Sonlu eleman yöntemi ile çok bağımlı bölgelerin C-süreklilik problemlerinin incelenmesi
Başlık çevirisi mevcut değil.
- Tez No: 55920
- Danışmanlar: DOÇ.DR. NECLA KADIOĞLU
- Tez Türü: Yüksek Lisans
- Konular: İnşaat Mühendisliği, Civil Engineering
- Anahtar Kelimeler: Belirtilmemiş.
- Yıl: 1996
- Dil: Türkçe
- Üniversite: İstanbul Teknik Üniversitesi
- Enstitü: Fen Bilimleri Enstitüsü
- Ana Bilim Dalı: Belirtilmemiş.
- Bilim Dalı: Belirtilmemiş.
- Sayfa Sayısı: 101
Özet
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Özet (Çeviri)
FDMITE ELEMENT ANALYSIS OF C°-CONTINUÎTY PROBLEMS OF MULTIPLY CONNECTED REGIONS SUMMARY Oftentimes exact solutions to differential equations are not easily obtained. in fâet, quite frequently, it is not even possible to obtain an exact solution with currently available mathematical techniques. This is particulariy true when the geometry is irregular, ör the properties vary spatially, ör perhaps, the properties are a function of the field variable. Problems of the İatter variety are said to be nonlinear. Engineers find approximate solulion methods indispensable in these cases. Virtually ali problems that are describable by ordinary and partial differential equations can be solved by the finite element method. Moreover, linear and nonlinear problems may be solved in nearly the same way, although nonîinear problems generally require an iterative soluüon. in this thesis, only steady-state problems are studied. By steady-state it is meant that the field variable is a function of spati'al coordinates, and not a function of time. in structural and stress analysis, time-independent problems are referred to as static ör eguitibrium problems. in ali steady state, static, ör equilibrium problems, a system of algebraic equations results that is always in the form, {KMa} + {f}-0 The vector {a} always contains the nodal unknovms. in the displacement- finite element method, nodal displacement components are taken as the dependent variables. it is selected an admissable displacement field, defined in piecewise fashion so that displacements within any element are interpolated from nodal degrees of freedom of that element. The finite element characteristics can be derived using either variaüonal ör weighted-resUktal methods. Hovvever, in stress and sîructural analysis applications, the characteristics are more easily derived by invoking öne of the following; -The principle of stationary potential energy. -The prineiple of virtual displacements. -The miûimum complementary energy principle. -The principle of virtual stresses. -Reissner*s principle. -Hamilton*s principle. Here the principle of stationary potential energy has been used to make the formulation, which is as follows; Among ali admissable confıgurations of a conservative system, those that satisjy the equations ofequilibrium make the potential energy stationary with respect to small admissable variations of displacement. xiiiA if If the same shape functions arc used to define the global coordinates as the field variable, the formulation is referred to as isoparametric. Then the element stiffness matrix is obtained by numerical integration. Gauss-Legendre quadrature has been used in this thesis. The number of Gauss points has a lower limit, because, in the limit of the mesh refinement, element volume must be integrated exactly. In a plane bilineer element of constant thickness, one Gauss point is sufficient. On the other hand, for a displacement mode which is not a rigid body motiion, it is possible to evaluate the strains in one Gauss point to be zero. Then the element stiffness matrix becomes a zero matrix at this point This yields a mechanism or a zero-energy mode. If the plane bilineer element is integrated using only one Gauss point, two kinematic modes may appear. Hence bilinear elements are to be evaluated using two by two quadrature to avoid such pitfalls. In a displacement-finite element analysis, stresses are less accurate than displacements. In low-order elements, stresses are often more accurate at the element centroid, less accurate at midsides, and least accurate at comers. Elements of higher - order generally display multiple points of optimal accuracy for stresses. The locations of these points depend on the element geometry and the displacement field chosen. For isoparametric elements, it often happens mat stresses (especially shear stresses) are most accurate at Gauss points of a quadrature rule, one order less than that used for integration of the element stiffness matrix. For distorted elements, Gauss points may not be the optimal locations, but they remain as very good choices. Bilinear elements become suffer when the element aspect ratio increases (or element Jacobian index, which is the ratio of the minimum Jacobian to the average Jacobian in the element, decreases). This may lead even locking of the whole system when bending prevails. This is because not only the vertical cross sections but also the horizontal cross sections remain linear even in pure bending. Against this, incompatible quadratic displacement modes may be added to the shape functions of the bilinear element as well as quadratic elements may be used. Or instead, the stress field may be defined in the element by °xx =Pl+P2y
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