| Author | Effendy Tanojo |
| Call Number | AIT Thesis no.ST-02-5 |
| Subject(s) | Iterative methods (Mathematics)
|
| Note | A thesis submitted in partial fulfillment of the requirements for the degree of Master
of Engineering. |
| Publisher | Asian Institute of Technology |
| Abstract | In the previous work, an Iterative Moving Least Squares (IMLS) Method was proposed and
applied successfully to 1 D and 2D heat conduction problems. In the IMLS method, the
governing equations are solved in an iterative scheme, and the Moving Least Squares
approximation is used. This method, like the Finite Point Method (PPM), is a meshless
method based on the point collocation weighted residual method. Point collocation
weighted residual methods have the benefit that no integration is required since the
governing equations need to be satisfied in only a set of collocation points.
In this thesis, an improved formulation of the Iterative Moving Least Squares method is
presented and applied to several test problems in two-dimensional elasticity. Improvements
are made to ensure the consistency and reliability of the iteration procedure, to enhance the
convergence of the method, and to define the parameters that affect the accuracy and
stability of the method. Several troublesome issues from the use of point collocation
weighted residual method, as used in the PPM, for elasticity problems are also addressed.
These issues are the prescription of the vectors normal to the boundary at the collocation
nodes, the necessity to employ a stabilization procedure, the inconsistency that arises from
the usage of the Weighted Least-Squares approximation, and the large amount of storage
required to form the global stiffness matrix and the global force vector.
The methods to improve the formulation in terms of both accuracy and efficiency are
discussed, and it is shown tlu·ough the test problems that the proposed approach yields
good accuracy and efficiency. |
| Year | 2002 |
| Type | Thesis |
| School | School of Engineering and Technology (SET) |
| 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 Joseph |
| Examination Committee(s) | Worsak Kanok-Nukulchai;Pichai Nimityongskul;Pennung Wamitchai |
| Scholarship Donor(s) | Asian Development Bank - Japan |
| Degree | Thesis (M.Eng.) - Asian Institute of Technology, 2002 |