Deformability and Stability of Rectangular Sandwich Panels with Cuts under In-Plane Loading

Gela Kipiani

Abstract


In this work the method of defining the critical load for rectangular sandwich panels having within themselves definite length cuts in a direction parallel with one of their sides is described. The coefficients of stability are determined by equating to zero the bending moments and the shear forces at the borders of the cut. This condition together with the rest of the boundary conditions for a panel forms the system of homogeneous equations.  By equating to zero the determinant the critical load is obtained.


Keywords


cut; panel; hole; stability; generalized function; in-plane loading

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References


Guz' A.N. (1971) Ustoichivost' trekhmernykh deformiruemykh tel [Stability of three-dimensional stressed bodies], Naukova Dumka, Kiev, USSR.

Grigoliuk E.I, Chulkov P.P. (1973) Ustoichivost' i kolebaniia trekhsloinykh obolochek [Stability and oscillations of three-layer shells], Mashinostroenie, Moscow, USSR.

Savin E.I. (1968) Raspredelenie napriazhenii okolo otverstii [Stress distribution near the holes], Naukova Dumka, Kiev, USSR.

Preobrazhenskii I.N. (1981) Ustoichivost' i kolebaniia plastinok i obolochek s otverstiiami [Stability and oscillations of plates and shells with holes], Mashinostroenie, Moscow, USSR.

Mikhailov B.K. (1980) Plastiny i obolochki s razryvnymi parametrami [Пластины и оболочки с разрывными параметрами], Izdatel'stvo LGU, Leningrad, USSR.

Alumiae N.A. (1972) Teoriia uprugikh obolochek i plastinok. Mekhanika v SSSR za 50 let [The theory of elastic shells and plates. Mechanics in the USSR for over 50 years], Nauka, Moscow, USSR, pp. 227-266.

Oniashvili O.D. (1957) Raschet obolochek i drugikh tonkostennykh prostranstvennykh konstruktsii. Stroitel'naia mekhanika v SSSR. 1917-1957 [Calculation of shells and other thin-walled spatial structures]. Stroitel'naia mekhanika v SSSR 1917-1957 [Structural mechanics in the USSR 1917-1957], Gosstroiizdat, Moscow, pp. 160-196.

Oniashvili O.D. (1969) Raschet obolochek i drugikh tonkostennykh prostranstv ennykhkonstruktsii [Calculation of shells and other thin-walled spatial structures]. Stroitel'naia mekhanika v SSSR. 1917-1969 [Structural mechanics in the USSR. 1917-1969 ], Stroiizdat, Moscow, pp. 165-202.

Джанелидзе Г.И. (1948) Obzor rabot po teorii izgiba tonkikh plit, opublikovannykh v SSSR [A review of published in the USSR studies on the theory of bending of thin plates], Journal of Applied Mathematics and Mechanics, Vol. 12, Issue 1, pp. 109-128.

Nash W.A. (1957) Bibliography of shells and shell-like structures. Part I/ David Taylor Model Basis. Report, 803 1954. Part II. Dep. Of Eng. Mech. Univ. of Florida

Naghdi P.M. (1972) The theory of shells and plates. Flugge’s and Truesdell C. (eds) Handbook der Physiks, VI a/2 (Festkörpermechanik), Springer Verlag, Berlin, Germany, pp. 425-640.

Kurshin L.M. (1962) Obzor rabot po raschetu trekhsloinykh plastin i obolochek [A review of studies on the calculation of three-layer plates and shells]. In Raschet prostranstvennykh konstruktsii [Calculation of spatial structures], Issue. 7, Stroiizdat, Moscow, pp. 163-192.

Mikhailov B.K., Kipiani G.O. (1987) Obzor rabot ob issledovaniiakh ustoichivosti trekhsloinykh plastin s priamougol'nymi otverstiiami i vyrezami [A review of works on the studies of stability of three-layer plates with rectangular holes and cuts]. Leningrad Institution of Civil Engineering, VINITI, Leningrad, USSR.

Kipiani G.O. (2013) Review of works on the calculation of thin-walled spatial systems with discontinuous parameters (1980-2013). In Aktual'nye problemy arkhitektury i stroitel'stva [Advanced topics of architecture and construction], proceedings of V international conference, 25-28 June 2013, In 2 vol., Vol. 1, Saint Petersburg, pp. 262-267.

Vol'mir A.S.(1967) Ustoichivost' deformiruemykh sistem [The stability of deformable systems]. NaukaMoscow, USSR.

Mikhailov B.K., Kipiani G.O. (1996) Deformirovannost' i ustoichivost' prostranstvennykh plastinchatykh sistem s razryvnymi parametrami [Deformation and stability of spatial platelike systems with discontinuous parameters]. Stroiizdat SPB, Saint Petersburg, RF.

Mikhailov B.K., Kipiani G.O. (1988) Prakticheskii metod rascheta na ustoichivost' elementov zdanii v vide trekhsloinykh panelei s priamougol'nymi proemami [A practical method for calculating the stability of the building elements in the form of three-layer panels with rectangular openings]. In Proektirovanie i raschet stroitel'nykh konstruktsii [Design and calculation of building structures], Leningrad, pp. 59-64.

Mikhailov B.K., Kipiani G.O. (1988) Ustoichivost' trekhsloinykh rebristykh plastin [Stability of three-layer ribbed plates]. Izvestiia Vuzov. Stroitel'naia mekhanika, collection of scientific papers. Karaganda technical university, Karaganda, pp. 64-68.

Mikhailov B.K., Kipiani G.O. (1989) Ustoichivost' trekhsloinykh priamougol'nykh plastinok, podkreplennykh rebrami [Stability of three-layer rectangular plates, supported by ribs]. Izvestiia Vuzov. Stroitel'stvo i arkhitektura, Novosibirsk, No. 1, 29-30.

Kipiani G.O. (1995) Issledovanie napriazhenno-deformirovannogo sostoianiia sbornykh trekhsloinykh panelei s otverstiiami [A study of stress-strain state of the three-layer modular panels with holes]. Matematicheskoe modelirovanie, chislennye metody i kompleksy programm [Mathematical modeling, numerical methods and complexes of programs]. Saint Petersburg, RF, pp. 142-146.

Kipiani G.O., Mikhailov B.K., Moskaleva V.G. (1992) Ustoichivost' trekhsloinykh obolochek i plastin s narusheniiami sploshnosti v vide razrezov i otverstii [Stability of three-layer shells and plates with discontinuities in the form of cuts and holes]. Issledovanie po teorii plastin i obolochek [Research on the theory of plates and shells], 25:115-120.

Kipiani G. (2008) Design procedure on stability of three-layered plate with cuts and holes. Georgian International Journal of Science and Technology, vol. 1, № 4, Nova Science Publishers Inc, pp. 327-342.

Mikhailov B.K., Kipiani G.O., Moskaleva V.G. (1991) Osnovy teorii i metody rascheta na ustoichivost' trekhsloinykh plastin s razrezami [Fundamentals of the theory and methods for calculating the stability of three-layer plates with cuts]. Metsniereba, Tbilisi, Georgia.

Kipiani G., Gegenava G., Rajczyk Marlena, Kakhidze R. (2012) Stability of three-layered plates with rectangular cuts calculation of new anti-snow avalanche construction. Proceedings of the 4th International Conference on Contemporary Problems in Architect and construction Sustainaible Building Industry to the Future. Vol. II, edited by Jaroslaw Rajczyk, Arnold Fabian, September 24-27, 2012, Szenstochowa, Poland, pp. 41-47.

Kipiani G., Okroshidze A. (2013) Method of analysis of three-layered plates with anchor links between layers on stability and deformability. Problems of Mechanics 4(53), Tbilisi, pp. 99-103.

Kipiani G. (2014) Definition of critical loading on three-layered plate with cuts by transition from static problem to stability problem. Contemporary Problems in Architect and Construction. Selected peer reviewed papers the 6th International Conference on Contemporary Problems of Architect and Construction, June 24-27, 2014, Ostrava, Czech Republic/ Edited by Darja Kubeckova, Trans. Techn. Publications LTD, Switzerland, pp. 143-150




DOI: https://doi.org/10.23968/2500-0055-2016-1-1-26-30

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