the Eshelby tensor 2. The displacement field and the Eshelby tensor for polygonal inclusions

Page 2 Page 3 Page 4 Page 5 Page 6 Page 7 Page 8 Page 9 Page 10 Page 11 Page 12 Page 13 Page 14 Page 15 Page 16 Page 17 Page 18 Page 19 Page 20 Page 21 Page 22 Page 23 Page 24 Page 25 Page 26 Page 27 Page 28 Page 29 Page 30 Page 31 Page 32 Page 33 Page 34 Page 35 Page 36 Page 37 Page 38 Page 39 Page 40 Page 41 Page 42 Page 43 Page 44 Page 45 Page 46 Page 47 Page 48 Page 49 Page 50 Page 51 Page 52 Page 53 Page 54 Page 55 Page 56 Page 57 Page 58 Page 59 Page 60 Page 61 Page 62 Page 63 Page 64 Page 65 Page 66 Page 67 Page 68 Page 69 Page 70 Page 71 Page 72 Page 73 Page 74 Page 75 Page 76 Page 77 Page 78 Page 79 Page 80 Page 81 Page 82 Page 83 Page 84 Page 85 Page 86 Page 87 Page 88 Page 89 Page 90 Page 91 Page 92 Page 93 Page 94 Page 95 Page 96 Page 97 Page 98 Page 99 Page 100 Page 101 Page 102 Page 103 Page 104 Page 105 Page 106 Page 107 Page 108 Page 109 Page 110 Page 111 Page 112 Page 113 Page 114 Page 115 Page 116 Page 117 Page 118 Page 119 Page 120 Page 121 Page 122 Page 123 Page 124 Page 125 Page 126 Page 127 Page 128 Page 129 Page 130 Page 131 Page 132 Page 133 Page 134 Page 135 Page 136 Page 137 Page 138 Page 139 Page 140 Page 141 Page 142 Page 143 Page 144 Page 145 Page 146 Page 147 Page 148 Page 149 Page 150 Page 151 Page 152 Page 153 Page 154 Page 155 Page 156 Page 157 Page 158 Page 159 Page 160 Page 161 Page 162 Page 163 Page 164 Page 165 Page 166 Page 167 Page 168 Page 169 Page 170 Page 171 Page 172 Page 173 Page 174 Page 175 Page 176 Page 177 Page 178 Page 179 Page 180 Page 181 Page 182 Page 183 Page 184 Page 185 Page 186 Page 187 Page 188 Page 189 Page 190 Page 191 Page 192 Page 193 Page 194 Page 195 Page 196 Page 197 Page 198 Page 199 Page 200

Made with FlippingBook. PDF to flipbook with ease