sapiСистемный анализ и прикладная информатика«System analysis and applied information science»2309-49232414-0481Belarusian National Technical University10.21122/2309-4923-2022-2-67-75sapi-565Research ArticleИнформационные технологии в образованииInformation technologies in educationМКЭ-анализ напряжений Пизанской башни как путь освоения студентами сферы виртуальных исптынийFEA stress analysis of the Tower of Pisa as a way for students to explore the sphere of virtual testingДовнарС. С.DounarS. S.

Довнар Станислав Станиславович – кандидат технических наук, доцент кафедры «Технологическое оборудование» машиностроительного факультета

 

dovnar@bntu.byАвсиевичА. М.AusiyevichA. M.

Andrej Ausiyevich – candidate of technical sciences, docent, dean of informational technologies and robotization faculty

ausi@tut.byЛапукаА. Д.LapukaA. D.penkina@bntu.byШведоваД. Н.ShvedovaD. N.dasha.shvedova111@gmail.comРоденяА. В.RodeniaA. V.mtools@bntu.byБелорусский национальный технический университетБеларусьBelarusian National Technical UniversityBelarus202217062022026775Copyright © Довнар С.С., Авсиевич А.М., Лапука А.Д., Шведова Д.Н., Роденя А.В., 20222022Довнар С.С., Авсиевич А.М., Лапука А.Д., Шведова Д.Н., Роденя А.В.Dounar S.S., Ausiyevich A.M., Lapuka A.D., Shvedova D.N., Rodenia A.V.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://sapi.bntu.by/jour/article/view/565

Выполнена МКЭ-оценка напряженного состояния Пизанской башни. Виртуальные испытания проведены для проектного вертикального и реального наклонного состояний. Выявлено несовместность деформирования барабана колонн и ствола башни. Обнаружено двукратное перенапряжение колонн нижнего яруса. Выявлены концентраторы сжатия в башне. Концентрация напряжений сопровождает винтовой ход внутри ствола. Описан дуговой концентратор сжатия, возникающий на переходе от ствола к базису. Даны рекомендации по мониторингу системы.

Собран методический опыт, позволяющий студентам полноценно участвовать в командной работе в серьезных виртуальных испытаниях в сфере CAE.

FEA of stress state for Pisa Tower is accomplished. Imaginary vertical orientation of the tower is simulated as well as its actual leaning position too. Moderate deformational incompatibility between “column drum” and “stem” load-bearing systems is revealed. Twofold overstressing of lower colonnade is found comparatively to the stem surface. Tower’s compressive stress concentrators are described. The inner helical passage into stem causes a periodical stress concentration about 1.5 – 2 times in the passage vicinity. Arch compression concentrator tied to stem – basis transition is revealed. Places for priority monitoring of marble masonry are pointed out.

Some methodic experience is gained due to lively and successful student participation in all phases of the Pisa Tower FEM simulation.

МКЭкомпьютерный аудитобразование студентовANSYSисторическая несущая системаПизанаклонная башняконцентратор сжатиянесовместность деформацийнапряжениеживучестьмониторингFEAcomputer auditstudent educationANSYSlegacy load-bearing systemPisaleaning towerconcentrator of compressionstrain incompatibilitystressdurabilitymonitoringReferencesBritannica Online Encyclopedia (2009) Leaning Tower of Pisa (Tower, Pisa, Italy). https://www.britannica.com/topic/Leaning-Tower-of-PisaBritannica Online Encyclopedia (2009) Leaning Tower of Pisa (Tower, Pisa, Italy). https://www.britannica.com/topic/Leaning-Tower-of-PisaBlack, C.B. (1898) The Riviera, or the Coast from Marseilles to Leghorn: Including the Interior Towns of Carrara, Lucca, Pisa and Pistoia. A. & C. Black, London, 148.Black, C.B. (1898) The Riviera, or the Coast from Marseilles to Leghorn: Including the Interior Towns of Carrara, Lucca, Pisa and Pistoia. A. & C. Black, London, 148.J.B. Burland, M. Jamiolkowski, C. Viggiani, (2003) The Stabilisation of the Leaning Tower of Pisa, Soils and Foundations, Volume 43, Issue 5, Pages 63-80, https://doi.org/10.3208/sandf.43.5_63J.B. Burland, M. Jamiolkowski, C. Viggiani, (2003) The Stabilisation of the Leaning Tower of Pisa, Soils and Foundations, Volume 43, Issue 5, Pages 63-80, https://doi.org/10.3208/sandf.43.5_63Burland, J.B., Jamiolkowski M., Squeglia N. and Viggiani, C. (2013) The Leaning Tower of Pisa. In: Bilotta, E., Flora, A., Lirer, S. and Viggiani, C., Eds., Geotechnics and Heritage, CRC Press, London, 207-227. https://doi.org/10.1201/b14965-11Burland, J.B., Jamiolkowski M., Squeglia N. and Viggiani, C. (2013) The Leaning Tower of Pisa. In: Bilotta, E., Flora, A., Lirer, S. and Viggiani, C., Eds., Geotechnics and Heritage, CRC Press, London, 207-227. https://doi.org/10.1201/b14965-11ZIENKIEWICZ, O.C. and TAYLOR, R.L. (2000) The finite element method. Butterworth-Heinemann, vol. 1: Basis. Oxford.ZIENKIEWICZ, O.C. and TAYLOR, R.L. (2000) The finite element method. Butterworth-Heinemann, vol. 1: Basis. Oxford.Geng, J. , Meng, Z. , Yin, B. and Zhu, L. (2020) Simulation on Sequential Construction Process and Structure of the Pisa Tower. Journal of Building Construction and Planning Research, 8, 30-41. doi: https://doi.org/10.4236/jbcpr.2020.81003Geng, J. , Meng, Z. , Yin, B. and Zhu, L. (2020) Simulation on Sequential Construction Process and Structure of the Pisa Tower. Journal of Building Construction and Planning Research, 8, 30-41. doi: https://doi.org/10.4236/jbcpr.2020.81003Konstantina Papadopoulou, George Gazetas (2017) Leaning instability of the Tower of Pisa, re-examined by 3D F.E. analyses. Proceedings of the 19th International Conference on Soil Mechanics and Geotechnical Engineering, Seoul.Konstantina Papadopoulou, George Gazetas (2017) Leaning instability of the Tower of Pisa, re-examined by 3D F.E. analyses. Proceedings of the 19th International Conference on Soil Mechanics and Geotechnical Engineering, Seoul.Roca, P., Cervera, M., Gariup, G., & Pela’, L. (2010). Structural Analysis of Masonry Historical. Constructions. Classical and Advanced Approaches. Archives of Computational Methods in Engineering, 17(3), 299–325. http://doi.org/10.1007/s11831-010-9046-1Roca, P., Cervera, M., Gariup, G., & Pela’, L. (2010). Structural Analysis of Masonry Historical. Constructions. Classical and Advanced Approaches. Archives of Computational Methods in Engineering, 17(3), 299–325. http://doi.org/10.1007/s11831-010-9046-1Palermo, M., Silvestri, S., Gasparini, G., Baraccani, S., & Trombetti, T. (2015). An approach for the mechanical characterisation of the Asinelli Tower (Bologna) in presence of insufficient experimental data. Journal of Cultural Heritage. http://doi.org/10.1016/j.culher.2014.05.002Palermo, M., Silvestri, S., Gasparini, G., Baraccani, S., & Trombetti, T. (2015). An approach for the mechanical characterisation of the Asinelli Tower (Bologna) in presence of insufficient experimental data. Journal of Cultural Heritage. http://doi.org/10.1016/j.culher.2014.05.002Squeglia, N., Bentivoglio, G. (2015) Role of monitoring in historical building restoration: The case of Leaning Tower of Pisa. International J. of Architectural Heritage: Conservation, Analysis, and Restoration, 9(1), 38-47.Squeglia, N., Bentivoglio, G. (2015) Role of monitoring in historical building restoration: The case of Leaning Tower of Pisa. International J. of Architectural Heritage: Conservation, Analysis, and Restoration, 9(1), 38-47.

The authors declare that there are no conflicts of interest present.