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

Download

index.pdf

Date

2007

Author

Uygur, Pelin

Metadata

Show full item record

Item Usage Stats

124
views

60
downloads

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.

Subject Keywords

Numerical Analysis.

URI

http://etd.lib.metu.edu.tr/upload/12608224/index.pdf
https://hdl.handle.net/11511/16614

Collections

Graduate School of Natural and Applied Sciences, Thesis

Suggestions

OpenMETU
Core

A discontinuous subgrid eddy viscosity method for the time-dependent Navier-Stokes equations Kaya Merdan, Songül (Society for Industrial & Applied Mathematics (SIAM), 2005-01-01) In this paper we provide an error analysis of a subgrid scale eddy viscosity method using discontinuous polynomial approximations for the numerical solution of the incompressible Navier-Stokes equations. Optimal continuous in time error estimates of the velocity are derived. The analysis is completed with some error estimates for two fully discrete schemes, which are first and second order in time, respectively.
Development of an incompressible navier-stokes solver with alternating cell direction implicit method on structured and unstructured quadrilateral grids Baş, Onur; Tuncer, İsmail Hakkı; Department of Aerospace Engineering (2007) In this research, the Alternating Cell Direction Implicit method is used in temporal discretisation of the incompressible Navier-Stokes equations and compared with the well known and widely used Point Gauss Seidel scheme on structured and quadrilateral unstructured meshes. A two dimensional, laminar and incompressible Navier-Stokes solver is developed for this purpose using the artificial compressibility formulation. The developed solver is used to obtain steady-state solutions with implicit time stepping m...
Solution of helmholtz type equations by differential quadrature method Kuruş, Gülay; Tezer, Münevver; Department of Mathematics (2004) This thesis presents the Differential Quadrature Method (DQM) for solving Helmholtz, modified Helmholtz and Helmholtz eigenvalue-eigenvector equations. The equations are discretized by using Polynomial-based and Fourier-based differential quadrature technique wich use basically polynomial interpolation for the solution of differential equation.
Implementation of different flux evaluation schemes into a two-dimensional Euler solver Eraslan, Elvan; Aksel, Mehmet Haluk; Department of Mechanical Engineering (2006) This study investigates the accuracy and efficiency of several flux splitting methods for the compressible, two-dimensional Euler equations. Steger-Warming flux vector splitting method, Van Leer flux vector splitting method, The Advection Upstream Splitting Method (AUSM), Artificially Upstream Flux Vector Splitting Scheme (AUFS) and Roe’s flux difference splitting schemes were implemented using the first- and second-order reconstruction methods. Limiter functions were embedded to the second-order reconstruc...
A unified approach for the formulation of interaction problems by the boundary element method Mengi, Y; Argeso, H (Wiley, 2006-04-30) A unified formulation is presented, based on boundary element method, in a form suitable for performing the interaction analyses by substructure method for solid-solid and soil-structure problems. The proposed formulation permits the evaluation of all the elements of impedance and input motion matrices simultaneously at a single step in terms of system matrices of the boundary element method without solving any special problem, such as, unit displacement or load problem, as required in conventional methods....

Citation Formats

P. Uygur, “Generalized finite differences for the solution of one dimensional elastic plastic problems of nonhomogeneous materials,” M.S. - Master of Science, Middle East Technical University, 2007.