Home
Tags
No Tags
A STABILIZATION TECHNIQUE BASED ON MESHFREE METHOD
| Title: | A STABILIZATION TECHNIQUE BASED ON MESHFREE METHOD |
| Author: | TANNERU, VENKAT SUNIL |
| Description: | Locking in finite elements has been a major concern since its early developments. The main reason behind locking phenomena is poor numerical interpolation that leads to an over-constrained system. A procedure called stabilized reduced integration method based on an assumed strain approach is proposed to solve this problem. In this method, a gradient matrix is constructed using a Taylor series expansion with respect to the centriod of the sub-domains of the problem and using this gradient matrix, an explicit expression for the rank-sufficient stiffness matrix is obtained. The derived stiffness matrix has two parts, one-point-quadrature stiffness matrix and stabilized part of the stiffness matrix. The stabilized part of the stiffness matrix is modified in such a way that it is related to the deviatoric part and can work better in the case of pure bending. To evaluate the gradient matrix, meshfree technique offers advantages over classical finite-element method because of the higher order continuity properties. The meshfree shape functions and their first and second derivatives are derived using a set of nodes distributed over a domain of the problem. In finite-element method, the shape functions are constructed using the mesh structure, and hence are not better suited to cope with geometric changes of the domain of interest. In contrast, meshfree technique does not require element connectivity but definition of nodes and description of boundaries. Meshfree technique based on Moving Least Squares approximation is considered in this thesis. A procedure for enforcing essential boundary conditions is described because shape functions based on Moving Least Squares approximation do not satisfy the Kronecker delta function at nodal locations. The procedure modifies the meshfree interpolant such that the new shape functions at essential boundary possess the Kronecker delta and satisfies the partition of unity property. It is demonstrated through three numerical examples that the present formulation eliminates locking effectively. |
| Permanent Link: |
http://rave.ohiolink.edu/etdc/view?acc_num=ucin1130385545
http://hdl.handle.net/2374.OX/10917 |
| Date: | 2005 |
Files in this item
| Files | Size | Format | View |
|---|---|---|---|
|
There are no files associated with this item. |
|||