Kriging-based finite element method for analyses of plates and shells | |
| Author | Tjong, Wong Foek |
| Call Number | AIT Diss. no.ST-09-01 |
| Subject(s) | Finite element method Kriging Shells (Engineering) |
| Note | A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Structural Engineering, School of Engineering and Technology |
| Publisher | Asian Institute of Technology |
| Series Statement | Dissertation ; no. ST-09-01 |
| Abstract | An enhancement of the finite element method using Kriging shape functions CK-FEM) was recently proposed. The K-KEM preserves most advantages of mesh-free methods and inherits the computational procedure of the FEM so that any existing finite element code can be easily extended to include the enhanced method. In this dissertation, the K-FEM was developed and applied to analyze plates and general shells. The governing equations for the plate were derived based on Reissner-Mindlin theory and for the shell were based on degenerated 3D elasticity theory. The shape functions were constructed using Kriging interpolation over a set of nodes encompassing a number of layers of triangular elements. In the K-FEM for shells, these shape functions were used to approximate both the displacement field and the geometry of the shell mid-surface. The parameterization of the shell mid-surface was performed element-by-element by mapping curved triangular elements onto flat planes passing through the element nodes. Shear and membrane lockings were alleviated by using high order polynomial basis, i.e. cubic or higher order basis. The developed plate bending and curved triangular shell elements were named K-Plate and K-Shell, respectively. Along with this development, several issues associated with the K-FEM were scrutinized. The first issue concerns with the correlation function and its parameter. In addition to the commonly used Gaussian correlation function, a quartic spline CQS) function with an adaptive correlation parameter was proposed. With this new correlation function, a user of the K-FEM is not required to key in a value of parameter in an analysis. Moreover, the convergence characteristics of the K-FEM with the QS correlation function are satisfactory. The second issue concerns with the incompatibility. In the K-FEM, the interpolation functions are not continuous along the inter-element boundaries. The effects ofthe incompatibility on the convergence were studied. It was found that the K-FEM with appropriate Qhoice of correlation function passed the weak patch test and therefore the convergence is guaranteed. Comprehensive numerical tests of the K-Plate and K-Shell elements were performed to investigate various important issues including shear and membrane lockings, convergence and accuracy. The results show that for the case where shear or membrane locking is not an issue, the elements perform extremely well. Exceptionally accurate displacement and very fine stress fields can be achieved in a relatively coarse mesh. For thin shells with highly-localized displacement fields, however, the present elements need a fine mesh in order to relieve shear and membrane lockings. In all cases, the K-Plate and K-Shell have excellent convergence characteristics. Various shell shapes considered in the tests demonstrate the applicability of the K-Shell for analyses of smooth shells of arbitrary geometry. Future research should be directed on developing locking-free K-Plate and K-Shell. |
| Year | 2009 |
| Corresponding Series Added Entry | Asian Institute of Technology. Dissertation ; no. ST-09-01 |
| Type | Dissertation |
| 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) | Worsak Kanok-Nukulchai; |
| Examination Committee(s) | Park, Kyung-Ho;Anwar, Naveed;Belytschko, Ted; |
| Scholarship Donor(s) | Petra Christian University;Asian Institute of Technology Fellowship; |
| Degree | Thesis (Ph.D.) - Asian Institute of Technology, 2009 |