Rizzi, Peter; Sander, Evelyn; Wanner, Thomas Cyclic symmetry induced pitchfork bifurcations in the diblock copolymer model. (English) Zbl 07789742 Discrete Contin. Dyn. Syst., Ser. B 29, No. 2, 666-701 (2024). MSC: 37G40 37M20 65G20 65P30 37C81 65G30 74G60 74N15 PDFBibTeX XMLCite \textit{P. Rizzi} et al., Discrete Contin. Dyn. Syst., Ser. B 29, No. 2, 666--701 (2024; Zbl 07789742) Full Text: DOI arXiv
Beluch, W.; Hatłas, M.; Ptaszny, J. Granular computational homogenisation of composite structures with imprecise parameters. (English) Zbl 1528.74088 Arch. Mech. 75, No. 3, 271-300 (2023). MSC: 74Q05 74E30 74S05 74S99 PDFBibTeX XMLCite \textit{W. Beluch} et al., Arch. Mech. 75, No. 3, 271--300 (2023; Zbl 1528.74088) Full Text: DOI
Liu, Yaru; Wang, Lei; Ng, Bing Feng Load-independent multi-objective sensor placement method for localization and reconstruction of external excitations under interval uncertainties. (English) Zbl 1527.74059 Comput. Methods Appl. Mech. Eng. 416, Article ID 116344, 27 p. (2023). MSC: 74P15 65G30 90C29 PDFBibTeX XMLCite \textit{Y. Liu} et al., Comput. Methods Appl. Mech. Eng. 416, Article ID 116344, 27 p. (2023; Zbl 1527.74059) Full Text: DOI
Rizzi, Peter; Sander, Evelyn; Wanner, Thomas Equilibrium validation for triblock copolymers via inverse norm bounds for fourth-order elliptic operators. (English) Zbl 1505.74009 Commun. Nonlinear Sci. Numer. Simul. 115, Article ID 106789, 27 p. (2022). MSC: 74A60 74H60 35Q74 PDFBibTeX XMLCite \textit{P. Rizzi} et al., Commun. Nonlinear Sci. Numer. Simul. 115, Article ID 106789, 27 p. (2022; Zbl 1505.74009) Full Text: DOI arXiv
Alazwari, Mashhour A.; Rao, Singiresu S. Uncertainty analysis of large structures using universal grey number theory. (English) Zbl 1510.65093 Appl. Math. Comput. 416, Article ID 126735, 18 p. (2022). MSC: 65G30 74S99 15B15 74G99 PDFBibTeX XMLCite \textit{M. A. Alazwari} and \textit{S. S. Rao}, Appl. Math. Comput. 416, Article ID 126735, 18 p. (2022; Zbl 1510.65093) Full Text: DOI
Zieniuk, Eugeniusz; Kapturczak, Marta Interval arithmetic in modeling and solving Laplace’s equation problems with uncertainly defined boundary shape. (English) Zbl 1464.74360 Eng. Anal. Bound. Elem. 125, 110-123 (2021). MSC: 74S15 65N38 65N30 65G40 68T37 74S05 PDFBibTeX XMLCite \textit{E. Zieniuk} and \textit{M. Kapturczak}, Eng. Anal. Bound. Elem. 125, 110--123 (2021; Zbl 1464.74360) Full Text: DOI
Jiang, Chao; Li, J. W.; Ni, Bing-Yu; Fang, T. Some significant improvements for interval process model and non-random vibration analysis method. (English) Zbl 1435.74040 Comput. Methods Appl. Mech. Eng. 357, Article ID 112565, 48 p. (2019). MSC: 74H50 65G30 PDFBibTeX XMLCite \textit{C. Jiang} et al., Comput. Methods Appl. Mech. Eng. 357, Article ID 112565, 48 p. (2019; Zbl 1435.74040) Full Text: DOI
Chen, Ning; Hu, Yingbin; Yu, Dejie; Liu, Jian; Beer, Michael A polynomial expansion approach for response analysis of periodical composite structural-acoustic problems with multi-scale mixed aleatory and epistemic uncertainties. (English) Zbl 1440.74020 Comput. Methods Appl. Mech. Eng. 342, 509-531 (2018). MSC: 74A40 65G30 74S05 65N30 76Q05 PDFBibTeX XMLCite \textit{N. Chen} et al., Comput. Methods Appl. Mech. Eng. 342, 509--531 (2018; Zbl 1440.74020) Full Text: DOI
Lü, Hui; Cai, Zicheng; Feng, Qianlang; Shangguan, Wen-Bin; Yu, Dejie An improved method for fuzzy-interval uncertainty analysis and its application in brake instability study. (English) Zbl 1440.74476 Comput. Methods Appl. Mech. Eng. 342, 142-160 (2018). MSC: 74S99 65G30 74H55 PDFBibTeX XMLCite \textit{H. Lü} et al., Comput. Methods Appl. Mech. Eng. 342, 142--160 (2018; Zbl 1440.74476) Full Text: DOI
Huang, Youqin An interval algorithm for uncertain dynamic stability analysis. (English) Zbl 1427.74067 Appl. Math. Comput. 338, 567-587 (2018). MSC: 74H55 37N20 74H45 PDFBibTeX XMLCite \textit{Y. Huang}, Appl. Math. Comput. 338, 567--587 (2018; Zbl 1427.74067) Full Text: DOI
Wanner, Thomas Computer-assisted bifurcation diagram validation and applications in materials science. (English) Zbl 1406.35040 van den Berg, Jan Bouwe (ed.) et al., Rigorous numerics in dynamics. AMS short course, Seattle, WA, USA, January 4–5, 2016. Lecture notes. Providence, RI: American Mathematical Society (AMS) (ISBN 978-1-4704-2814-3/hbk; 978-1-4704-4729-8/ebook). Proceedings of Symposia in Applied Mathematics 74, 123-174 (2018). MSC: 35B32 35B40 35B41 35K55 65G20 65G30 65P30 74N99 PDFBibTeX XMLCite \textit{T. Wanner}, Proc. Symp. Appl. Math. 74, 123--174 (2018; Zbl 1406.35040) Full Text: DOI
Truong, Van Huy; Liu, Jie; Meng, Xianghua; Jiang, Chao; Nguyen, Trong Tien Uncertainty analysis on vehicle-bridge system with correlative interval variables based on multidimensional parallelepiped model. (English) Zbl 1404.74207 Int. J. Comput. Methods 15, No. 5, Article ID 1850030, 17 p. (2018). MSC: 74S30 74H50 65G30 PDFBibTeX XMLCite \textit{V. H. Truong} et al., Int. J. Comput. Methods 15, No. 5, Article ID 1850030, 17 p. (2018; Zbl 1404.74207) Full Text: DOI
Wu, Di; Gao, Wei Hybrid uncertain static analysis with random and interval fields. (English) Zbl 1439.74496 Comput. Methods Appl. Mech. Eng. 315, 222-246 (2017). MSC: 74S60 65N75 65G30 74A10 PDFBibTeX XMLCite \textit{D. Wu} and \textit{W. Gao}, Comput. Methods Appl. Mech. Eng. 315, 222--246 (2017; Zbl 1439.74496) Full Text: DOI
Chakraverty, S.; Hladík, Milan; Behera, D. Formal solution of an interval system of linear equations with an application in static responses of structures with interval forces. (English) Zbl 1476.65069 Appl. Math. Modelling 50, 105-117 (2017). MSC: 65G30 65G40 74S05 PDFBibTeX XMLCite \textit{S. Chakraverty} et al., Appl. Math. Modelling 50, 105--117 (2017; Zbl 1476.65069) Full Text: DOI
Lessard, Jean-Philippe; Sander, Evelyn; Wanner, Thomas Rigorous continuation of bifurcation points in the diblock copolymer equation. (English) Zbl 1404.35030 J. Comput. Dyn. 4, No. 1-2, 71-118 (2017). MSC: 35B32 35B40 65G20 65P30 35B41 35K55 65G30 65N35 74N99 58E09 35K35 PDFBibTeX XMLCite \textit{J.-P. Lessard} et al., J. Comput. Dyn. 4, No. 1--2, 71--118 (2017; Zbl 1404.35030) Full Text: DOI
Xie, Longxiang; Liu, Jian; Zhang, Jinan; Man, Xianfeng Evidence-theory-based analysis for structural-acoustic field with epistemic uncertainties. (English) Zbl 1404.74062 Int. J. Comput. Methods 14, No. 2, Article ID 1750012, 18 p. (2017). MSC: 74H50 65G30 74H45 PDFBibTeX XMLCite \textit{L. Xie} et al., Int. J. Comput. Methods 14, No. 2, Article ID 1750012, 18 p. (2017; Zbl 1404.74062) Full Text: DOI
Belkhayat, Alicja Piasecka; Korczak, Anna Numerical modelling of the transient heat transport in a thin gold film using the fuzzy lattice Boltzmann method with \(\alpha\)-cuts. (English) Zbl 1462.74045 J. Appl. Math. Comput. Mech. 15, No. 1, 123-135 (2016). MSC: 74F05 74K35 74S99 80A21 65G30 PDFBibTeX XMLCite \textit{A. P. Belkhayat} and \textit{A. Korczak}, J. Appl. Math. Comput. Mech. 15, No. 1, 123--135 (2016; Zbl 1462.74045) Full Text: DOI
Behnke, Henning Curve veering for the parameter-dependent clamped plate. (English) Zbl 1354.74123 Nehmeier, Marco (ed.) et al., Scientific computing, computer arithmetic, and validated numerics. 16th international symposium, SCAN 2014, Würzburg, Germany, September 21–26, 2014. Revised selected papers. Cham: Springer (ISBN 978-3-319-31768-7/pbk; 978-3-319-31769-4/ebook). Lecture Notes in Computer Science 9553, 259-268 (2016). MSC: 74K20 PDFBibTeX XMLCite \textit{H. Behnke}, Lect. Notes Comput. Sci. 9553, 259--268 (2016; Zbl 1354.74123) Full Text: DOI
Jiang, C.; Zheng, J.; Ni, B. Y.; Han, X. A probabilistic and interval hybrid reliability analysis method for structures with correlated uncertain parameters. (English) Zbl 1359.74023 Int. J. Comput. Methods 12, No. 4, Article ID 1540006, 24 p. (2015). MSC: 74A40 62N05 65G30 62P35 90B25 PDFBibTeX XMLCite \textit{C. Jiang} et al., Int. J. Comput. Methods 12, No. 4, Article ID 1540006, 24 p. (2015; Zbl 1359.74023) Full Text: DOI
Garloff, Jürgen; Popova, Evgenija D.; Smith, Andrew P. Solving linear systems with polynomial parameter dependency with application to the verified solution of problems in structural mechanics. (English) Zbl 1311.65033 Chinchuluun, Altannar (ed.) et al., Optimization, simulation, and control. New York, NY: Springer (ISBN 978-1-4614-5130-3/hbk; 978-1-4614-5131-0/ebook). Springer Optimization and Its Applications 76, 301-318 (2013). MSC: 65F10 65G30 65G20 74S05 PDFBibTeX XMLCite \textit{J. Garloff} et al., Springer Optim. Appl. 76, 301--318 (2013; Zbl 1311.65033) Full Text: DOI
Samarkanov, Dmitry; Gillon, Frédéric; Brochet, Pascal; Laloy, Daniel Optimal design of induction machine using interval algorithms. (English) Zbl 1358.78089 COMPEL 31, No. 5, 1492-1502 (2012). MSC: 78M50 90C90 74P15 74F15 PDFBibTeX XMLCite \textit{D. Samarkanov} et al., COMPEL 31, No. 5, 1492--1502 (2012; Zbl 1358.78089) Full Text: DOI
Muscolino, Giuseppe; Sofi, Alba Response statistics of linear structures with uncertain-but-bounded parameters under Gaussian stochastic input. (English) Zbl 1448.74053 Int. J. Struct. Stab. Dyn. 11, No. 4, 775-804 (2011). MSC: 74H50 65G30 74S60 PDFBibTeX XMLCite \textit{G. Muscolino} and \textit{A. Sofi}, Int. J. Struct. Stab. Dyn. 11, No. 4, 775--804 (2011; Zbl 1448.74053) Full Text: DOI
Ma, Juan; Gao, Wei; Wriggers, Peter; Wu, Tao; Sahraee, Shahab The analyses of dynamic response and reliability of fuzzy-random truss under stationary stochastic excitation. (English) Zbl 1398.74165 Comput. Mech. 45, No. 5, 443-455 (2010). MSC: 74H50 74S60 70L05 74G60 65G30 74S30 PDFBibTeX XMLCite \textit{J. Ma} et al., Comput. Mech. 45, No. 5, 443--455 (2010; Zbl 1398.74165) Full Text: DOI
García, Oscar; Vehí, Josep; Campos e Matos, Jose; Henriques, António Abel; Casas, Joan Ramon Structural assessment under uncertain parameters via interval analysis. (English) Zbl 1388.74122 J. Comput. Appl. Math. 218, No. 1, 43-52 (2008). MSC: 74S30 74R99 65G30 PDFBibTeX XMLCite \textit{O. García} et al., J. Comput. Appl. Math. 218, No. 1, 43--52 (2008; Zbl 1388.74122) Full Text: DOI
Qiu, Zhiping; Xia, Yuying; Yang, Jialing The static displacement and the stress analysis of structures with bounded uncertainties using the vertex solution theorem. (English) Zbl 1173.74355 Comput. Methods Appl. Mech. Eng. 196, No. 49-52, 4965-4984 (2007). MSC: 74K99 65G40 PDFBibTeX XMLCite \textit{Z. Qiu} et al., Comput. Methods Appl. Mech. Eng. 196, No. 49--52, 4965--4984 (2007; Zbl 1173.74355) Full Text: DOI
Corliss, George; Foley, Christopher; Kearfott, R. Baker Formulation for reliable analysis of structural frames. (English) Zbl 1106.74040 Reliab. Comput. 13, No. 2, 125-147 (2007). MSC: 74K99 74S30 62N05 65G30 PDFBibTeX XMLCite \textit{G. Corliss} et al., Reliab. Comput. 13, No. 2, 125--147 (2007; Zbl 1106.74040) Full Text: DOI
Neumaier, Arnold; Pownuk, Andrzej Linear systems with large uncertainties, with applications to truss structures. (English) Zbl 1117.65063 Reliab. Comput. 13, No. 2, 149-172 (2007). Reviewer: Günter Mayer (Rostock) MSC: 65F30 65G30 74S05 PDFBibTeX XMLCite \textit{A. Neumaier} and \textit{A. Pownuk}, Reliab. Comput. 13, No. 2, 149--172 (2007; Zbl 1117.65063) Full Text: DOI
Pownuk, Andrzej Numerical solutions of fuzzy partial differential equations and its applications in computational mechanics. (English) Zbl 1124.74308 Nikravesh, Masoud (ed.) et al., Fuzzy partial differential equations and relational equations. Reservoir characterization and modeling. Berlin: Springer (ISBN 3-540-20322-2/hbk). Studies in Fuzziness and Soft Computing 142, 308-347 (2004). MSC: 74H15 35R99 65G30 65N99 PDFBibTeX XMLCite \textit{A. Pownuk}, Stud. Fuzziness Soft Comput. 142, 308--347 (2004; Zbl 1124.74308)
Qiu, Z. P.; Mueller, P. C.; Frommer, A. The new nonprobabilistic criterion of failure for dynamical systems based on convex models. (English) Zbl 1112.93038 Math. Comput. Modelling 40, No. 1-2, 201-215 (2004). MSC: 93C41 65G30 70J99 70Q05 74R99 PDFBibTeX XMLCite \textit{Z. P. Qiu} et al., Math. Comput. Modelling 40, No. 1--2, 201--215 (2004; Zbl 1112.93038) Full Text: DOI
Guo, Shuxiang; Lü, Zhenzhou; Feng, Lifu Fuzzy arithmetic and solving of the static governing equations of fuzzy finite element method. (English) Zbl 1113.74422 Appl. Math. Mech., Engl. Ed. 23, No. 9, 1054-1061 (2002). MSC: 74S05 74S30 74K99 65G30 PDFBibTeX XMLCite \textit{S. Guo} et al., Appl. Math. Mech., Engl. Ed. 23, No. 9, 1054--1061 (2002; Zbl 1113.74422) Full Text: DOI
Guo, Shuxiang; Lü, Zhenzhou Interval arithmetic and static interval finite element method. (English) Zbl 0991.74522 Appl. Math. Mech., Engl. Ed. 22, No. 12, 1390-1396 (2001). MSC: 74S05 74K10 65G30 PDFBibTeX XMLCite \textit{S. Guo} and \textit{Z. Lü}, Appl. Math. Mech., Engl. Ed. 22, No. 12, 1390--1396 (2001; Zbl 0991.74522) Full Text: DOI
Paredes, M.; Sartor, M.; Masclet, C. An optimization process for extension spring design. (English) Zbl 0999.74095 Comput. Methods Appl. Mech. Eng. 191, No. 8-10, 783-797 (2001). MSC: 74P10 74P05 74S99 PDFBibTeX XMLCite \textit{M. Paredes} et al., Comput. Methods Appl. Mech. Eng. 191, No. 8--10, 783--797 (2001; Zbl 0999.74095) Full Text: DOI
Worden, Keith; Osegueda, Roberto; Ferregut, Carlos; Nazarian, Soheil; George, Debra L.; George, Mary J.; Kreinovich, Vladik; Kosheleva, Olga; Cabrera, Sergio Interval methods in non-destructive testing of material structures. (English) Zbl 1045.65043 Reliab. Comput. 7, No. 4, 341-352 (2001). Reviewer: Jiří Rohn (Praha) MSC: 65G30 74S30 74M99 PDFBibTeX XMLCite \textit{K. Worden} et al., Reliab. Comput. 7, No. 4, 341--352 (2001; Zbl 1045.65043) Full Text: DOI
Quarteroni, Alfio; Sacco, Riccardo; Saleri, Fausto Numerical mathematics. (English) Zbl 0957.65001 Texts in Applied Mathematics. 37. New York, NY: Springer. xx, 654 p. (2000). Reviewer: Werner H.Schmidt (Greifswald) MSC: 65-01 00A06 65D32 65D05 65D07 65F05 65F10 65F15 65F50 65Gxx 65Hxx 65Kxx 65Lxx 65Mxx 74K10 78A55 82D37 92C35 92C55 PDFBibTeX XMLCite \textit{A. Quarteroni} et al., Numerical mathematics. New York, NY: Springer (2000; Zbl 0957.65001)
Nakagiri, Shigeru; Suzuki, Keiko Finite element interval analysis of external loads identified by displacement input with uncertainty. (English) Zbl 0957.74054 Comput. Methods Appl. Mech. Eng. 168, No. 1-4, 63-72 (1999). MSC: 74S05 74K99 65G30 93B30 PDFBibTeX XMLCite \textit{S. Nakagiri} and \textit{K. Suzuki}, Comput. Methods Appl. Mech. Eng. 168, No. 1--4, 63--72 (1999; Zbl 0957.74054) Full Text: DOI
Kulpa, Zenon; Pownuk, Andrzej; Skalna, Iwona Analysis of linear mechanical structures with uncertainties by means of interval methods. (English) Zbl 1071.74653 Comput. Assist. Mech. Eng. Sci. 5, No. 4, 443-477 (1998). MSC: 74K99 65G30 PDFBibTeX XMLCite \textit{Z. Kulpa} et al., Comput. Assist. Mech. Eng. Sci. 5, No. 4, 443--477 (1998; Zbl 1071.74653)
Qiu, Zhiping; Elishakoff, Isaac Antioptimization of structures with large uncertain-but-non-random parameters via interval analysis. (English) Zbl 0947.74046 Comput. Methods Appl. Mech. Eng. 152, No. 3-4, 361-372 (1998). MSC: 74P10 74S30 74K99 65G30 PDFBibTeX XMLCite \textit{Z. Qiu} and \textit{I. Elishakoff}, Comput. Methods Appl. Mech. Eng. 152, No. 3--4, 361--372 (1998; Zbl 0947.74046) Full Text: DOI
Rao, S. S.; Berke, L. Analysis of uncertain structural systems using interval analysis. (English) Zbl 0902.73082 AIAA J. 35, No. 4, 727-735 (1997). MSC: 74S30 74K99 65G30 PDFBibTeX XMLCite \textit{S. S. Rao} and \textit{L. Berke}, AIAA J. 35, No. 4, 727--735 (1997; Zbl 0902.73082) Full Text: DOI
Wieners, Christian A numerical existence proof of nodal lines for the first eigenfunction of the plate equation. (English) Zbl 0854.65092 Arch. Math. 66, No. 5, 420-427 (1996). Reviewer: Ch.Wieners (Stuttgart) MSC: 65N25 65N30 74S05 65N15 35P15 74K20 PDFBibTeX XMLCite \textit{C. Wieners}, Arch. Math. 66, No. 5, 420--427 (1996; Zbl 0854.65092) Full Text: DOI
Qiu, Z. P.; Chen, S. H.; Elishakoff, I. Natural frequencies of structures with uncertain but nonrandom parameters. (English) Zbl 0836.65061 J. Optimization Theory Appl. 86, No. 3, 669-683 (1995). MSC: 65F15 74H45 65G30 PDFBibTeX XMLCite \textit{Z. P. Qiu} et al., J. Optim. Theory Appl. 86, No. 3, 669--683 (1995; Zbl 0836.65061) Full Text: DOI
Behnke, H.; Goerisch, F. Inclusions for eigenvalues of selfadjoint problems. (English) Zbl 0838.65060 Herzberger, Jürgen, Topics in validated computations. Proceedings of the IMACS-GAMM international workshop, Oldenburg, Germany, 30 August - 3 September 1993. Amsterdam: Elsevier. Stud. Comput. Math. 5, 277-322 (1994). Reviewer: H.Fischer (München) MSC: 65J10 65-02 65L15 65N25 65G30 74K20 74H45 47A75 PDFBibTeX XMLCite \textit{H. Behnke} and \textit{F. Goerisch}, Stud. Comput. Math. 5, 277--322 (1994; Zbl 0838.65060)
Elishakoff, Isaac Some questions in eigenvalue problems in engineering. (English) Zbl 0719.73027 Numerical treatment of eigenvalue problems. Vol. 5, Proc. Workshop, Oberwolfach/Germ. 1990, ISNM 96, 71-107 (1991). MSC: 74H45 74H50 74S30 74K20 74E30 PDFBibTeX XML
Dong, W. M.; Chiang, W.-L.; Wong, F. S. Propagation of uncertainties in deterministic systems. (English) Zbl 0609.73098 Comput. Struct. 26, 415-423 (1987). MSC: 74K99 93B15 93B99 65G30 PDFBibTeX XMLCite \textit{W. M. Dong} et al., Comput. Struct. 26, 415--423 (1987; Zbl 0609.73098) Full Text: DOI
Adams, Ernst On sets of solutions of collections of nonlinear systems in \({\mathbb{R}}^ n\). (English) Zbl 0539.65035 Interval mathematics, Proc. int. Symp., Freiburg/Ger. 1980, 247-256 (1980). Reviewer: L.B.Rall MSC: 65H10 65F10 65G30 74G60 PDFBibTeX XML
Berger, Neil Estimates for stress derivatives and error in interior equations for shells of variable thickness with applied forces. (English) Zbl 0234.73032 SIAM J. Appl. Math. (1972). MSC: 74K15 74B10 65G30 PDFBibTeX XML