Bileşik dönel yüzeysel taşıyıcı sistemlerin sonlu elemanlar hesabı ve parametrik bir çalışma
Başlık çevirisi mevcut değil.
- Tez No: 75487
- Danışmanlar: PROF. DR. METİN AYDOĞAN
- Tez Türü: Yüksek Lisans
- Konular: İnşaat Mühendisliği, Civil Engineering
- Anahtar Kelimeler: Arıtma tesisleri, Sonlu elemanlar yöntemi, Taşıyıcı sistemler, Shell of revolution-Circular Plate Systems -Finite Element Method xlx, Treatment plants, Finite element method, Supporting systems
- Yıl: 1998
- Dil: Türkçe
- Üniversite: İstanbul Teknik Üniversitesi
- Enstitü: Fen Bilimleri Enstitüsü
- Ana Bilim Dalı: İnşaat Mühendisliği Ana Bilim Dalı
- Bilim Dalı: Belirtilmemiş.
- Sayfa Sayısı: Belirtilmemiş.
Özet
ÖZET Arıtma Tesisleri ve sıvı haznelerinin teşkilinde çoğunlukla dönel kabuk ve dairesel plakların bileşiminden oluşan sistemlerle karşılaşılmakta ve bu sistemlerde genellikle dönel simetrik yükler hakim olmaktadır. Bu çalışmada ise Bileşik Dönel Yüzeysel Taşıyıcı Sistemlerin Sonlu Elemanlar Deplasman Yöntemiyle Hesabı anlatılmıştır. Dönel simetriden ötürü çubuk benzeri iki düğüm noktalı ve bir düğüm noktasında 2 yerdeğiştirme, bir dönme olmak üzere 3 serbestlik (toplam 6 serbestlik) olan bir sonlu eleman kullanılmıştır. Genel bir kesik konik kabuk sonlu eleman formülasyonu yeterli olmakta ve Winkler anlamında zemine yataklarıma dikkate alınabilmektedir. Bu amaçla aynı zamanda Sonlu Elemanlar Yönteminin esaslarından kısaca bahsedilmiş, bileşik dönel yüzeysel taşıyıcı sistemler ve bu sistemlere dönel simetrik yükler etkimesi hali anlatılmıştır. Bu çalışma kapsamında, bileşik dönel yüzeysel taşıyıcı sistemlerin sonlu elemanlarla hesabına ilişkin yazılmış olan DOKAB isimli bir bilgisayar program kullanılmıştır. Çalışmanın son bölümünde bu programın akış diyagramı verilmiş, uygulamalar yapılmış ve zeminle ilgili parametrik çalışmalar yapılmıştır. Xiii
Özet (Çeviri)
THE ANALYSIS OF COMMON SHELL OF REVOLUTION-CIRCULAR PLATE SYSTEMS BY FINITE ELEMENT DIPLACEMENT METHOD AND A PARAMETRIC STUDY In the cleaning systems and liquid containers it is encountered generally with the shell of revolution-circular plate systems under the symmetrical loading. In this study the solution of these systems is achieved by finite element displacement method. The used element has two nodes with three degrees of freedom Per node, namely two displacements and one rotation similar to bar element considering the rotational symmetry. Only a general rotational symmetric conic element is formulated to solve this problem. Embedment on Winkler foundation can be taken into account in this formulation. In this study a program written by Prof. Dr. Metin AYDOGAN in Computer language FORTRAN for“The Analysis Of The Common Shell Of Revolution- Circular Plate Systems Under Rotational Symmetrical Loading”, called DOKAB has been used. This study includes seven main parts; First part is the Introduction of this subject and mentions the necessarity of numerical methods. The real solution of such problems is always so difficult and numerical Integration methods such as Finite Element Displacement Method is used. The second part includes the summary of Plates and Shells, A shell is a structure which can be derived from a thin plate by initially forming the middle plane to a singly curved surface. If the strain elements which effect in the shell are linearly distributed during thickness than this assumption results by Membrane Position. The Membrane formulation is as below, M9«0, Me*0, M,e = M(V*0, Q<p«0, Qe«0 At the axi- symmetrical loading loads and strain elements are not respected to 9. At the rotational cylindrical shell ri=oo and r2=a (that ri and r2 are the curvatures of a shell) xlvrotation axes ABsds- Figure 1 Co-ordinates of Axi- Symmetric Shell Figure 2 Stress Resultants of a Shell XV+î»^“b v^.^ Q*<* :*»j t i Qy.djt î fe.* gt-4^, (^+^^>dx Figure 3 Plate Equilibrium Equations Third part mentions about Finite Element Displacement Method Formulation and general equations of Finite Element Displacement Method. After giving the general equations some special cases for ”Shells Under Rotational Symmetrical Loading“ is mentioned and the formulation is given. Shell represented as a series of conical frustra. For this case some assumptions has been done,. Shell is thick. Linear Elastic Theory is used. Loads effects at the central surface It will be found that considerable simplification can be achieved if account is taken of axial symmetry of the structure. In particular if both the shell and the loading are axi- symmetric it will be found that the elements become ”one dimensional“. The first approach to the finite element solution of axi- symmetric shells was presented by Grafton and Strome. In this the elements are simple conical frustra and a direct approach via displacement functions is used. In axi-symetrical shells in common with all other shells both bending and ”in plane“ or ”membrane" forces will occur. For example in an axi-symmetric shell under axi- symmetric loading the displacement of a point on the middle surface is determined by two components u and w in the tangential and normal directions. xvlThe four strain components are given by the following expression, provided the angle <)) does not vary {e} Xs Xe du/ds (wcos^+usin«j))/r -d2w/ds2 (-sin$/r).(dw/ds) This results in four internal stress resultants and related to the strains by an elastisity matrix [D] {o}= Ns No Ms Me [»] {e} Element Characteristics-Axi Symmetrical Loads > Let the shell be divided by nodal surfaces into a series of conical frustra, as shown in Figure 4. The nodal displacements at points such as i and j will have to define uniquely the deformations of the element via prescribed shape functions. At each node the axial and radial movements and a rotation will be prescribed. All three components are necessary as the shell can carry bending moments. The displacement of a node I can thus be defined by three components Ui {8} - Jwi xvflFigure 4 An element of an axi -symmetric shell The element with two nodes, ij, thus possesses six degrees of freedom, determined by the element displacements, m The displacements within the element have to be uniquely determined by the nodal displacements {8e} and the position s, w= > [NHöy If u is taken as varying linearly with s and w as a cubic in s we shall have six undetermined constants, which can be determined from the nodal values of u, w and Fourth part includes the computer program. The data cards and flow diagram of the program has been given. This program was prepared by Prof. Dr. Metin AYDOGAN by using the computer language FORTRAN. The explanations of the terms which are used in the data cards are also given at this part. Fifth part gives examples of such problems. For this aim four examples are solved Solutions of that problems have been done by using the above mentioned program. The data cards, results and explanations of the systems have been given. At the first example only water load inside and gravitational weight of the system have been taken into account and at the fourth example also sou load outside have been taken and the results for each case have been given. These examples and results have shown us the satisfactory results of this computer program. xvlllSixth part includes a parametric study when C parameter changes, how it effects on system and how displacements, moments Mx, Mt and Normal forces Ns, Nt changes. At the final stage of this study, solutions and comments are given as a result in accordance to the parametric studies. And also the change ratio of w, Nt, Mx in accordance to C (foundation coefficient kN/m3) parameter are given. For example if C increases from 10.000 kN/m3 to 100.000 kN/m3 than Nt decreases from 321.47 to 246.34 for the point 7 of the system that is used for the parametric study. At the annexes, the solution diagrams of Examples and the Tables showing the displacements and moments and normal forces have been given.
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