An enhancement of finite element method with moving kriging shape functions | |
| Author | Kittiputh Plengkhom |
| Call Number | AIT Diss. no.ST-13-02 |
| Subject(s) | Kriging Finite element method |
| Note | A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Engineering, School of Engineering and Technology |
| Publisher | Asian Institute of Technology |
| Series Statement | Dissertation ; no. ST-13-02 |
| Abstract | This study presents an application of moving Kriging (MK) interpolation in the finite element method (FEM) by substituting the traditional element shape functions with MK shape functions. Kriging interpolation is a geostatistical technique for spatial interpolation. The basic idea of Kriging is that any unknown point can be interpolated from known scatter points in a specific domain. Using MK interpolation, shape functions can be generated over any finite set of nodes which are not tied to the element geometry. With this property, MK shape functions can be referred as element-free method. This leads to an idea to extend the influence of a node beyond the layer of surrounding elements to enhance the global smoothness of the field variable and its derivatives. The present study proposes a concept of layered domain of influence. Hence, characteristic arrays of an element, such as the element stiffness, have contributions from all visible nodes that include a set of satellite nodes unattached to the element leading to the term domain of nodal visibility. By mean of this development, the shortcomings of FEM due to the strict attachment of the shape functions to the element structure can be eliminated. Whilst, the interpolation property needed to satisfy essential boundary conditions is still maintained automatically. The validation of the method is confirmed through numerical examples of one- and twodimensional problems. The results show remarkable accuracy and global smoothness. The correlation parameter which is a statistic or trial-error parameter in the original Kriging interpolation is rationalized to be the numerical parameter through the new concept of layered domain of influence. Existing general-purpose finite element programs can be simply modified to accommodate the proposed element concept; thus, the method has a high chance to be accepted in practice. |
| Year | 2013 |
| Corresponding Series Added Entry | Asian Institute of Technology. Dissertation ; no. ST-13-02 |
| Type | Dissertation |
| 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) | Worsak Kanok-Nukulchai; |
| Examination Committee(s) | Anwar, Naveed ;Pennung Warnitchai ;Punchet Thammarak;Loo, Yew-Chaye ; |
| Scholarship Donor(s) | The Royal Thai Government (RTG); |
| Degree | Thesis (Ph.D.) - Asian Institute of Technology, 2013 |