Genel biçimli kabuklar için bir sonlu eleman formülasyanı / Tülay Aksu

Abstract

Kabuklar hem matematik formülasgonu hem de geometrisi nedeni ile karmaşık ya.pi. sistemleri olarak bilinirler. Pek çok mühendislik yapısında karşılaşılan, eğilme tesir lerinin önemli olduğu genel biçimli kalın sayılabilecek kabukların kullanımının artması sonucu Ki rchof f -Love hipotezi yerine daha doğru bir teori geliştirmek zorunlu olmuştur. Kalın sayılabilecek kabuklar için geliştiril miş bir çözüm yolu olarak yer değiştirmelerin kalınlık doğrultusundaki değişimi için bir seri alınması ve bu serinin yeterli sayıda teriminin hesaba katılması söylenebilir.

Shells are known as complex, structural systems due to complexity in mathematical formulation and geometric shape. For that reason, both in theoretical and experimental analysis, certain problems were met and only systems with severely idealized situations under certain conditions were solvable. With the development of computer systems, numerical analysis has become an essential tool in engineering mechanics and finite element method came into definition as an extension to matrix structural analysis. The finite element method has made possible the development of computer programs which may be used for analyzing complete arbitrary structural systems. Different methods of analysis are used for analysis of shells to obtain adequate solutions, with increasing thickness-radius ratio. On the other hands, thickness shear deformations and the ratio z/R near unity is neglected for thin shells. They have to be considered for moderate ones, while asymptotic expansions or basic equations of elasticity must be used for thicker shells. One of the refined solutions for small deflections theory of shells is to express the displacements in power series taking into account of sufficient number of terms, instead of using Ki rchof f -Love hypotesis. There are various solution methods developed especially for the computer application, where thickness shear deformation is taken into account and the first three terms of power series of l/(l+z/R) are considered for integration, as (l-z/R+z2/R2). Novozhilov, stated that additional terms of refinements of order