ENGINEERING RESEARCHAND EXAMINATION OF BUILDINGS. SPECIAL-PURPOSE CONSTRUCTION

PURPOSE AND ADVANCED METHODS OF GEODETIC TOOL MONITORING FOR MONUMENTS OF CIVIL ARCHITECTURE

Vestnik MGSU 5/2013
  • Rubtsov Igor’ Vladimirovich - Moscow State University of Civil Engineering (MGSU) Candidate of Technical Sciences, Associate Professor, Chair, Department of Engineering Surveying; +7 (499) 183-98-97, Moscow State University of Civil Engineering (MGSU), 26 Yaroslavskoe shosse, Moscow, 129337, Russian Federation.
  • Pyatnitskaya Tat’yana Aleksandrovna - Moscow State University of Civil Engineering (MGSU) Senior Lecturer, Department of Design of Buildings, Moscow State University of Civil Engineering (MGSU), 26 Yaroslavskoe shosse, Moscow, 129337, Russian Federation.

Pages 80-86

The authors summarize the results of long-term studies of the monuments of civil architecture on the territory of the Russian Federation. Legislative and engineering aspects of the process of monitoring of the aforesaid monuments are described in the article. Geodetic monitoring is the most efficient method of systematic observations. Unlike traditional geometric leveling that solely contemplates the identification of sediment values for displacement points, geodetic monitoring employs the method of trigonometric leveling. This method makes it possible to conduct systematic observations of both the vertical strain in the points of observation and their horizontal displacement. Thus, trigonometric leveling makes it possible to identify the sediment differences and to determine deviations from design surfaces and their time dependence, which is very important in case of cultural heritage items.The authors describe various methods of geodetic monitoring of civil architecture monuments: linear-and-angular measurements, method of side leveling, use of vertical projection devices, etc. It also provides information concerning methods of measurements of crack opening values.The authors provide references to regulatory documents and sources covering the problems of monitoring (systematic observations over a long time period) of industrial and civil projects; they cover the monitoring of architectural monuments, particularly, in hazardous situations.

DOI: 10.22227/1997-0935.2013.5.80-86

References
  1. Rubtsov I.V. Zadachi monitoringa na stadii vozvedeniya sooruzheniya [Monitoring Objectives at the Stage of Construction]. Integral. 2007, no. 5, pp. 86—87.
  2. Rubtsov I.V., Nazarov I.A., Lavrinenko E.D., Savushkina V.P. Uchet temperaturnykh deformatsiy pri geodezicheskom soprovozhdenii stroitel’stva vysotnykh monolitnykh zdaniy [Consideration of Thermal Deformations in the Process of Geodetic Support of Construction of Monolithic High-rise Buildings]. Vestnik MGSU [Proceedings of Moscow State University of Civil Engineering]. 2010, no. 4, pp. 329—334.
  3. Kho Ch., Zotova E.V., Akopyan V.F., Gusarenko S.P. Chislennaya otsenka NDS konstruktsiy po rezul’tatam geodezicheskikh nablyudeniy za deformatsiyami zdaniya [Numerical Evaluation of Stress-and-strain State of Structures Based on Findings of Geodetic Observations over Building Deformations]. Vestnik Tomskogo gosudarstvennogo arkhitekturnostroitel’nogo universiteta [Proceedings of Tomsk State University of Architecture and Civil Engineering]. 2012, no. 1, pp. 151—159.
  4. Kudrin A.Yu., Kachanov S.A., Nigmetov G.M., Proshlyakov M.Yu. Metodicheskie osnovy distantsionnogo monitoringa sostoyaniya stroitel’nykh konstruktsiy zdaniy i sooruzheniy [Methodological Fundamentals of Distant Monitoring of the State of Structural Elements of Buildings and Structures]. Tekhnologii grazhdanskoy bezopasnosti [Civil Safety Technologies]. 2006, vol. 3, no. 3, pp. 80—83.
  5. Korgin A.V., Zakharchenko M.A., Ermakov V.A. Monitoring tekhnicheskogo sostoyaniya otvetstvennykh sooruzheniy s ispol’zovaniem sovremennykh geodezicheskikh metodov izmereniy i chislennogo analiza metodom konechnykh elementov [Monitoring of Technical Condition of High-responsibility Structures Using Advanced Geodetic Measurement Methods and FEM-based Numerical Analysis]. Monitoring. Nauka i bezopasnost’. [Monitoring. Science and Safety.] 2011, no. 3, pp. 58—63.
  6. Korgin A.V. Informatsionnoe obespechenie inzhenernykh izyskaniy i obsledovaniy pri rekonstruktsii sooruzheniy [Information Support of Engineering Surveying and Inspection Projects in the Process of Reconstruction of Structures]. Geotekhnika [Geotechnical Engineering]. 2010, no. 1, pp. 49—54.
  7. Shakhramanjyan M.A., Nigmetov G.M., Larionov V.I., Nikolaev A.V. Advanced Procedures for Risk Assessment and Management in Russia. International Journal of Risk Assessment & Management. 2001, vol. 3, no. 4, p. 303.
  8. Cowling P. Precise Monitoring of Public Buildings. Facilities. 1995, vol. 13, no. 1, pp. 25—27.

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Geotechnical monitoring while constructingthe “diaphragm wall” in restricted conditions

Vestnik MGSU 7/2015
  • Yugov Anatoliy Mikhaylovich - Donbas National Academy of Civil Engineering and Architecture (DonNACEA) Doctor of Technical Sciences, Professor, chair, Department of Technologies and Organization of Construction, Donbas National Academy of Civil Engineering and Architecture (DonNACEA), 2 Derzhavina str., Makeevka-23d., Donetsk Province, 86123, Republic of Ukraine; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .
  • Novikov Nikita Sergeevich - Donbas National Academy of Civil Engineering and Architecture (DonNACEA) postgraduate student, Department of Technologies and Organization of Construction, Donbas National Academy of Civil Engineering and Architecture (DonNACEA), 2 Derzhavina str., Makeevka-23d., Donetsk Province, 86123, Republic of Ukraine; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .
  • Gavrilyuk Anastasiya Sergeevna - Donbas National Academy of Civil Engineering and Architecture (DonNACEA) Master Student, Donbas National Academy of Civil Engineering and Architecture (DonNACEA), 2 Derzhavina str., Makeevka-23d., Donetsk Province, 86123, Republic of Ukraine; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .

Pages 57-68

A diaphragm wall is a highly effective way to erect building substructures in urban conditions. A diaphragm wall construction minimizes urban environment violation, prevents air, surface and groundwater pollution, ensures firmness of the closely located buildings, their foundations and engineering services, and prevents settling of the ground and its surface. Geotechnical monitoring in the process of diaphragm wall construction allows revealing the influence and progress of unfavourable factors during the building activities in the conditions of the existing historical development. In the given article the current composition of geotechnical monitoring while constructing “diaphragm wall” in restricted conditions is considered. Its role in assuring safety of the construction object and the environment is discussed.

DOI: 10.22227/1997-0935.2015.7.57-68

References
  1. STO NOSTROY 2.5.74—2012. Osnovaniya i fundamenty. Ustroystvo «steny v grunte». Pravila, kontrol’ vypolneniya i trebovaniya k rezul’tatam rabot [STO NOSTROY 2.5.74—2012. Bases and Foundations. Diaphragm Wall Arrangement. Rules, Control and Requirements to the Results]. Moscow, BST Publ., 2014, 86 p. (In Russian)
  2. Rekomendatsii po proektirovaniyu i ustroystvu osnovaniy i fundamentov pri vozvedenii zdaniy vblizi sushchestvuyushchikh v usloviyakh plotnoy zastroyki v g. Moskve [Recommendations on Design and Arrangement of Bases and Foundations During Construction of Buildings Close to the Existing Ones in the Conditions of Dense Development in the Moscow City]. Moscow, Moskomarkhitektura Publ., 1999. Elektronnyy fond pravovoy i normativno-tekhnicheskoy dokumentatsii [Electronic Fund of Legislative and Normative and Technical Documentation]. Available at: http://docs.cntd.ru/document/1200003454/. Date of access: 25.03.2015. (In Russian)
  3. Rukovodstvo po proektirovaniyu sten sooruzheniy i protivofil’tratsionnykh zaves, ustraivaemykh sposobom «stena v grunte» [Manual on Designing Walls and Curtain Grouting of Buildings, Arranged as Diaphragm Walls]. Moscow, Stroyizdat Publ., 1977, 128 p. (In Russian)
  4. Maslov N.V., Gorpinchenko V.M. Monitoring nesushchikh konstruktsiy kak sostavnaya chast’ obespecheniya nadezhnosti i bezopasnosti otvetstvennykh zdaniy i sooruzheniy [Bearing Structures Monitoring as an Integral Part of Reliability and Safety of Responsible Buildings and Structures]. Seysmostoykoe stroitel’stvo. Bezopasnost’ sooruzheniy [Antiseismic Construction. Safety of Structures]. 2002, no. 5, pp. 34—37. (In Russian)
  5. Il’ichev V.A. Bezopasnost’ zhil’ya i gorodskoy sredy i ee normativno-pravovoe obespechenie [Accommodation and Urban Environment Safety and its Regulatory Support]. ACADEMIA: Arkhitektura i stroitel’stvo [ACADEMIA: Architecture and Construction]. 2004, no. 2, pp. 43—44. (In Russian)
  6. Dem’yanov A.A. Tipovaya tekhnologicheskaya karta na stroitel’stvo podzemnykh sooruzheniy. Primenenie sposoba «stena v grunte» dlya stroitel’stva sten podzemnykh sooruzheniy, fundamentov i protivofil’tratsionnykh zaves [Standard Flow Diagram for Construction of Undergound Stryctures. Application of Diaphragm Wall Method for Constructing the Walls of Underground Structures, Bases and Curtain Groutings]. Saint Petersburg, VITU Publ., 2011. (In Russian)
  7. Afanas’ev A.A., Inyutin M.A. Tekhnologiya vozvedeniya zaglublennykh chastey zdaniy v stesnennykh usloviyakh gorodskoy zastroyki [Arrangement Technology of the Buried Building Parts in the restricted urban conditions]. Aktual’nye voprosy stroitel’stva : materialy Vserossiyskoy nauchno-tekhnicheskoy konferentsii, Saransk [Current Problems of Civil Engineering. Materials of the All-Russian Scientific and Technical Conference, Saransk]. 2003, pp. 58—64. (In Russian)
  8. Petrukhin V.P., Shulyat’ev O.A., Mozgacheva O.A. Opyt proektirovaniya i monitoringa podzemnoy chasti Turetskogo torgovogo tsentra [The Experience of Design and Monitoring of the Turkish Mall Substructure]. Osnovaniya, fundamenty i mekhanika gruntov [Bases, Foundations and Soil Mechanics]. 2004, no. 5, pp. 2—8. (In Russian)
  9. Ulitskiy V.M., Shashkin A.G. Geotekhnicheskoe soprovozhdenie rekonstruktsii gorodov : Obsledovanie, raschety, vedenie rabot, monitoring [Geotechnical Support of the cities reconstruction : Inspection, Calculation, Working Process, Monitoring]. Moscow, ASV Publ., 1999, 324 p. (In Russian)
  10. Lim V.G. Inzhenernaya podgotovka organizatsionnykh resheniy stroitel’nogo proizvodstva pri rekonstruktsii promyshlennykh ob”ektov: avtoreferat dissertatsii doktora tekhnnicheskikh nauk : 05.23.2008 [Engineering preparation of the civil engineering organizational decisions during reconstruction of industrial objects: abstract of the thesis of Doctor of Technical Sciences: 05.23.2008]. Moscow, 2006, 38 p. (In Russian)
  11. Oleynik P.P. Organizatsiya stroitel’stva. Kontseptual’nye osnovy modeli i metody. Informatsionno-inzhenernye sistemy [Construction organization. Conceptual framework of the Model and Methods. Informational Engineering Systems]. Moscow, Profizdat Publ., 2001, 407 p. (In Russian)
  12. Oleynik P.P., Fomil’ L.Sh. Inzhenernaya podgotovka territorii stroitel’noy ploshchadki promyshlennogo predpriyatiya [Engineering Preparation of the Territory of Industrial Enterprise Building Site]. Moscow, Stroyizdat Publ., 1988, 240 p. (In Russian)
  13. Chang-Yu Ou. Deep Excavations. Theory and Practice. London, Taylor & Francis, 2006, 552 p.
  14. Stain V.M., Stain A.V. Reshenie geotekhnicheskikh zadach s pomoshch’yu programmnykh produktov kompanii MSC [Solving Geotechnical Tasks with the Help of MSC Software Products]. Voprosy stroitel’noy mekhaniki i nadezhnosti mashin i konstruktsiy : sbornik nauchnykh trudov MADI (GTU) [The Questions of Structural Mechanics and Safety of Machines and Constructions: Scientific Works of Moscow Automobile and Road Construction University (STU)]. Moscow, MADI Publ., 2008, pp. 128—138. (In Russian)
  15. Ragab A.A.M.A.R. Neue Planungskonzepte fuer Wustensiedlungen der Sinai-Halbinsel. Agypten: Diss. Stuttgart [s. n.], 1999, 231 p.
  16. Lee S.-J. Das Stadtbild als Aufgabe — Wege zu einer ganzheitlichen Stadtbildplanung: Diss. Stuttgart. 1995, 301 p.
  17. Zuziak Z.K. Strategie rewitalizacji przestrzeni srodmiejskiej. Krakow, 1998, 159 p.
  18. Goryachev O.M., Prykina L.V. Osobennosti vozvedeniya zdaniy v stesnennykh usloviyakh [Peculiarities of Building Influence in Restricted Conditions]. Moscow, Academia Publ., 2003, 272 p. (In Russian)
  19. Goryachev O.M., Bun’kin I.F., Prykina L.V. Organizatsionno-tekhnicheskie osnovy vozvedeniya zhilykh zdaniy v stesnennykh usloviyakh [Organizational and Technical Foundations of the Residential Buildings Construction in restricted conditions]. Mekhanizatsiya stroitel’stva [Mechanization of construction]. 2004, no. 1, pp. 6—7. (In Russian)

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Assessing the influence of wheel defects of a rolling stockon railway tracks

Vestnik MGSU 5/2015
  • Mazov Yuriy Nikolaevich - Moscow Directorate of the infrastructure of Moscow Railway head, flaw detector car, Moscow Directorate of the infrastructure of Moscow Railway, 20 Krasnoprudnaya str., Moscow, 107996, Russian Federation; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .
  • Loktev Aleksey Alekseevich - Moscow State University of Civil Engineering (MGSU) Doctor of Physical and Mathematical Sciences, Associate Professor, Department of Theoretical Mechanics and Aerodynamics, Moscow State University of Civil Engineering (MGSU), 26 Yaroslavskoe shosse, Moscow, 129337, Russian Federation; +7 (499) 183-24-01; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .
  • Sychev Vyacheslav Petrovich - Moscow State University of Railway Engineering (MIIT) Doctor of Technical Sciences, Professor, Department of Transport Construction, Moscow State University of Railway Engineering (MIIT), 22/2 Chasovaya str., Moscow, 125993, Russian Federation; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .

Pages 61-72

Transfer of the load from the wheels on the rail occurs at a very small area compared with the size of the wheels and rails. The materials near this site have a very large voltage. Determination of contact stresses is complicated by the fact that the magnitude of these stresses in the rails under actually revolving wheel load exceeds the yield and compressive strength of modern rail steel. We should note that the metal of the rail head, experiencing contact stresses, especially when the location of the pads is closer to the middle of the rail head, works in the conditions close to the compression conditions, and therefore can withstand higher voltage without plastic deformation than the standard compressible sample. But, as a rule, the observed hardening of the metal in the zone of contact stresses and lapping at the edges of the rail head indicates the presence of plastic deformation and, consequently, higher stresses in the wheel-rail contact zone than the yield strength of the metal rail even in the conditions of its operation in the rail head.The use of the design equations derived on the basis of the Hertz theory for metal behavior in elastic stage, is valid. The reason is that each individual dynamic application of wheel loads on the rail is very short, and the residual plastic deformation from the individual loads of the pair of wheels on the rail is actually small. This elastic-plastic deformation of the rail becomes visible as a result of gradual gaining of a missed tonnage of rails and wheels respectively. Irregularities on the running surface of the wheels are of two types. The most common are the so-called continuous bumps on the wheel, when due to the uneven wear of rail the original shape of the wheel across the tread surface distorts. But nowadays, more and more often there occur isolated smooth irregularities of the wheel pairs, due to the increased wear of the wheel because of the stopping and blocking of wheels of the vehicles - slides (potholes), etc.The motion of the wheels with irregularities on the surface of the rail leads to vertical oscillation of the wheel, resulting in the forces of inertia, which is an additional load on the rail. In case of movement of the wheel with isolated roughness on the tread surface of the slide there is a strike, having a very large additional impact on the rail. Such attacks can cause kinked rails, especially in the winter months when there is increased fragility of rail steel, because of lowered temperatures. This is an abnormal phenomenon and occurs relatively rarely, at a small number of isolated irregularities on a wheel of the rolling stock. As correlations connecting the contact force and local deformation in the interaction of the wheel-rail system, we use the quasi-static Hertz’s model, linear-elastic model and two elastoplastic contact models: Alexandrov-Kadomtsev and Kil’chevsky. According to the results of Loktev’s studies ratios of the contact Hertz’s theory are quite suitable for modeling the dynamic effects of wheel and rail for speeds up to 90 km/h for engineering calculations. Since the contact surface is homogeneous and isotropic, the friction forces in the contact zone are not taken into account, the size of the pad is small compared to the dimensions of the contacting bodies and characteristic radii of curvature of the undeformed surfaces, the contacting surfaces are smooth.When train is driving, the position of the wheelset in relation to the rails varies considerably, giving rise to different combinations of the contact areas of the wheel and rail. Even assuming constant axial load the normal voltage will vary considerably because of the differences in the radii of curvature of the contacting surfaces of these zones. Thus, the proposed method allows evaluating the influence of several types of wheel defects on the condition of the rail and the prospects of its use in the upper structure of a railway track on plots with different speed and traffic volumes. Also the results can be used to solve the inverse of the considered problems, for example, when designing high-speed highways, when setting the vehicle speed and axle load, and the solution results are the parameters of the defects, both wheelsets and the rails, in case of which higher requirements for the safe operation of railways are observed.

DOI: 10.22227/1997-0935.2015.5.61-72

References
  1. Tehnicheskie usloviya na raboty po rekonstruktsii (modernizatsii) i remontu zheleznodorozhnogo puti. Utverzhdennoe rasporyazhenie OAO “RZhD” ot 18.01.2013. № 75r [Technical Specifications for the Reconstruction (Modernization) and Repair of Railroad Tracks. The disposal of JSC “RZD” from 18.01.2013 no. 75r]. Moscow, 2013, 225 p. (In Russian)
  2. Loktev A.A. Dynamic Contact of a Spherical Indenter and a Prestressed Orthotropic Uflyand-Mindlin Plate. Acta Mech. 2011, vol. 222 (1—2), pp. 17—25. DOI: http://dx.doi.org/10.1007/s00707-011-0517-8.
  3. Loktev A.A. Non-Elastic Models of Interaction of an Impactor and an Uflyand-Mindlin Plate. International Journal of Engineering Science. 2012, vol. 50, no. 1, pp. 46—55. DOI: http://dx.doi.org/10.1016/j.ijengsci.2011.09.004.
  4. Loktev A.A., Sycheva A.V., Vershinin V.V. Modeling of Work of a Railway Track at the Dynamic Effects of a Wheel Pair. Proceeding of the 2014 International Conference on Theoretical Mechanics and Applied Mechanics, Venice, Italy, March 15—17, 2014. Pp. 16—19.
  5. Sargsyan А.Е., Dvoryanchikov N.V., Dzhinchvelashvili G.А. Stroitel’naya mekhanika. Osnovy teorii s primerami raschetov [Structural Mechanics. Fundamentals of the Theory with Examples of Calculations]. Moscow, ASV Publ., 1998, 424 p. (In Russian)
  6. Klassifikatsiya defektov rel’sov NTD/TsP-1-93. Katalog defektov rel’sov NTD/TsP-2-93. Priznaki defektnykh i ostrodefektnykh rel’sov NTD/TsP-3-93 : normativno-tekhnicheskaya dokumentatsiya [Classification of Rail Defects NTD/TsP-1-93. Catalogue of Rail Defects NTD/TsP-2-93. Signs of Defective and Fatal Cropped Rails NTD/TsP-3-93 : Normative and Technical Documentation]. Moscow, Transport Publ., 1993. (In Russian)
  7. Abdurashitov A.Yu., Georgiev M.N., Krysanov L.G. Nadezhnost’ raboty rel’sov v razlichnikh klimaticheskikh usloviyakh [Reliability of Rails in Various Climatic Conditions]. Мoscow, VNIIZhT Publ., 1987, 138 p. (In Russian)
  8. Kogan A.Ya., Verkhotin А.А. Raschet vozdeystviya na put’ kolesnoy pary s polzunom [Calculation of the Impact on the Path of a Wheelset with a Slider]. Issledovaniya vozmozhnostey povysheniya skorostey dvizheniya poezdov : sbornik nauchnykh trudov [Investigating the Possibilities of Increasing the Velocities of Train Performance : Collection of Scientific Works]. Moscow, Transport Publ., 1984, 224 p. (In Russian)
  9. Kryasanov L.G., Abdurashitov A.Yu. Svoystva rel’sov s kontaktno-ustalostnymi povrezhdeniyami [Properties of Rails with Contact Fatigue Damages]. Put’ i putevoe khozyaystvo [Railway and Track Facilities]. 1998, no. 8, pp. 2—4. (In Russian)
  10. Sychev V.P., Cherkashin Yu.M. O stokhasticheskikh metodakh resheniya zadach ustoychivosti i bezopasnosti funktsionirovaniya sistem zheleznodorozhnogo transporta [Stochastic Methods for Solving the Stability and Security Problems of Railway Transport Systems Functioning]. Kachestvennye svoystva, asimptotika i stabilizatsiya nelineynykh dinamicheskikh sistem : mezhvuzovskiy sbornik nauchnykh trudov : posvyashchaetsya 90-letiyu so dnya rozhdeniya professora A.A. Shestakova [Qualitative Properties, Asymptotics and Stabilization of Nonlinear Dynamic Systems : Interuniversity Collection of Scientific Works :Dedicated to the 90th Anniversary of Professor A.A. Shestakov]. Saransk, Mordova State University Publ., 2010, pp. 125—131. (In Russian)
  11. Abdurashitov A.Yu., Kuznetsov S.V. O vybore optimal’nykh profiley v sisteme «koleso — rel’s» [On Choosing the Best Profiles in the
  12. Agostinacchio M., Ciampa D., Diomedi M., Olita S. Parametrical Analysis of the Railways Dynamic Response at High Speed Moving Loads. Journal of Modern Transportation. 2013, vol. 21, no. 3, pp. 169—181.
  13. Olsson R., Donadon M.V., Falzon B.G. Delamination Threshold Load for Dynamic Impact on Plates. International Journal of Solids and Structures. 2006, vol. 43, no. 10, pp. 3124—3141. DOI: http://dx.doi.org/10.1016/j.ijsolstr.2005.05.005.
  14. Abrate S. Modelling of Impact on Composite Structures. Compos Struct. 2001, vol. 51, pp. 129—138.
  15. Abrate S. Impact on Laminated Composite Materials. Applied Mechanics Reviews. 1991, vol. 44, no. 4, pp. 155—190. DOI: http://dx.doi.org/10.1115/1.3119500.
  16. Chen P., Xiong J., Shen Z. Thickness Effect on the Contact Behavior of a Composite Laminate Indented by a Rigid Sphere. Mechanics of Materials. 2008, vol. 40, pp. 183—194.
  17. Christoforou A.P., Elsharkawy A.A., Guedouar L.H. An Inverse Solution for Low-Velocity Impact in Composite Plates. Computers and Structures. 2001, vol. 79, no. 29—30, pp. 2607—2619.
  18. Kukudzjanov V.N. Investigation of Shock Wave Structure in Elasto-Visco-Plastic Bar Using the Asymptotic Method. Archive of Mechanics. 1981, vol. 33, no. 5, pp. 739—751.
  19. Evans G.R., Jones B.C., McMillan A.J., Darby M.I. A New Numerical Method for the Calculation of Impact Forces. Journal of Physics D: Applied Physics. 1991, vol. 24, no. 6, pp. 854—858. DOI: http://dx.doi.org/10.1088/0022-3727/24/6/009.
  20. Fisher H.D. The Impact of an Elastic Sphere on a Thin Elastic Plate Supported by a Winkler Foundation. Transactions of the ASME. Journal of Applied Mechanics. 1975, vol. 42, no. 1, pp.133—135. DOI: http://dx.doi.org/10.1115/1.3423503.
  21. Jaeger J. Analytical Solutions of Contact Impact Problems. Applied Mechanics Reviews. 1994, vol. 47, no.2, pp. 35—44.

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