Sonlu elemanlar yöntemiyle kiriş ve düzlem gerilme elemanları arasında geçiş elemanı oluşturulması ve boşluklu perdelerde uygulanması
Determination of transient element between beam and plane stress elements using fintte element method and its applications to shear-walls with openings
- Tez No: 66685
- Danışmanlar: PROF. DR. M. ERTAÇ ERGÜVEN
- Tez Türü: Yüksek Lisans
- Konular: İnşaat Mühendisliği, Civil Engineering
- Anahtar Kelimeler: Belirtilmemiş.
- Yıl: 1997
- Dil: Türkçe
- Üniversite: İstanbul Teknik Üniversitesi
- Enstitü: Fen Bilimleri Enstitüsü
- Ana Bilim Dalı: İnşaat Ana Bilim Dalı
- Bilim Dalı: Yapı Mühendisliği Bilim Dalı
- Sayfa Sayısı: 105
Özet
ÖZET Yüksek lisans tezi olarak sunulan bu çalışma genel olarak Sonlu elemanlar yöntemi ile geçiş elemanı oluşturulması ve Yatay yük etkisi altındaki boşluklu perdelerin hesap yöntemlerinin incelenmesidir. İnşaat mühendisliği problemlerinde, her türlü yapının tasarımı ve çözümünde, son yıllarda popülaritesi son derece artan Sonlu elemanlar yöntemi; malzeme özelliklerinin değişkenliği, sınır koşullarının farklılığı gibi unsurları çözüme kolaylıkla dahil edebilen nümerik bir metot olarak kullanılmaktadır. Bu tez çalışmasında Büyük boşluklu perdelerin sonlu elemanlar yöntemi ile Geçiş elemanı kullanılarak çözümü ve Fiktif çerçeve çözümü sayısal örneklerle verilerek karşılaştırılmıştır. Tezin ilk bölümlerinde önce sonlu elemanların genel formülasyonu, bir ve iki boyutlu elemanlar ve rijitlik matrislerinin hesabı yapılmıştır. Daha sonraki bölümde Büyük boşluklu perdelerin hesabında kullanılmak üzere perde ve bağlantı kirişi arasında bir Geçiş elemanı oluşturulmuş ve rijitlik matrisi hesaplanmıştır. Son bölümde ise Büyük boşluklu perdelerin çerçeve çözümü için gerekli birim deplasman sabitleri verildikten soma üç katlı antimetrik yüklü, simetrik bir boşluklu perdenin, önce sonlu elemanlar yöntemi ile çözümü (Geçiş elemanı kullanılarak) somada aynı sistemin çerçeve olarak ele alınarak, Kirişlerin perde içinde kalan kısımlarının perde kenarından itibaren ne kadar uzaklıkta sonsuz rijit alınabileceğini gösteren çeşitli X uzunlukları için Açı yöntemi ile çözümleri yapılmıştır. Daha sonra aynı örnek boyudan değiştirilerek aynı yöntemlerle çözülmüş ve gerek Sonlu elemanlar yöntemi ile gereksede Açı yöntemi ile elde edilen sonuçlar aynı tablo üzerinde verilerek karşılaştırma yapılmıştır. Ayrıca aynı örneklerin SAP90 çözümleride tabloda verilmiştir. Yapılan sayısal örneklerin Sonlu elemanlar yöntemi ile çözümünde iyi sonuçlar elde edilmesi için sistem birçok elemana ayrılmıştır. Bu sistemin çözümü için“Bosper”fortran programı geliştirilerek Sonlu elemanlar yöntemi ile çözümlerde bu program kullanılmıştır. XI
Özet (Çeviri)
SUMMARY Finite Element Method: in recent years, numerical methods have continued to expand and diversify into ali the majör fields of scientific and engineering studies. They have become popular due to rapid advancements in computer technology and its availability to engineer. in these methods, Finite Element Method is the most popular method in engineering science. it has been applied to a large number of problems in widely diflferent fields. it has now applications in a wide variety of field such as solid mechanics, fluid mechanics, heat transfer, semiconductor devices, electricity and magnetism, biomechanics, ete. The development of the finite element method as an analysis tool essentially began with the advent of the electronic digital computer. For the numerical solution of a structural ör continuum problem it is basically necessary to establish and solve algebric equations that gövem the response of the system. Using the finite element method on a digital computer, it becomes possible to establish and solve the governing equations for complex in a very effective way. it is mainly due to the generality of the structure ör continuum that can be analyzed, as well as the relative case of establishing the governing equations, and for the good numerical properties of the system matrices involved that the finite element method has found wide appeal. As is often the case with original development, it is rather difficult to quote an exact date on which the finite element method was invented, but the roots of the method can be traced back to three separate research groups: engineers, physicists and applied mathematicians. Although in principle published already, the finite element method obtained its real impetus from the independent developments carried out by engineers. Important original contributions appeared in papers by Turner and Argyris and Kelsey. The name“ finite element”was coined in a paper by Clough, in which the technique was presented for plane stress analysis. Since then, a large amount of research has been devoted to the technique, and a very large number of publications on the finite element method is available at present. The method essentially involves dividing the body in smaller elements of various shapes (truss in one-dimensional case, triangules ör rectangules in two- dimensional cases and tetrahedron ör brick in three-dimensional cases, ete.) held together at the nodes which are corners of elements. The more number of element used to model the problem, the berter approximation to the solution obtained. Displacement at the nodes are treated as unknowns and are calculated. The displacements at any point with an element are related to the xiidisplacement at the nodes by making certain assumptions. Displacements are fundamental variables. From the displacement field within the element, strain can be calculated. From the strains, using the stress-strain relationship, stresses can be calculated. The finite element method has a lots of advantages. The methods strength lies in its generality and flexibility to handle all types of loads, sequences of constructions, installation of supports etc. One of the superioirty of the finite element method is introducing the boundary conditions after setting up the system stiffness matrices. Because of these advantages, Finite Element Method has been extremely popular with engineers. Inspite of above advantages, Finite element method has some disadvantages. The major disadvantage of the method is that considerable effort is required in preparing data for a problem and using a large high speed digital computer. Preparing data problem is particularly crucial in three-dimensional problems and has led to mesh generation programs. These program produce the input data required for the finite element method program. The method is also expensive in computer time. A large set of simultaneous equations have to be solved to obtain solutions. The computer time goes up further if the problem is nonlinear. For a nonlinear problem, the set of simultaneous equations are required to be solved a lot of times. The general description the finite element method can be detailed in a step by step procedure. This sequence of steps describe the actual solution process that that is followed in setting up and solving any equlibrium problem. First step: The first step is to divide the continuum or solution domain into the element. The continuum or solution domain is the physical body, structure or solid being analyzed. The element shape and sizes have to be convenient for the form of boundary and the property of continuity of the domain. Sometimes it is not only desirable but also necessary to use different types of elements in the same problem. Although the number and the type of elements to be used to in given problem are matters of engineering judgement, the analist can rely on the experience of the others for quideliness. Second step: The second step is to assign nodes to each element and to determine the necessary number of the nodal parameters. The choose type of interpolation function to represent the variation of the field variable over the element. The field variable may be a scalar, a vector or a high order tensor. Generally, polynomials are often selected as interpolation function for the field variable. Because they are easy to integrate and differentiate. The degree of the polynomials chosen depends on the number of nodes and certain continuity requirements imposed at nodes and along the element boundaries. The magnitude of field of field variable as well as the magnitude of its derivatives at nodes may be taken as node parameters. Third step: Once the finite element model has been established, users are ready to determine equations expressing the properties of the individual elements. The xmderivation of the finite element equation may be achieved by direct, varitional or the residuals methods. Fourth step: If the local coordinates axes are used for determining the behaviour of equation of the elements, they should be transformed to the global coordinate system. Fifth step: If there are any nodes apart from the corners, especially in the element, they shoul be compensated for. Sixth step: Assembly of the algebric equations for the overall discretized continuum. This process includes the assembly of overall or global stiflhess matrix for the entire body from the individual element stiflhess matrices, and the overall or global force or load vector from the element nodal force vectors. The most common assembly technique is known as the Direct stiffness method. Seventh step: In the seventh step, the boundary conditions should be introduced into the system of the system behaviour equations. Eighth step: The algebric equations assembled in the step six are solved for the unknown nodal parameters. If the equations in the system are linear, a number of standart solution techniques can be used easly. But if the equations are nonlinear, their solution is more difficult to obtain. Ninth step: Computation of the elements nodal parameters and calculation of strains and stresses. In certain cases the magnitudes of the primary unknowns, that is the nodal displacements, will be all that are required for an engineering solution. More often, however, other quantities derived from the primary unknowns, such as strains and stresses, must be computed. Transient element : The main aim of this thesis is using finite element method producing Transient element between beam element and plane stress elements. Beam element Plane stress element Transient element XIVAs shown in figure above this element is connecting beam and plane stress elements. As shown, this element has three nodes: Two of them are coming from plane stress element and one of them is coming from beam element. As known, Plane stress elements nodal degree of freedom is 2 (u and v). But beam elements nodal degree of freedom is 3 (u, v and 0). tY i ?Uı B u2 To establish the element stiffness matrix, firstly nodal interpolation functions must be defined. h^l + rXl + s) h2=i(l + r)(l-s) K 4(l-r) After that, using interpolation functions, the displacements of elements can be obtained. u(r,S) = (l(l + rXl + s))u,+(i(l + r)(l-s))u2+(l(l-r))u,-(iS(l(1-r)))eî v(r,s) = (I(l + r)(l + s))v1+(I(l + rXl-s))v2+(l(l-r))v, After that, using these displacements, [B] matrix can be found. [B] = 1 + s o 0 1 + r 2B 1 + r 1 + s 1-s 2A 0 1 + r 0 1 + r " 2B 1-s 2B 2A 2B 2A XVFinally, using [B] and [D] (material matrix), Element stiffness matrix can be found. M = tJJ[Br[D][B]dV Shear-walls with openings : Structural walls are widely used as lateral load bearing elements in designing earthquake resisteant multi-storey buildings. Walls with openings as comprising of wall parts connected with coupling beams. The two types of idealization are used for the lateral load analysis of coupled shear-walls. 1) Finite element idealization. 2) Frame idealization. In this work, the finite element approach is adopted for the basic analysis of shear-walls with openings structures, where in a specially developed Transient element is utilized. For the finite element solution, computer programme which is named as Bosper is developed. With this programme, using transient element, (between beam and plane stress elements) shear-walls with openings applications solved. Frame idealization is considered to be both practical and accurate. This model consists of the vertical wall parts and horizontal coupling beams. Certain portions of the coupling beams within the walls are assumed to be infinitely rigid. In this idealization, the problem is determination of the lenght of rigid portions of the beams for computing their effective stiffness. This thesis is divided into seven chapter. The first and second chapters give some informations and formulations about Finite element method. In the third and fourth chapters, one and two dimensional elements element stiffness matrix calculated. In the fifth chapter, Transient element is developed by using finite element method. In the last two chapters, the calculation methods of shear-wall structures with openings are given with example. In this example, two kind of solution are given. Firstly, The finite element method solution is given. (Using transient elements). In the second, the system is idealized as a frame is calculated for the different lenghts X by using Slope-Deflection Method. Finally, these two idealizations results are compared with and results are given. XVI
Benzer Tezler
- Betonarme yapı elemanlarında sonlu eleman yönteminin uygulamaları
Başlık çevirisi yok
FUAT DEMİR
Doktora
Türkçe
1998
İnşaat Mühendisliğiİstanbul Teknik ÜniversitesiYapı Ana Bilim Dalı
PROF. DR. ZEKAİ CELEP
- Levhalarda burkulma probleminin sonlu elemanlar yöntemiyle analizi
A Analysis of buckling in plates by finite element methods
KENAN ÜNGAN
Yüksek Lisans
Türkçe
2001
İnşaat MühendisliğiAtatürk Üniversitesiİnşaat Mühendisliği Ana Bilim Dalı
YRD. DOÇ. DR. AHMET BUDAK
- Planda düzensiz yapılarda kat döşemelerinin deprem etkileri altındaki davranışı
Seismic behaviour of floor slabs in multy-story buildings with plan irregulality
MUSTAFA SERDAR ATABEY
- Yatay yükler etkisindeki dolgulu betonarme düzlem çerçevelerin malzeme bakımından non-lineer analizi
Analysis of infilled planar RC frames in termes of nonlinearity material under lateral loads
MUHİDDİN BAĞCI
Doktora
Türkçe
2003
İnşaat MühendisliğiBalıkesir Üniversitesiİnşaat Mühendisliği Ana Bilim Dalı
PROF. DR. ŞERİF SAYLAN
- Geometri değişimleri bakımından doğrusal olmayan kutu kesitli köprülerin düzlem ve eğrisel kalın kabuk sonlu elemanlarla statik ve serbest titreşim hesabı
Static and free vibration analysis of geometrically non-linear box girder bridges using rectangular and curved thick shell finite elements
ÜLKÜ HÜLYA ÇALIK KARAKÖSE
Doktora
Türkçe
2010
İnşaat Mühendisliğiİstanbul Teknik Üniversitesiİnşaat Mühendisliği Ana Bilim Dalı
PROF. DR. ENGİN ORAKDÖĞEN