Edit Profile (opens in new tab) Elishakoff, Isaac Compute Distance To: Compute Author ID: elishakoff.isaac Published as: Elishakoff, Isaac; Elishakoff, I.; Elishakoff, I. B.; Elishakoff, Issac; Elishakov, I. B.; Elishakov, I. more...less External Links: Wikidata · Google Scholar · ResearchGate · dblp · GND · IdRef · theses.fr Documents Indexed: 233 Publications since 1973, including 9 Books 13 Contributions as Editor · 1 Further Contribution Biographic References: 1 Publication Co-Authors: 143 Co-Authors with 189 Joint Publications 1,889 Co-Co-Authors all top 5 Co-Authors 46 single-authored 13 Starnes, James H. jun. 11 Ren, Yongjian 10 Challamel, Noël 10 Li, Yiwei 9 Shinozuka, Masanobu 8 Qiu, Zhiping 6 Ruta, Giuseppe Claudio 5 Caliò, Ivo 5 Falsone, Giovanni 5 Impollonia, Nicola 5 Pentaras, Demetris 4 Becquet, Roland 4 Cederbaum, Gabriel 4 Fang, Jianjie 4 Guédé, Zakoua 4 Hache, Florian 4 Stavsky, Yehuda 4 Wang, Chien-Ming 4 Zhu, Liping 4 Zingales, Massimiliano 3 Arbocz, Johann 3 Baruch, Menahem 3 Gentilini, Cristina 3 Livshits, David 3 Muscolino, Giuseppe 3 Sternberg, Alexander 3 Wang, Xiaojun 2 Aboudi, Jacob 2 Andriamasy, Lova 2 Ari-Gur, Judah 2 Baratta, Alessandro 2 Ben-Haim, Yakov 2 Bernardini, Alberto 2 Caimi, Raoul 2 Candan, Suleyman 2 Colajanni, P. 2 Collet, Bernard A. 2 Colombi, Pierluigi 2 Crandall, Stephen Harry 2 De Bellis, Maria Laura 2 Di Paola, Mario 2 Givoli, Dan 2 Hasofer, Abraham M. 2 Kaplunov, Julius D. 2 Librescu, Liviu I. 2 Marzani, Alessandro 2 Michelitsch, Thomas M. 2 Neuringer, Joseph L. 2 Picandet, Vincent 2 Rollot, Olivier 2 Santoro, Roberta 2 Settineri, Dario 2 Soret, Clement 2 Storch, Joel A. 2 Tonon, Fulvio 2 Tonzani, Giulio Maria 2 Viola, Erasmo 2 Wang, Qishen 2 Zhang, Lihua 1 Ajenjo, Antoine 1 Ammon, D. 1 Archaud, E. 1 Ariaratnam, Sinnathamby T. 1 Augusti, Giuliano 1 Aydogdu, Metin 1 Babcock, C. D. jun. 1 Bégin-Drolet, André 1 Bekel, Yannis 1 Bellomo, Nicola 1 Benaroya, Haym 1 Bérard, Pierre H. 1 Bert, Charles W. 1 Bigi, Dante 1 Brząkała, Włodzimierz 1 Bushnell, David H. 1 Casciati, Fabio 1 Catellani, Giulia 1 Cazzulo, R. 1 Corsanego, Alfredo 1 Daphnis, A. 1 Das, Partha S. 1 DiMaggio, Frank L. 1 Ditlevsen, Ove 1 Dogliani, M. 1 Dolley, Melanie 1 Ducreux, Baptiste 1 Elisseeff, Pierre 1 Erbaş, Bariş 1 Faghidian, S. Ali 1 Faravelli, Lucia 1 Ferracuti, Barbara 1 Ganguly, Ranjan 1 Ghosh, Debraj 1 Gilat, Rivka 1 Glegg, Stewart A. L. 1 Gomez, Thomas 1 Grasman, Johan 1 Grigoriu, Mircea D. 1 Guagenti, E. 1 Gusella, Vittorio ...and 80 more Co-Authors all top 5 Serials 22 Chaos, Solitons and Fractals 21 Acta Mechanica 20 International Journal of Solids and Structures 18 Journal of Applied Mechanics 18 Journal of Sound and Vibration 17 Computer Methods in Applied Mechanics and Engineering 10 Computers and Structures 9 Meccanica 7 Mathematics and Mechanics of Solids 6 Archive of Applied Mechanics 5 AIAA Journal 5 International Journal of Non-Linear Mechanics 4 Proceedings of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 4 European Journal of Mechanics. A. Solids 3 International Journal of Engineering Science 3 Applied Mathematical Modelling 3 Mathematical Problems in Engineering 3 CISM International Centre for Mechanical Sciences. Courses and Lectures 3 Studies in Applied Mechanics 3 International Journal of Structural Stability and Dynamics 2 Journal of the Acoustical Society of America 2 Continuum Mechanics and Thermodynamics 2 Philosophical Transactions of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 2 Acta Mechanica Sinica 1 Applied Scientific Research 1 IMA Journal of Applied Mathematics 1 Israel Journal of Technology 1 ZAMP. Zeitschrift für angewandte Mathematik und Physik 1 Applied Mathematics and Computation 1 Fuzzy Sets and Systems 1 Industrial Mathematics 1 Journal of Optimization Theory and Applications 1 Mechanics Research Communications 1 Mathematical and Computer Modelling 1 Prikladnaya Mekhanika 1 Memoirs on Differential Equations and Mathematical Physics 1 ZAMM. Zeitschrift für Angewandte Mathematik und Mechanik 1 Communications in Nonlinear Science and Numerical Simulation 1 Archives of Computational Methods in Engineering 1 Scientiae Mathematicae Japonicae 1 Structural and Multidisciplinary Optimization 1 Theoretical and Applied Mechanics 1 Inverse Problems in Science and Engineering 1 AMD-Volumes 1 Lecture Notes in Engineering 1 Oxford Texts in Applied and Engineering Mathematics 1 Bulletin of the Georgian National Academy of Sciences. New Series 1 Advances in Theoretical and Applied Mechanics all top 5 Fields 221 Mechanics of deformable solids (74-XX) 26 Mechanics of particles and systems (70-XX) 16 Numerical analysis (65-XX) 13 Statistics (62-XX) 12 General and overarching topics; collections (00-XX) 10 Probability theory and stochastic processes (60-XX) 6 History and biography (01-XX) 6 Fluid mechanics (76-XX) 6 Systems theory; control (93-XX) 4 Ordinary differential equations (34-XX) 4 Computer science (68-XX) 4 Operations research, mathematical programming (90-XX) 3 Calculus of variations and optimal control; optimization (49-XX) 3 Geophysics (86-XX) 2 Mathematical logic and foundations (03-XX) 2 Partial differential equations (35-XX) 2 Statistical mechanics, structure of matter (82-XX) 2 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 1 Special functions (33-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Operator theory (47-XX) 1 Information and communication theory, circuits (94-XX) 1 Mathematics education (97-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 181 Publications have been cited 1,163 times in 658 Documents Cited by ▼ Year ▼ Convex models of uncertainty in applied mechanics. Zbl 0703.73100Ben-Haim, Yakov; Elishakoff, Isaac 151 1990 Antioptimization of structures with large uncertain-but-non-random parameters via interval analysis. Zbl 0947.74046Qiu, Zhiping; Elishakoff, Isaac 83 1998 Essay on uncertainties in elastic and viscoelastic structures: From A. M. Freudenthal’s criticisms to modern convex modeling. Zbl 0921.73004Elishakoff, I. 41 1995 Structural design under bounded uncertainty – Optimization with anti-optimization. Zbl 0878.73041Elishakoff, I.; Haftka, R. T.; Fang, J. 29 1994 Probabilistic methods in the theory of structures. Zbl 0572.73094Elishakoff, Isaac 28 1983 Nonprobabilistic, convex-theoretic modeling of scatter in material properties. Zbl 0804.73079Elishakoff, Isaac; Elisseeff, Pierre; Glegg, Stewart A. L. 23 1994 Combination of probabilistic and convex models of uncertainty when scarce knowledge is present on acoustic excitation parameters. Zbl 0812.73036Elishakoff, Isaac; Colombi, Pierluigi 22 1993 The bird’s eye view on finite element method for structures with large stochastic variations. Zbl 0953.74063Elishakoff, Isaac; Ren, Yongjian 19 1999 Derivation of multi-dimensional ellipsoid convex model for experimental data. Zbl 0857.73081Zhu, L. P.; Elishakoff, I.; Starnes, J. H. jun. 19 1996 Probabilistic interval reliability of structural systems. Zbl 1169.74578Qiu, Zhiping; Yang, Di; Elishakoff, Isaac 19 2008 Optimization and anti-optimization of structures under uncertainty. Zbl 1196.90004Elishakoff, Isaac; Ohsaki, Makoto 19 2010 Improved finite element method for stochastic problems. Zbl 0926.74108Elishakoff, I.; Ren, Y. J.; Shinozuka, M. 19 1995 Discrete systems behave as nonlocal structural elements: bending, buckling and vibration analysis. Zbl 1406.74376Challamel, Noel; Wang, C. M.; Elishakoff, I. 19 2014 Eigenvalues of inhomogeneous structures: Unusual closed-form solutions. Zbl 1082.74002Elishakoff, Isaac 16 2005 Stress concentration at a nearly circular hole with uncertain irregularities. Zbl 0825.73084Givoli, Dan; Elishakoff, Isaac 16 1992 Non-linear buckling of a column with initial imperfection via stochastic and non-stochastic convex models. Zbl 0796.73020Elishakoff, I.; Cai, G. Q.; Starnes, J. H. jun. 15 1994 Non-probabilistic set-theoretic model for structural safety measure. Zbl 1151.74378Wang, Xiaojun; Qiu, Z.; Elishakoff, I. 15 2008 Static response bounds of Timoshenko beams with spatially varying interval uncertainties. Zbl 1401.74176Sofi, A.; Muscolino, G.; Elishakoff, I. 15 2015 Uncertain buckling: Its past, present and future. Zbl 0980.74022Elishakoff, Isaac 14 2000 Probability and convexity concepts are not antagonistic. Zbl 1381.74176Wang, Xiaojun; Wang, Lei; Elishakoff, Isaac; Qiu, Zhiping 13 2011 Inverse buckling problem for inhomogeneous columns. Zbl 1009.74021Elishakoff, Isaac 13 2001 Natural frequencies of structures with uncertain but nonrandom parameters. Zbl 0836.65061Qiu, Z. P.; Chen, S. H.; Elishakoff, I. 12 1995 A deterministic method to predict the effect of unknown-but-bounded elastic moduli on the buckling of composite structures. Zbl 0845.73031Elishakoff, I.; Li, Y. W.; Starnes, J. H. jun. 12 1994 Applicatin of Krein’s method for determination of natural frequencies of periodically supported beam based on simplified Bresse-Timoshenko equations. Zbl 0606.73070Abramovich, H.; Elishakoff, I. 12 1987 Some exact solutions for the bending of beams with spatially stochastic stiffness. Zbl 0920.73075Elishakoff, I.; Ren, Y. J.; Shinozuka, M. 11 1995 Anti-optimization technique – a generalization of interval analysis for nonprobabilistic treatment of uncertainty. Zbl 1172.74322Qiu, Zhiping; Elishakoff, Isaac 10 2001 Finite element methods for structures with large stochastic variations. Zbl 1037.74001Elishakoff, Isaac; Ren, Yongjian 10 2003 Buckling mode localization in elastic plates due to misplacement in the stiffener location. Zbl 0926.74030Elishakoff, I.; Li, Y. W.; Starnes, J. H. jun. 10 1995 Non-classical problems in the theory of elastic stability. Zbl 0995.74002Elishakoff, Isaac; Li, Yiwei; Starnes, James H. jun. 9 2001 Three-dimensional analysis of an all-round clamped plate made of functionally graded materials. Zbl 1082.74029Elishakoff, I.; Gentilini, C.; Viola, E. 9 2005 Application and extension of the stochastic linearization by Anh and di Paola. Zbl 1162.70020Elishakoff, Isaac; Andriamasy, Lova; Dolley, Melanie 9 2009 Buckling of a stochastically imperfect finite column on a nonlinear elastic foundation. A reliability study. Zbl 0405.73035Elishakoff, Isaac 8 1979 New closed-form solutions for buckling of a variable stiffness column by Mathematica. Zbl 1235.74042Elishakoff, I.; Rollot, O. 8 1999 Computerized symbolic solution for a nonconservative system in which instability occurs by flutter in one range of a parameter and by divergence in another. Zbl 0607.73051Elishakoff, Isaac; Hollkamp, Joseph 8 1987 Non-probabilistic models of uncertainty in the nonlinear buckling of shells with general imperfections: Theoretical estimates of the knockdown factor. Zbl 0709.73026Ben-Haim, Yakov; Elishakoff, Isaac 7 1989 Closed-form solutions for axially graded beam-columns. Zbl 1236.74141Caliò, Ivo; Elishakoff, Isaac 7 2005 Vibrations of asymptotically and variationally based Uflyand-Mindlin plate models. Zbl 1423.74540Elishakoff, I.; Hache, F.; Challamel, Noel 7 2017 Who developed the so-called Timoshenko beam theory? Zbl 1446.74003Elishakoff, Isaac 7 2020 A closed-form solution for the generalized Euler problem. Zbl 0984.74029Elishakoff, I. 7 2000 Nonlinear response of a beam under stationary random excitation by improved stochastic linearization method. Zbl 0826.73042Fang, Jianjie; Elishakoff, Isaac; Caimi, Raoul 6 1995 A comparison of stochastic and interval finite elements applied to shear frames with uncertain stiffness properties. Zbl 0922.73061Köylüoǧlu, H. Uǧur; Elishakoff, Isaac 6 1998 Clamped-free double-walled carbon nanotube-based mass sensor. Zbl 1381.74102Elishakoff, I.; Versaci, C.; Muscolino, G. 6 2011 New exact solutions for randomly loaded beams with stochastic flexibility. Zbl 0930.74028Elishakoff, I.; Impollonia, N.; Ren, Y. J. 6 1999 Critical flow speeds of pipes conveying fluid using the generalized differential quadrature method. Zbl 1402.76096Tornabene, Francesco; Marzani, Alessandro; Viola, Erasmo; Elishakoff, Isaac 6 2010 Buckling under the external pressure of cylindrical shells with variable thickness. Zbl 1176.74070Nguyen, Hien Luong T.; Elishakoff, I.; Nguyen, Vinh T. 6 2009 Apparently first closed-form solution for frequencies of deterministically and/or stochastically inhomogeneous simply supported beams. Zbl 1110.74361Candan, S.; Elishakoff, I. 6 2001 Does a partial elastic foundation increase the flutter velocity of a pipe conveying fluid? Zbl 1110.74428Elishakoff, I.; Impollonia, N. 6 2001 Some closed-form solutions in random vibration of Bernoulli-Euler beams. Zbl 0556.73088Elishakoff, Isaac; Livshits, David 6 1984 Exact solutions for buckling of some divergence-type nonconservative systems in terms of Bessel and Lommel functions. Zbl 0615.73052Elishakoff, Isaac; Pellegrini, Flavio 6 1988 Random vibrations with MACSYMA. Zbl 0588.73157Rehak, M. L.; Dimaggio, F. L.; Benaroya, H.; Elishakoff, I. 6 1987 Apparently the first closed-from solution of inhomogeneous elastically restrained vibrating beams. Zbl 1243.74086Elishakoff, Issac; Pentaras, Demetris 6 2006 Generalization of Eringen’s result for random response of a beam on elastic foundation. Zbl 1477.74048Elishakoff, Isaac; Ajenjo, Antoine; Livshits, David 5 2020 Towards the resolution of the Smith-Herrmann paradox. Zbl 1066.74033Ruta, G. C.; Elishakoff, I. 5 2004 Euler’s problem revisited: 222 years later. Zbl 1049.74566Elishakoff, Isaac 5 2001 Simulation of space-random fields for solution of stochastic boundary- value problems. Zbl 0393.73016Elishakoff, I. 5 1979 Apparently first closed-form solutions for inhomogeneous vibrating beams under axial loading. Zbl 1007.74044Guédé, Z.; Elishakoff, I. 5 2001 Random vibration of a nonlinearly deformed beam by a new stochastic linearization technique. Zbl 0874.73079Elishakoff, I.; Fang, J.; Caimi, R. 5 1995 New formulation of FEM for deterministic and stochastic beams through generalization of Fuchs’ approach. Zbl 0892.73058Elishakoff, I.; Ren, Y. J.; Shinozuka, M. 5 1997 Hybrid probabilistic and convex modeling of excitation and response of periodic structures. Zbl 0962.74506Zhu, L. P.; Elishakoff, I. 5 1996 Dynamic instability of shear-deformable viscoelastic laminated plates by Lyapunov exponents. Zbl 0749.73040Cederbaum, Gabriel; Aboudi, Jacob; Elishakoff, Isaac 5 1991 Closed-form trigonometric solutions for inhomogeneous beam-columns on elastic foundation. Zbl 1205.35306Caliò, Ivo; Elishakoff, Isaac 5 2004 A novel formulation leading to closed-form solutions for buckling of circular plates. Zbl 1099.74022Elishakoff, I.; Ruta, G. C.; Stavsky, Y. 5 2006 Statics and dynamics of nanorods embedded in an elastic medium: nonlocal elasticity and lattice formulations. Zbl 1406.74078Challamel, Noël; Aydogdu, Metin; Elishakoff, Isaac 5 2018 Fuzzy sets based interpretation of the safety factor. Zbl 1100.74044Elishakoff, Isaac; Ferracuti, Barbara 5 2006 A novel local stochastic linearization method via two extremum entropy principles. Zbl 1346.70022Ricciardi, Giuseppe; Elishakoff, Isaac 5 2002 Reliability of axially compressed cylindrical shells with random axisymmetric imperfections. Zbl 0485.73054Elishakoff, Isaac; Arbocz, Johann 5 1982 Apparently the first closed-form solution of vibrating inhomogeneous beam with a tip mass. Zbl 1243.74052Elishakoff, Isaac; Johnson, V. 5 2005 The hypothesis of equal wave speeds for stabilization of Timoshenko beam is not necessary anymore: the time delay cases. Zbl 1476.74067Almeida Júnior, D. S.; Elishakoff, I.; Ramos, A. J. A.; Miranda, L. G. Rosário 4 2019 Reconstructing the cross-sectional area of an axially vibrating non-uniform rod from one of its mode shapes. Zbl 1069.74026Ram, Yitshak M.; Elishakoff, Isaac 4 2004 Impact buckling of thin bar via Monte Carlo method. Zbl 0392.73040Elishakoff, I. 4 1978 Eigenfrequencies of continuous plates with arbitrary number of equal spans. Zbl 0418.73062Elishakoff, Isaac; Sternberg, Alexander 4 1979 Hoff’s problem in a probabilistic setting. Zbl 0432.73038Elishakoff, Isaac 4 1980 Remarks on the static and dynamic imperfection-sensitivity of nonsymmetric structures. Zbl 0436.73050Elishakoff, Isaac 4 1980 Class of analytical closed-form polynomial solutions for guided–pinned inhomogeneous beams. Zbl 1076.74527Becquet, Roland; Elishakoff, Isaac 4 2001 Buckling of an axially compressed cylindrical shell of variable thickness. Zbl 0802.73028Koiter, W. T.; Elishakoff, I.; Li, Y. W.; Starnes, J. H. jun. 4 1994 A transverse shear and normal deformable orthotropic beam theory. Zbl 0925.73243Soldatos, K. P.; Elishakoff, I. 4 1992 Finite element method for stochastic beams based on variational principles. Zbl 0899.73543Ren, Y.-J.; Elishakoff, I.; Shinozuka, M. 4 1997 Reconstructing cantilever beams via vibration mode with a given node location. Zbl 1398.74159Wu, Lei; Zhang, Li-Hua; Wang, Qi-Shen; Elishakoff, Isaac 4 2011 A new look at the stochastic linearization technique for hyperbolic tangent oscillator. Zbl 0965.70037Colajanni, P.; Elishakoff, I. 4 1998 Buckling mode localization in a multi-span periodic structure with a disorder in a single span. Zbl 0926.74029Li, Y. W.; Elishakoff, I.; Starnes, J. H. jun. 4 1995 Revisiting finite difference and finite element methods applied to structural mechanics within enriched continua. Zbl 1406.74628Challamel, Noël; Picandet, Vincent; Collet, Bernard; Michelitsch, Thomas; Elishakoff, Isaac; Wang, C. M. 4 2015 On nonlocal computation of eigenfrequencies of beams using finite difference and finite element methods. Zbl 1359.74198Challamel, Noël; Picandet, Vincent; Elishakoff, Issac; Wang, Chien Ming; Collet, Bernard; Michelitsch, Thomas 4 2015 Effect of boundary conditions in three alternative models of Timoshenko-Ehrenfest beams on Winkler elastic foundation. Zbl 1390.74087Elishakoff, Isaac; Tonzani, Giulio Maria; Marzani, Alessandro 4 2018 Three-dimensional flexure of rectangular plates made of functionally graded materials. Zbl 1111.74393Elishakoff, Isaac; Gentilini, Cristina 4 2005 Accuracy of the finite difference method in stochastic setting. Zbl 1243.74195Santoro, Roberta; Elishakoff, Isaac 4 2006 Essay on the contributors to the elastic stability theory. Zbl 1098.74004Elishakoff, Isaac 3 2005 Some unexpected results in vibration of non-homogeneous beams on elastic foundation. Zbl 1002.74041Elishakoff, Isaac 3 2001 Axial impact buckling of a column with random initial imperfections. Zbl 0385.73041Elishakoff, I. 3 1978 Wide-band random axisymmetric vibration of cylindrical shells. Zbl 0407.73072Elishakoff, I.; van Zanten, A. Th.; Crandall, S. H. 3 1979 Novel closed-form solutions in buckling of inhomogeneous columns under distributed variable loading. Zbl 1076.74518Elishakoff, Isaac; Guédé, Zakoua 3 2001 Hybrid analysis of uncertainty: Probability, fuzziness and anti-optimization. Zbl 1013.74500Tonon, Fulvio; Bernardini, Alberto; Elishakoff, Isaac 3 2001 Class of analytical closed-form polynomial solutions for clamped-guided inhomogeneous beams. Zbl 1172.74314Becquet, Roland; Elishakoff, Isaac 3 2001 New results in finite element method for stochastic structures. Zbl 0932.74069Ren, Y. J.; Elishakoff, I. 3 1998 Symbolic computations and their impact on mechanics. Zbl 0850.73022 3 1990 Hybrid theoretical, experimental and numerical study of vibration and buckling of composite shells with scatter in elastic moduli. Zbl 1167.74449Wang, Xiaojun; Elishakoff, Isaac; Qiu, Zhiping; Kou, Changhe 3 2009 Generalization of the super ellipsoid concept and its application in mechanics. Zbl 1480.70001Ni, B. Y.; Elishakoff, I.; Jiang, C.; Fu, C. M.; Han, X. 3 2016 Localization of the bending response in the presence of axial load. Zbl 0992.74036Zingales, Massimiliano; Elishakoff, Isaac 3 2000 Probabilistic methods in the theory of structures. Strength of materials, random vibrations, and random buckling. 3rd corrected and expanded edition. Zbl 1360.74004Elishakoff, Isaac 3 2017 Sixty years of stochastic linearization technique. Zbl 1371.65007Elishakoff, Isaac; Crandall, Stephen H. 3 2017 Mechanics of functionally graded material structures. Zbl 1338.74001Elishakoff, Isaac; Pentaras, Demetris; Gentilini, Cristina 3 2016 Nonlinear flexure mechanics of mixture unified gradient nanobeams. Zbl 07634567Faghidian, S. Ali; Żur, Krzysztof Kamil; Elishakoff, Isaac 1 2023 Who developed the so-called Timoshenko beam theory? Zbl 1446.74003Elishakoff, Isaac 7 2020 Generalization of Eringen’s result for random response of a beam on elastic foundation. Zbl 1477.74048Elishakoff, Isaac; Ajenjo, Antoine; Livshits, David 5 2020 The hypothesis of equal wave speeds for stabilization of Timoshenko beam is not necessary anymore: the time delay cases. Zbl 1476.74067Almeida Júnior, D. S.; Elishakoff, I.; Ramos, A. J. A.; Miranda, L. G. Rosário 4 2019 Asymptotic derivation of nonlocal beam models from two-dimensional nonlocal elasticity. Zbl 07254362Hache, Florian; Challamel, Noël; Elishakoff, Isaac 2 2019 Asymptotic derivation of nonlocal plate models from three-dimensional stress gradient elasticity. Zbl 1442.74116Hache, Florian; Challamel, Noël; Elishakoff, I. 1 2019 JP Den Hartog about SP Timoshenko: fifty years later. Zbl 1446.74002Elishakoff, Isaac 1 2019 Statics and dynamics of nanorods embedded in an elastic medium: nonlocal elasticity and lattice formulations. Zbl 1406.74078Challamel, Noël; Aydogdu, Metin; Elishakoff, Isaac 5 2018 Effect of boundary conditions in three alternative models of Timoshenko-Ehrenfest beams on Winkler elastic foundation. Zbl 1390.74087Elishakoff, Isaac; Tonzani, Giulio Maria; Marzani, Alessandro 4 2018 Vibrations of asymptotically and variationally based Uflyand-Mindlin plate models. Zbl 1423.74540Elishakoff, I.; Hache, F.; Challamel, Noel 7 2017 Probabilistic methods in the theory of structures. Strength of materials, random vibrations, and random buckling. 3rd corrected and expanded edition. Zbl 1360.74004Elishakoff, Isaac 3 2017 Sixty years of stochastic linearization technique. Zbl 1371.65007Elishakoff, Isaac; Crandall, Stephen H. 3 2017 Free vibration analysis of plates taking into account rotary inertia and shear deformation via three alternative theories: a Lévy-type solution. Zbl 1384.74017Hache, F.; Elishakoff, I.; Challamel, N. 1 2017 Generalization of the super ellipsoid concept and its application in mechanics. Zbl 1480.70001Ni, B. Y.; Elishakoff, I.; Jiang, C.; Fu, C. M.; Han, X. 3 2016 Mechanics of functionally graded material structures. Zbl 1338.74001Elishakoff, Isaac; Pentaras, Demetris; Gentilini, Cristina 3 2016 Closed-form solutions and uncertainty quantification for gravity-loaded beams. Zbl 1341.74101Sarkar, Korak; Ganguli, Ranjan; Ghosh, Debraj; Elishakoff, Isaac 1 2016 Static response bounds of Timoshenko beams with spatially varying interval uncertainties. Zbl 1401.74176Sofi, A.; Muscolino, G.; Elishakoff, I. 15 2015 Revisiting finite difference and finite element methods applied to structural mechanics within enriched continua. Zbl 1406.74628Challamel, Noël; Picandet, Vincent; Collet, Bernard; Michelitsch, Thomas; Elishakoff, Isaac; Wang, C. M. 4 2015 On nonlocal computation of eigenfrequencies of beams using finite difference and finite element methods. Zbl 1359.74198Challamel, Noël; Picandet, Vincent; Elishakoff, Issac; Wang, Chien Ming; Collet, Bernard; Michelitsch, Thomas 4 2015 A contribution to the stability of an overhanging pipe conveying fluid. Zbl 1341.74053De Bellis, Maria Laura; Ruta, Giuseppe C.; Elishakoff, Isaac 1 2015 A new class of interdependent shape polynomials for the FE dynamic analysis of Mindlin plate Timoshenko beam. Zbl 1317.74085Falsone, G.; Settineri, D.; Elishakoff, I. 1 2015 Discrete systems behave as nonlocal structural elements: bending, buckling and vibration analysis. Zbl 1406.74376Challamel, Noel; Wang, C. M.; Elishakoff, I. 19 2014 A new locking-free finite element method based on more consistent version of Mindlin plate equation. Zbl 1341.74148Falsone, G.; Settineri, D.; Elishakoff, I. 1 2014 Random vibration of a point-driven two-span beam on an elastic foundation. Zbl 1353.74038Elishakoff, Isaac; Santoro, Roberta 1 2014 Modified Monte Carlo method for buckling analysis of nonlinear imperfect structures. Zbl 1293.74433Elishakoff, I.; Archaud, E. 3 2013 A celebration of mechanics: from nano to macro. The J. Michael T. Thompson Festschrift issue. Zbl 1321.00092 2 2013 Virus sensor based on single-walled carbon nanotube: improved theory incorporating surface effects. Zbl 1327.74016Elishakoff, Isaac; Challamel, Noël; Soret, Clément; Bekel, Yannis; Gomez, Thomas 2 2013 The tale of stochastic linearization technique: over half a century of progress. Zbl 1279.74042Elishakoff, Isaac; Andriamasy, Lova 2 2012 Buckling of a column made of functionally graded material. Zbl 1293.74117Elishakoff, Isaac 2 2012 Erratum to: “Free vibration of triple-walled carbon nanotubes”. Zbl 1401.74134Pentaras, Demetris; Elishakoff, Isaac 1 2012 Nonlocal refined theory for nanobeams with surface effects. Zbl 1246.74027Elishakoff, Isaac; Soret, Clement 1 2012 Probability and convexity concepts are not antagonistic. Zbl 1381.74176Wang, Xiaojun; Wang, Lei; Elishakoff, Isaac; Qiu, Zhiping 13 2011 Clamped-free double-walled carbon nanotube-based mass sensor. Zbl 1381.74102Elishakoff, I.; Versaci, C.; Muscolino, G. 6 2011 Reconstructing cantilever beams via vibration mode with a given node location. Zbl 1398.74159Wu, Lei; Zhang, Li-Hua; Wang, Qi-Shen; Elishakoff, Isaac 4 2011 Free vibration of triple-walled carbon nanotubes. Zbl 1398.74151Pentaras, Demetris; Elishakoff, Isaac 1 2011 Comparison of asymptotic method with explicit solutions in random vibration. Zbl 1293.70073Elishakoff, I.; Livshits, D. 1 2011 Optimization and anti-optimization of structures under uncertainty. Zbl 1196.90004Elishakoff, Isaac; Ohsaki, Makoto 19 2010 Critical flow speeds of pipes conveying fluid using the generalized differential quadrature method. Zbl 1402.76096Tornabene, Francesco; Marzani, Alessandro; Viola, Erasmo; Elishakoff, Isaac 6 2010 Influence of a Wieghardt foundation on the dynamic stability of a fluid conveying pipe. Zbl 1271.74065De Bellis, M. L.; Ruta, G. C.; Elishakoff, I. 3 2010 Application and extension of the stochastic linearization by Anh and di Paola. Zbl 1162.70020Elishakoff, Isaac; Andriamasy, Lova; Dolley, Melanie 9 2009 Buckling under the external pressure of cylindrical shells with variable thickness. Zbl 1176.74070Nguyen, Hien Luong T.; Elishakoff, I.; Nguyen, Vinh T. 6 2009 Hybrid theoretical, experimental and numerical study of vibration and buckling of composite shells with scatter in elastic moduli. Zbl 1167.74449Wang, Xiaojun; Elishakoff, Isaac; Qiu, Zhiping; Kou, Changhe 3 2009 Probabilistic interval reliability of structural systems. Zbl 1169.74578Qiu, Zhiping; Yang, Di; Elishakoff, Isaac 19 2008 Non-probabilistic set-theoretic model for structural safety measure. Zbl 1151.74378Wang, Xiaojun; Qiu, Z.; Elishakoff, I. 15 2008 Combination of structural reliability and interval analysis. Zbl 1257.74188Qiu, Zhiping; Yang, Di; Elishakoff, Isaac 2 2008 Apparently the first closed-from solution of inhomogeneous elastically restrained vibrating beams. Zbl 1243.74086Elishakoff, Issac; Pentaras, Demetris 6 2006 A novel formulation leading to closed-form solutions for buckling of circular plates. Zbl 1099.74022Elishakoff, I.; Ruta, G. C.; Stavsky, Y. 5 2006 Fuzzy sets based interpretation of the safety factor. Zbl 1100.74044Elishakoff, Isaac; Ferracuti, Barbara 5 2006 Accuracy of the finite difference method in stochastic setting. Zbl 1243.74195Santoro, Roberta; Elishakoff, Isaac 4 2006 Buckling of a column on a Wieghardt foundation. Zbl 1097.74024Ruta, Giuseppe C.; Elishakoff, Isaac 2 2006 Eigenvalues of inhomogeneous structures: Unusual closed-form solutions. Zbl 1082.74002Elishakoff, Isaac 16 2005 Three-dimensional analysis of an all-round clamped plate made of functionally graded materials. Zbl 1082.74029Elishakoff, I.; Gentilini, C.; Viola, E. 9 2005 Closed-form solutions for axially graded beam-columns. Zbl 1236.74141Caliò, Ivo; Elishakoff, Isaac 7 2005 Apparently the first closed-form solution of vibrating inhomogeneous beam with a tip mass. Zbl 1243.74052Elishakoff, Isaac; Johnson, V. 5 2005 Three-dimensional flexure of rectangular plates made of functionally graded materials. Zbl 1111.74393Elishakoff, Isaac; Gentilini, Cristina 4 2005 Essay on the contributors to the elastic stability theory. Zbl 1098.74004Elishakoff, Isaac 3 2005 An unusual exact, closed-form solution for axisymmetric vibration of inhomogeneous simply supported circular plates. Zbl 1237.74061Elishakoff, Isaac; Storch, Joel A. 2 2005 A paradox of non-monotonicity in stability of pipes conveying fluid. Zbl 1120.74449Elishakoff, I.; Vittori, P. 1 2005 Towards the resolution of the Smith-Herrmann paradox. Zbl 1066.74033Ruta, G. C.; Elishakoff, I. 5 2004 Closed-form trigonometric solutions for inhomogeneous beam-columns on elastic foundation. Zbl 1205.35306Caliò, Ivo; Elishakoff, Isaac 5 2004 Reconstructing the cross-sectional area of an axially vibrating non-uniform rod from one of its mode shapes. Zbl 1069.74026Ram, Yitshak M.; Elishakoff, Isaac 4 2004 Finite element methods for structures with large stochastic variations. Zbl 1037.74001Elishakoff, Isaac; Ren, Yongjian 10 2003 Notes on philosophy of the Monte Carlo method. Zbl 1121.74490Elishakov, I. 2 2003 Large variation finite element method for beams with stochastic stiffness. Zbl 1103.74362Rollot, Olivier; Elishakoff, Isaac 2 2003 Contrasting probabilistic and anti-optimization approaches in an applied mechanics problem. Zbl 1052.74022Elishakoff, I.; Zingales, M. 1 2003 A novel local stochastic linearization method via two extremum entropy principles. Zbl 1346.70022Ricciardi, Giuseppe; Elishakoff, Isaac 5 2002 Modern problems of structural stability. Papers of a course on structural stability, Udine, Italy, 16–20 July, 2001. Zbl 1031.74008 1 2002 Inverse buckling problem for inhomogeneous columns. Zbl 1009.74021Elishakoff, Isaac 13 2001 Anti-optimization technique – a generalization of interval analysis for nonprobabilistic treatment of uncertainty. Zbl 1172.74322Qiu, Zhiping; Elishakoff, Isaac 10 2001 Non-classical problems in the theory of elastic stability. Zbl 0995.74002Elishakoff, Isaac; Li, Yiwei; Starnes, James H. jun. 9 2001 Apparently first closed-form solution for frequencies of deterministically and/or stochastically inhomogeneous simply supported beams. Zbl 1110.74361Candan, S.; Elishakoff, I. 6 2001 Does a partial elastic foundation increase the flutter velocity of a pipe conveying fluid? Zbl 1110.74428Elishakoff, I.; Impollonia, N. 6 2001 Euler’s problem revisited: 222 years later. Zbl 1049.74566Elishakoff, Isaac 5 2001 Apparently first closed-form solutions for inhomogeneous vibrating beams under axial loading. Zbl 1007.74044Guédé, Z.; Elishakoff, I. 5 2001 Class of analytical closed-form polynomial solutions for guided–pinned inhomogeneous beams. Zbl 1076.74527Becquet, Roland; Elishakoff, Isaac 4 2001 Some unexpected results in vibration of non-homogeneous beams on elastic foundation. Zbl 1002.74041Elishakoff, Isaac 3 2001 Novel closed-form solutions in buckling of inhomogeneous columns under distributed variable loading. Zbl 1076.74518Elishakoff, Isaac; Guédé, Zakoua 3 2001 Hybrid analysis of uncertainty: Probability, fuzziness and anti-optimization. Zbl 1013.74500Tonon, Fulvio; Bernardini, Alberto; Elishakoff, Isaac 3 2001 Class of analytical closed-form polynomial solutions for clamped-guided inhomogeneous beams. Zbl 1172.74314Becquet, Roland; Elishakoff, Isaac 3 2001 Turning around a method of successive iterations to yield closed-form solutions for vibrating inhomogeneous bars. Zbl 1038.74022Elishakoff, Isaac; Baruch, Menahem; Becquet, Roland 2 2001 A remarkable nature of the effect of boundary conditions on closed-form solutions for vibrating inhomogeneous Bernoulli-Euler beams. Zbl 1060.74566Elishakoff, I.; Guédé, Z. 2 2001 Constructing the axial stiffness of longitudinally vibrating rod from fundamental mode shape. Zbl 1052.74027Candan, Suleyman; Elishakoff, Isaac 2 2001 A fifth-order polynomial that serves as both buckling and vibration mode of an inhomogeneous structure. Zbl 1014.74031Guédé, Zakoua; Elishakoff, Isaac 1 2001 Uncertain buckling: Its past, present and future. Zbl 0980.74022Elishakoff, Isaac 14 2000 A closed-form solution for the generalized Euler problem. Zbl 0984.74029Elishakoff, I. 7 2000 Localization of the bending response in the presence of axial load. Zbl 0992.74036Zingales, Massimiliano; Elishakoff, Isaac 3 2000 A selective review of direct, semi-inverse and inverse eigenvalue problems for structures described by differential equations with variable coefficients. Zbl 0987.74003Elishakoff, I. 3 2000 Buckling mode localization in rib-stiffened plates with misplaced stiffeners – Kantorovich approach. Zbl 0969.74026Xie, W.-C.; Elishakoff, I. 2 2000 Anti-optimization versus probability in an applied mechanics problem: vector uncertainty. Zbl 1110.74810Zingales, M.; Elishakoff, I. 2 2000 Both static deflection and vibration mode of uniform beam can serve as a buckling mode of a non-uniform column. Zbl 1237.74060Elishakoff, I. 1 2000 Elastic stability: from Euler to Koiter there was none like Koiter. Zbl 0987.74005Elishakoff, Isaac 1 2000 The bird’s eye view on finite element method for structures with large stochastic variations. Zbl 0953.74063Elishakoff, Isaac; Ren, Yongjian 19 1999 New closed-form solutions for buckling of a variable stiffness column by Mathematica. Zbl 1235.74042Elishakoff, I.; Rollot, O. 8 1999 New exact solutions for randomly loaded beams with stochastic flexibility. Zbl 0930.74028Elishakoff, I.; Impollonia, N.; Ren, Y. J. 6 1999 Concept of random sets as applied to the design of structures and analysis of expert opinions for aircraft crash. Zbl 0967.62084Tonon, F.; Bernardini, A.; Elishakoff, I. 2 1999 Refined theories may be needed for vibration analysis of structures with overhang. Zbl 0940.74023Elishakoff, Isaac; Ari-Gur, Judah; Das, Partha S. 1 1999 Antioptimization of structures with large uncertain-but-non-random parameters via interval analysis. Zbl 0947.74046Qiu, Zhiping; Elishakoff, Isaac 83 1998 A comparison of stochastic and interval finite elements applied to shear frames with uncertain stiffness properties. Zbl 0922.73061Köylüoǧlu, H. Uǧur; Elishakoff, Isaac 6 1998 A new look at the stochastic linearization technique for hyperbolic tangent oscillator. Zbl 0965.70037Colajanni, P.; Elishakoff, I. 4 1998 New results in finite element method for stochastic structures. Zbl 0932.74069Ren, Y. J.; Elishakoff, I. 3 1998 ...and 81 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 942 Authors 81 Elishakoff, Isaac 43 Qiu, Zhiping 24 Wang, Xiaojun 18 Wang, Lei 15 Challamel, Noël 15 Wang, Chong 12 Han, Xu 10 Li, Yunlong 9 Falsone, Giovanni 9 Jiang, Chao 9 Kanno, Yoshihiro 9 Liu, Jie 9 Yu, Dejie 8 Kang, Zhan 8 Moens, David 8 Wu, Di 8 Xu, Menghui 7 Papadopoulos, Vissarion 7 Wang, Chien-Ming 7 Xia, Baizhan 6 Faghidian, S. Ali 6 Impollonia, Nicola 6 Matthies, Hermann Georg 6 Nguyen Dong Anh 6 Papadrakakis, Manolis 5 Adali, Sarp 5 Babuška, Ivo 5 Chen, Ning 5 Faes, Matthias G. R. 5 Guo, Xu 5 Lü, Zhenzhou 5 Meng, Zeng 5 Ni, Bingyu 5 Ramos, Anderson J. A. 5 Ruta, Giuseppe Claudio 5 Takewaki, Izuru 5 Tin-Loi, Francis 5 Tornabene, Francesco 5 Żur, Krzysztof Kamil 4 Caliò, Ivo 4 Frommer, Andreas 4 Guo, Shuxiang 4 Hache, Florian 4 Hao, Peng 4 Hlaváček, Ivan 4 Hu, Juxi 4 Liu, Jian 4 Liu, Yisi 4 Luo, Yangjun 4 Lv, Zheng 4 Müller, Peter Chr. 4 Muscolino, Giuseppe 4 Popova, Evgeniya D. 4 Rudakov, Igor Alekseevich 4 Soufyane, Abdelaziz 4 Starnes, James H. jun. 4 Vandepitte, Dirk 4 Viola, Erasmo 4 Wang, Qishen 4 Zhang, Lihua 4 Zhou, Huanlin 3 Ahmadian, Mohammad Taghi 3 Beer, Michael A. 3 Behera, Diptiranjan 3 Ben-Haim, Yakov 3 Bi, Rengui 3 Chakraverty, Snehashish 3 Chen, Suhuan 3 Chen, Weiqiu 3 Collet, Bernard A. 3 Deng, Zhongmin 3 Deodatis, George 3 Do, Duy Minh 3 Du, Jianke 3 Freitas, Mirelson M. 3 Ganguly, Ranjan 3 Gao, Kang 3 Givoli, Dan 3 Haftka, Raphael T. 3 He, Min 3 Hieu, Nguyen Ngoc 3 Laudani, Rossella 3 Li, Luyi 3 Li, Yiwei 3 Liu, Yongshou 3 Luo, Zhen 3 Ma, Yujia 3 Mackerle, Jaroslav 3 Michelitsch, Thomas M. 3 Quaranta, Giuseppe 3 Rajasekaran, Sundaramoorthy 3 Reddy, Junuthula Narasimha 3 Sadek, Ibrahim S. 3 Santoro, Roberta 3 Settineri, Dario 3 Sinou, Jean-Jacques 3 Sofi, Alba 3 Song, Chongmin 3 Stefanou, George Demetrios 3 Tangaramvong, Sawekchai ...and 842 more Authors all top 5 Cited in 106 Serials 130 Computer Methods in Applied Mechanics and Engineering 67 Applied Mathematical Modelling 64 Acta Mechanica 24 International Journal for Numerical Methods in Engineering 23 European Journal of Mechanics. A. Solids 21 Chaos, Solitons and Fractals 18 Meccanica 16 Acta Mechanica Sinica 15 International Journal of Computational Methods 14 Archive of Applied Mechanics 14 Mathematical Problems in Engineering 14 International Journal of Structural Stability and Dynamics 13 Applied Mathematics and Computation 12 International Journal of Engineering Science 11 Mathematics and Mechanics of Solids 10 Journal of Vibration and Control 8 Structural and Multidisciplinary Optimization 7 Computational Mechanics 7 Engineering Analysis with Boundary Elements 6 International Journal of Solids and Structures 6 Fuzzy Sets and Systems 6 Applied Mathematics and Mechanics. (English Edition) 6 Nonlinear Dynamics 6 Engineering Optimization 5 Mechanics Research Communications 4 Computers & Mathematics with Applications 4 Mathematical and Computer Modelling 4 Communications in Numerical Methods in Engineering 4 Communications in Nonlinear Science and Numerical Simulation 4 Archives of Computational Methods in Engineering 4 Inverse Problems in Science and Engineering 3 Journal of Engineering Mathematics 3 ZAMP. Zeitschrift für angewandte Mathematik und Physik 3 Journal of Optimization Theory and Applications 3 Mathematics and Computers in Simulation 3 COMPEL 3 Applications of Mathematics 3 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences 3 Continuum Mechanics and Thermodynamics 3 Philosophical Transactions of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 3 Engineering Computations 3 Journal of Applied Mathematics 3 AMM. Applied Mathematics and Mechanics. (English Edition) 2 Journal of Computational Physics 2 Journal of the Franklin Institute 2 Automatica 2 BIT 2 Journal of Differential Equations 2 ZAMM. Zeitschrift für Angewandte Mathematik und Mechanik 2 Optimization and Engineering 2 Differential Equations 2 Nonlinear Analysis. Real World Applications 2 Sādhanā 2 Journal of Intelligent and Fuzzy Systems 2 Science China. Technological Sciences 1 Archives of Mechanics 1 Journal of Mathematical Analysis and Applications 1 Wave Motion 1 Zeitschrift für Angewandte Mathematik und Mechanik (ZAMM) 1 Annales Scientifiques de l’Université de Clermont-Ferrand II. Mathématiques 1 Journal of Computational and Applied Mathematics 1 Numerische Mathematik 1 Statistica Neerlandica 1 Stochastic Analysis and Applications 1 Acta Applicandae Mathematicae 1 Applied Numerical Mathematics 1 International Journal of Approximate Reasoning 1 Dynamics and Stability of Systems 1 Japan Journal of Industrial and Applied Mathematics 1 Numerical Algorithms 1 European Journal of Operational Research 1 International Journal of Computer Mathematics 1 Acta Mechanica Sinica. (English Edition) 1 Journal of Dynamics and Differential Equations 1 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 1 Advances in Engineering Software 1 Calculus of Variations and Partial Differential Equations 1 International Applied Mechanics 1 Journal of Mathematical Sciences (New York) 1 Computational and Applied Mathematics 1 Reliable Computing 1 Matematychni Metody ta Fizyko-Mekhanichni Polya 1 Multibody System Dynamics 1 Soft Computing 1 Journal of Applied Mechanics and Technical Physics 1 Journal of Shanghai University 1 Discrete Dynamics in Nature and Society 1 International Journal of Applied Mathematics and Computer Science 1 Computational Geosciences 1 Lobachevskii Journal of Mathematics 1 International Journal of Nonlinear Sciences and Numerical Simulation 1 The ANZIAM Journal 1 Journal of Nonlinear Mathematical Physics 1 Iranian Journal of Science and Technology. Transaction A: Science 1 Granular Matter 1 Acta Numerica 1 Journal of Zhejiang University. Science A 1 Monograph Series on Nonlinear Science and Complexity 1 Proceedings of the Estonian Academy of Sciences 1 Advances in Applied Mathematics and Mechanics ...and 6 more Serials all top 5 Cited in 32 Fields 504 Mechanics of deformable solids (74-XX) 134 Numerical analysis (65-XX) 63 Operations research, mathematical programming (90-XX) 48 Statistics (62-XX) 37 Mechanics of particles and systems (70-XX) 35 Probability theory and stochastic processes (60-XX) 25 Partial differential equations (35-XX) 24 Systems theory; control (93-XX) 19 Ordinary differential equations (34-XX) 18 Fluid mechanics (76-XX) 13 Computer science (68-XX) 10 Statistical mechanics, structure of matter (82-XX) 8 Calculus of variations and optimal control; optimization (49-XX) 8 Geophysics (86-XX) 7 Linear and multilinear algebra; matrix theory (15-XX) 7 Dynamical systems and ergodic theory (37-XX) 5 Classical thermodynamics, heat transfer (80-XX) 5 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 4 Optics, electromagnetic theory (78-XX) 3 History and biography (01-XX) 3 Real functions (26-XX) 3 Biology and other natural sciences (92-XX) 3 Information and communication theory, circuits (94-XX) 2 Mathematical logic and foundations (03-XX) 2 Special functions (33-XX) 2 Integral equations (45-XX) 2 Operator theory (47-XX) 1 General and overarching topics; collections (00-XX) 1 Topological groups, Lie groups (22-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 Quantum theory (81-XX) Citations by Year Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. 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