Fotoelastisitede sınır eleman yönteminin ayırma metodu olarak kullanılması
Fotoelastisitede sınır eleman yönteminin ayırma metodu olarak kullanılması
Dosyalar
Tarih
1992
Yazarlar
Özütok, Atilla
Süreli Yayın başlığı
Süreli Yayın ISSN
Cilt Başlığı
Yayınevi
Fen Bilimleri Enstitüsü
Özet
Deneysel bir yöntem olan fotoelasti siteden elde edi len verilerle asal gerilme farkları ve asal gerilme doğrultularına ait bilgiler doğrudan elde edilmektedir. Asal gerilmeleri veya gerilme bileşenlerini elde etmek için ilave deneyler veya bölgenin herhangi bir nokta sında asal gerilme toplamlarını veren çözümlerin yapıl ması gerekmektedir. Ayırma yöntemleri dediğimiz işlem leri uyguluyarak gerilme bileşenlerini tek tek elde e- debi liriz. Bu çalışmada Sınır Eleman Yönteminin fotoelasti sitede ayırma yöntemi olarak kullanılması araştırılmış ve prob lemlerin çözümü için Fortran kodlama dilinde bir bilgi sayar programı hazırlanmıştır. Giriş bölümünde f otoelastisi te, ve sınır eleman yön temine ait çalışmalar gözden geçirilmiş ve incelenen problem açıklanmıştır. İkinci bölümde ışık, ışığın vektörel karekteri, pola rize ışık, pol ar i zer 1 er, dalga plakası ve f otoelastisi te için uygulanan Jones vektörleri tanıtılmıştır. Üçüncü bölümde polariskop ve Jones matrisleri anlatı larak polariskop elemanları için Jones matrisleri anla tılmıştır. Dördüncü bölümde düzlem el ast i site teorisi için foto elasti site teorisi anlatılmıştır. Beşinci bölümde fotoelasti site deneylerinden elde edilen verilerin analizi açıklanmıştır. Altıncı bölümde kullanılan ayırma metodları açıklan mış ve bunlar hakkında bilgi verilmiştir. Yedinci bölümde sınır eleman yönteminin ayırma metodu olarak kullanılabileceği açıklanmış ve bu metoda ait bilgisayar programı verilmiştir. Sekizinci bölümde karşılıklı iki kenar ortay nokta sından eşit ve karşıt tekil kuvvetlere maruz kare levha- hanın çözümü yapılarak gerilme bileşenleri elde edilmiş tir. Yine aynı problemin yanlarına yarıçapları sabit kalmak üzere derinliği değişen çentik açılarak sınır elemanları yöntemiyle çözümleri yapılmıştır.
In case the geometric configuration of boundary of a structure is irregular, solution of the system will be troublesome. In this condition photoelasticity solution will be available. Brewster observed that a loaded glass sheat produces color lines which are seen by polar i scope and this observation of him constituted the base of the photoel asti ci ty. Neumann and Maxwell had been the first theoriers of photoelasticity. After their work, the optical coefficient of various materials had been calculated. In 1912 Mesnager had used photoelasticity for the first time in solving engineering problems by calculating the tension on a glass model. Coker has developed many practical investigations and techniques which made the engineering applications possible. After the works by Hetenyi, Drucker, Frocht, Midlin, Jesop and Kuske had been developed various photoel asti c measurements and experimental techniques. If the stressed model is examined by the polar i scope, the isoclonic lines and isochromatic lines are observed. The differ ance of the principle stresses and their oriantation at a certain point of material can be calculated by using two kinds of data lines. Also, isoclinic fringe pattern which gives the angle between x axis and principal stress direction at a certain point is used to calculate the shear stress, a -a t = * 2 sina© CEq.lD xy 2 The differance of the principle stresses is given by the following formula N.f a -a = - CEq.SZ) 1 2 h N appearing in the above equation is the isochromatic pat. tern number h is the thickness of material and term f is the optical coefficient of the material. Stresses in the zone can not be found directly by the photoelastic experimental data, however, those are on the boundary can be. If the boundary is free, then the principal stress normal to the boundary will be zero, and therefore the other principal stress can be determined directly from CEq. 23. If the boundary is not free and normal load which is applied is known, tangential boundary stress would be interpreted by following equation. stresses need a third relation. The ways for obtaining elements of the stress tensor are called the seperation methods. Seperation methods can be classified in three groups: semi -theoretical methods, another experimental methods or numerical methods. Amoung them, numerical methods has an appear ent advantage: once a numerical method is set then the whole solution in the zone can be obtained with the ai d of a computer. In this study, the boundary elements method is used as a seperation method in photoelasticity. The boundary elements method is more capable than other numerical methods. This separation method depends on the solution of Laplace equation. 72C» +
In case the geometric configuration of boundary of a structure is irregular, solution of the system will be troublesome. In this condition photoelasticity solution will be available. Brewster observed that a loaded glass sheat produces color lines which are seen by polar i scope and this observation of him constituted the base of the photoel asti ci ty. Neumann and Maxwell had been the first theoriers of photoelasticity. After their work, the optical coefficient of various materials had been calculated. In 1912 Mesnager had used photoelasticity for the first time in solving engineering problems by calculating the tension on a glass model. Coker has developed many practical investigations and techniques which made the engineering applications possible. After the works by Hetenyi, Drucker, Frocht, Midlin, Jesop and Kuske had been developed various photoel asti c measurements and experimental techniques. If the stressed model is examined by the polar i scope, the isoclonic lines and isochromatic lines are observed. The differ ance of the principle stresses and their oriantation at a certain point of material can be calculated by using two kinds of data lines. Also, isoclinic fringe pattern which gives the angle between x axis and principal stress direction at a certain point is used to calculate the shear stress, a -a t = * 2 sina© CEq.lD xy 2 The differance of the principle stresses is given by the following formula N.f a -a = - CEq.SZ) 1 2 h N appearing in the above equation is the isochromatic pat. tern number h is the thickness of material and term f is the optical coefficient of the material. Stresses in the zone can not be found directly by the photoelastic experimental data, however, those are on the boundary can be. If the boundary is free, then the principal stress normal to the boundary will be zero, and therefore the other principal stress can be determined directly from CEq. 23. If the boundary is not free and normal load which is applied is known, tangential boundary stress would be interpreted by following equation. stresses need a third relation. The ways for obtaining elements of the stress tensor are called the seperation methods. Seperation methods can be classified in three groups: semi -theoretical methods, another experimental methods or numerical methods. Amoung them, numerical methods has an appear ent advantage: once a numerical method is set then the whole solution in the zone can be obtained with the ai d of a computer. In this study, the boundary elements method is used as a seperation method in photoelasticity. The boundary elements method is more capable than other numerical methods. This separation method depends on the solution of Laplace equation. 72C» +
Açıklama
Tez (Yüksek Lisans) -- İstanbul Teknik Üniversitesi, Fen Bilimleri Enstitüsü, 1992
Anahtar kelimeler
Fotoelastisite,
Sınır elemanlar yöntemi,
Photoelasticity,
Boundary element method