Generalized finite differences for the solution of one dimensional elastic plastic problems of nonhomogeneous materials


Tezin Türü: Yüksek Lisans

Tezin Yürütüldüğü Kurum: Orta Doğu Teknik Üniversitesi, Mühendislik Fakültesi, Mühendislik Bilimleri Bölümü, Türkiye

Tezin Onay Tarihi: 2007

Öğrenci: PELİN UYGUR

Eş Danışman: AHMET NEDİM ERASLAN, TURGUT TOKDEMİR

Özet:

In this thesis, the Generalized Finite Difference (GFD) method is applied to analyze the elastoplastic deformation behavior of a long functionally graded (FGM) tube subjected to internal pressure. First, the method is explained in detail by considering the elastic response of a rotating FGM tube. Then, the pressurized tube problem is treated. A long FGM tube with fixed ends (axially constrained ends) is taken into consideration. The two cases in which the modulus of elasticity only and both the modulus of elasticity and the yield limit are graded properties are analyzed. The plastic model here is based on incremental theory of plasticity, Tresca's yield criterion and its associated flow rule. The numerical results are compared to those of analytical ones. Furthermore, the elastic response of an FGM tube with free ends is studied considering graded modulus of elasticity and Poisson's ratio. The results of these computations are compared to those of Shooting solutions. In the light of analyses and comparisons stated above, the applicability of the GFD method to the solution of similar problems is discussed. It is observed that, in purely elastic deformations the accuracy of the method is sufficient. However, in case of elastic-plastic deformations, the discrepancies between numerical and analytical results may increase in determining plastic displacements. It is also noteworthy that the predictions for tubes with two graded properties, i. e. the modulus of elasticity and the yield limit, turn out to be better than those with one graded property in this regard.