A wachspress meshless local petrov-galerkin method | |
| Author | Thulasi, Vinayagam |
| Call Number | AIT Thesis no.ST-02-6 |
| Subject(s) | Polynomials Finite element method Numerical grid generation (Numerical analysis) |
| Note | A thesis submitted in prutial fulfillment of the requirements for the degree of Master of Engineering. |
| Publisher | Asian Institute of Technology |
| Abstract | A Wachspress Meshless Local Petrov-Galerkin (WMLPG) method employing moving least-squares shape functions as the trial functions and Wachspress polynomial shape functions as the test functions is presented in this thesis. Polygonal sub-domains constructed from several convex polygons are employed as an alternative to the typically used circular sub-domains. The number of sides of the polygons has no limit in the WMLPG method, leading to increased flexibility in problem discretization which is one of the main advantage of the WMLPG method. Gaussian quadrature is employed for the integration of the weak form on the local sub-domains and on the problem domain boundaries. In cases where higher order Wachspress cells are employed to discretize the problem domain, higher order Gaussian quadrature schemes (up to 79 integration points) enables the WMLPG method to achieve a high level of accuracy. A coupled WFEM - WMLPG technique is introduced to impose essential boundary conditions for the plate with double-edge cracks numerical example so that the complexity of the integrand in the stiffness matrix and force vector formulation can be reduced. Convergence studies have been performed both by increasing the number of nodes and by increasing the order of the MLS basis functions. The results obtained from the WMLPG method employing linear and quadratic basis functions with either quartic spline weight functions or exponential weight functions are compared with the results obtained using the WFEM method. The numerical examples performed in Chapter 4 show that the WMLPG method provides a high degree of flexibility in discretizing the problem domain while retaining solution accuracy. |
| 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; |
| Examination Committee(s) | Worsak Kanok-Nukulchai;Pichai Nimityongskul |
| Scholarship Donor(s) | The Government of Norway;Norwegian Agency for Development Co-operation (NORAD) |
| Degree | Thesis (M.Eng.) - Asian Institute of Technology, 2002 |