Nevurlu dairesel silindirik kabukların çözümü için bir yöntem

Abstract

IV ÖZET Mühendisler, denizaltı, roket, uçak, basınç kaplarının tasarımında rijitleştirilmiş kabuğu çok fazla kullandıkla rından, bu alanda araştırmalar sürekli ilgi çeker. Bu yüz den nervürlü kabuğun gerilme analizi problemi tasarım açı sından önemlidir. Rijitleştirilmiş kabukların çözümü için yapılan teorik, deneysel çalışmalar bilgisayarların kullanımı ile birlikte artmış ve sürekli gelişim içine girmiştir. Neryürlü kabuk çözümünün konu edildiği bu çalışmada Fourier serisi yaklaşımı kullanılarak nervür, kabuk ayrı dü şünülmüştür. Değişik sınır koşulları, rijitleştirme doğrul tusu, dış yük için çözüm elde edilmiştir. îki doğrultuda nervürlü kabuk için burada. -verilen çözüm yoluna benzer çalışmaya rastlanılmamıştır. Ayrıca bu çalış mada nervür, kabuk ayrı düşünüldüğü için dışmerkez rijitleş tirilmiş olması kolayca gözönüne alınabilir. Sekiz bölümden oluşan bu çalışmanın birinci bölümünde nervürlü kabuk problemi ile ilgili çalışmalar, çözümlerinde kullanılan yöntemler kısaca anlatılmıştır. İkinci bölümde, ince, elastik dairesel silindirik kabuk teorisinin temel bağıntıları çıkarılmıştır. Üçüncü bölümde, boyuna doğrultuda, çembersel doğrultuda, her iki doğrultuda nervürlü kabuk için seri yaklaşımı kulla nılarak çözüm yolu anlatılmış, gerekli ifadeler elde edil miştir. Ayrıca kullanılan büyüklüklerin tanımları yapılmış tır.Dördüncü bölümde, boyuna doğrultuda, çember sel doğrul tuda, her iki doğrultuda nervürlü kabuk için sınır koşulları yazılarak, üçüncü bölümde anlatılan içetkileşim yükleri etkisinde, çözümler bulunmuştur. Ayrıca dış yükün kabukta o- luşturduğu yer değiştirme, kuvvet bileşkeleri bu bölümde verilmiştir. Beşinci bölümde, kiriş, halkanın radyai, teğetsel içetkileşim yükleri etkisinde yerdeğiştirme, kuvvet bileşkeleri çeşitli yapıtlardan yararlanılarak elde edilmiş» bulunan sonuçlar tabloda gösterilerek karşılaştırma yapılmıştır. Altıncı bölümde, boyuna, çember sel, her iki doğrultuda nervürlü kabuklar için çözüm yapılmış sonuçlar tablo, gra fikler ile gösterilmiştir. Yedinci bölümde, sayısal uygulamalar için hazırlanan Fortran IV dilinde kodlanmış bilgisayar programı hakkında genel bilgi verilerek akış diağramları, program yapısı ve kullanılması anlatılmaktadır. Bu programlar yardımıyla değişik rijitleştirme doğrultuları, mesnetlenme biçimleri için çeşitli dış yük etkisindeki kabuklar çözülebilmektedir. Sekizinci ve son bölümde, sonuçlar verilmektedir.

VI SUMMARY Engineers designing submarines, missiles, aircrafts, pressure vessels, etc. use reinforced shells so extensively, that investigations in this area are of continuing interest. In this connection, the problem of stress analysis for a circular cylindrical shell stiffened by longitudinal strin gers and rings (ribs) which is externally loaded is import- tant in design considerations. Theoretical and experimental studies on the reinforced shells have increased with the use of the computers and are in the process of continuous development. In this thesis, the problem of computing the stress- strain states of ribbed shells using Fourier series methods which take into account the discrete disposition of ribs is considered. The solutions are obtained for different support conditions, reinforcing directions and loads. According to the knowledge of the author such a. sol ution for shells reinforced with ribs in two directions, does not exist. Furthermore, since the formulation takes the discrete disposition of ribs into account, the effect of ec centricity between shell median surface and rib centerline may be investigated for cylindrical shells subjected to ex ternal loads. In this study three different types of reinforcement are considered. Firstly, a closed circular cylindrical shell having longitudinal stringers subjected to statical loads is inves-VII t i gated. In this case the cylindrical shell is assumed to be simply supported or infinitely long. In the second case, a closed circular cylindrical shell having a single ring at its midlength subjected to statical loads is investigated. The circular cylindrical shell is as sumed to be simply supported or infinitely long. In the third case, a closed circular cylindrical shell having longitudinal stringers and rings subjected to stat ical loads is investigated. The circular cylindrical shell is assumed to be simply supported. For the first case, the author was not able to find a comparable solution. Therefore no numerical result is given. The result of second and third cases are in agreement with the previously given data. In these cases maximum de flection of the shell does not occur under the load. The reason for a behaviour of this nature can be explained by considering the bending stresses. The eccentricity of the rib median line with respect to the shell median surface plays a significant role in determining the response of the structure to the applied loads. This thesis has eight sections. In the first section previous theoretical and experimental studies have been given for the ribbed shells are summarized. Also methods of solutio are explained briefly. In the second section, the assumptions for the theory of thin, elastic circular cylindrical shells, the governing equations, the internal forces and the equilibrium equationsVIII are sunmarized in accordance with Flügge' s equations. In the third section, shells reinforced in the longi tudinal direction, circumferential direction and the both directions are analyzed using Fourier series and the govern ing equations of the problem are obtained. Additionally the notation used in this section is explained. In the fourth section, boundary conditions are written for a shell ribbed in the longitudinal direction, circumfer ential direction and the both directions, and solution of the shell subjected to interaction loads, which are men tioned in third section, are obtained. Under the influence of the external loads for smooth shell the governing equations, the internal forces are ob tained in terms of Fourier series. In the fifth section, the stringer and the ring are investigated under the influence of radial and circumfer ential interaction loads. Displacements and stress result ants are obtained for the ring in three different ways as they were carried out by Langhaar, In an and Flügge. They are summarized in a table. In this way it has been possible to compare them easily with each other. After the analyses of the ring, stringer and the shell have each been completed, the solution of the ribbed shell can be obtained. Since all quantities regarding the ring and the stringer are obtained using Fourier series, it is convenient to use the same formulation for the shell. Thus, the radial and circumferential rib-shell interaction loadsIX are represented by such series with unknown harmonics an and bn. The equations of equilibrium are used to determine the solutions for a shell under the line loadings, which comes into the problem through the boundary conditions. The analy sis yields the displacements as a function of ajj and bn. Similarly» rib displacements are determined as a function of an, bn and external loads. Having completed the analysis of the rib and the shell problem, it is necessary to impose the compatibility condi tions along the line of contact so that the radial and cir cumferential displacements of the rib and shell are respect ively equal. These conditions yield infinite number of pairs of simultaneous equations for the interaction load harmonics an and bn. After these quantities have been obtained, the solution procedure can be continued for the displacements and stresses for the ribbed shell. Since, in general, rib axes are not in the shell middle surface, an eccentricity effect is thus introduced which has a pronounced influence on the bending stresses in the shell. In the sixth section, numerical results for the sol ution of shell ribbed in the longitudinal direction, circum ferential direction and the both directions are given in tables and in graphs. In the seventh section, the logic and the flow charts of the computer program are presented. This program is coded in Fortran IV and numerical computations are carried out in Burroughs 3700 computer. The program is explained and relatedgeneral Information is given. By means of this program the solution of closed circular cylindrical shell with different stiffening directions, support conditions, subjected to vari ous external loads can be analyzed. At the end of this section the input data and output information of the program is ex plained. In the eigtht and the last section conclusions are presented.