This dissertation is concerned with the development of a generalized meshfree (GMF) approximation to improve the accuracy and efficiency of conventional meshfree methods in the solid and fracture analysis. The particular focus of the dissertation is placed on both the mathematical and numerical analysis of the proposed approximation in terms of its convergence and stability properties. The GMF approximation can be considered as a general expression reproducing all the existing meshfree approximations as well as a new approximation utilizing different basis functions. In addition, the GMF approximation possess the so-called weak Kronecker delta property at the boundary that, in turn, allows us to directly impose the essential boundary conditions without complicated treatments as seen in the traditional meshfree approximations and therefore greatly improves the computational efficiency. Furthermore, by choosing certain basis function, the proposed approximation can be extended to a higher-order or specific enriched approximation without adding extra nodes and is naturally conforming. This unique feature leads to high accuracy and enables us to solve some challenging problems such as problem involving large deformation, moving discontinuity and high-gradients. The proposed approximation is further furnished with the element-free Galerkin (EFG) method for the solid and fracture analysis.
The proposed method is tested against several benchmark problems with analytical solutions as well as some practical problems with experimental data with regard to its predictive simulation capabilities. For the time-dependent problems, a stability analysis is performed to guarantee that the proposed method is stable and produces a bounded solution whenever the solution of the exact differential equation is bounded. In fracture analysis, the cohesive failure model is adopted and the meshfree visibility approach is utilized to define the crack and its initiation and propagation.
|Advisor:||Kan, Cing-Dao (Steve), Wu, Cheng-Tang|
|Commitee:||Eskandarian, Azim, Hamdar, Samer H., Manzari, Majid T.|
|School:||The George Washington University|
|Department:||Civil and Environmental Engineering|
|School Location:||United States -- District of Columbia|
|Source:||DAI-B 71/02, Dissertation Abstracts International|
|Subjects:||Civil engineering, Mechanical engineering|
|Keywords:||Basis functions, Cohesive fracture mechanics, Convex approximations, Kronecker-delta property, Meshfree methods, Nonconvex approximations|
Copyright in each Dissertation and Thesis is retained by the author. All Rights Reserved
The supplemental file or files you are about to download were provided to ProQuest by the author as part of a
dissertation or thesis. The supplemental files are provided "AS IS" without warranty. ProQuest is not responsible for the
content, format or impact on the supplemental file(s) on our system. in some cases, the file type may be unknown or
may be a .exe file. We recommend caution as you open such files.
Copyright of the original materials contained in the supplemental file is retained by the author and your access to the
supplemental files is subject to the ProQuest Terms and Conditions of use.
Depending on the size of the file(s) you are downloading, the system may take some time to download them. Please be