On iterative and direct point collocation methods for problems in 3D elastostatics | |
| Author | Nguyen Dinh Khoa |
| Call Number | AIT Thesis no.ST-03-32 |
| Subject(s) | Collocation methods Boundary value problems |
| Note | A thesis submitted in partial fulfillment of the requirements for the degree of Master of Engineering, School of Engineering and Technology |
| Publisher | Asian Institute of Technology |
| Series Statement | Thesis ; no. ST-03-32 |
| Abstract | A point collocation method based on the point collocation weighted residual method is extended and formulated for problems in three-dimensional elastostatics. The method is a point-based meshless method since the governing equations are satisfied in only a set of collocation points and no integration is required. The moving least-squares (MLS) approximations using exponential weight functions and variable domains of influence are utilized to efficiently construct shape functions and shape function derivatives. Several improvements are taken to overcome some troublesome issues from the use of the point collocation weighted residual method such as the prescription of the vectors normal to the boundary, the necessity to employ a stabilization procedure, and the inconsistency due to the usage of the weighted least-squares approximation. A direct solution technique using LU decomposition and an iterative solution technique based on the Iterative Moving Least-Squares method are applied and verified. Several troublesome issues that arise from the application of the Iterative Moving Least-Squares method are also addressed. To verify the accuracy and efficiency of the method, several numerical examples are presented. Results are compared to the available analytical solutions. |
| Year | 2003 |
| Corresponding Series Added Entry | Asian Institute of Technology. Thesis ; no. ST-03-32 |
| Type | Thesis |
| School | School of Engineering and Technology |
| Department | Department of Civil and Infrastucture Engineering (DCIE) |
| Academic Program/FoS | Structural Engineering (STE) /Former Name = Structural Engineering and Construction (ST) |
| Chairperson(s) | Barry, William; |
| Examination Committee(s) | Pennung Warnitchai ;Pichai Nimityongskul; |
| Scholarship Donor(s) | Government of Vietnam; |
| Degree | Thesis (M.Eng.) - Asian Institute of Technology, 2003 |