ANISOTROPIC H-ADAPTIVE (AH-ADAPTIVE) FINITE ELEMENT SCHEME FOR THREE-DIMENSIONAL MULTI-SCALE ANALYSES
Open Access
- Author:
- Tsau, Shih-Horng
- Graduate Program:
- Mechanical Engineering
- Degree:
- Doctor of Philosophy
- Document Type:
- Dissertation
- Date of Defense:
- September 29, 2006
- Committee Members:
- Panagiotis Michaleris, Committee Chair/Co-Chair
Ashok D Belegundu, Committee Member
Eric M Mockensturm, Committee Member
Francesco Costanzo, Committee Member - Keywords:
- nonzeros in tangent matrix
finite element
AH-adaptive
condensation theory
algorithm
large structure
multi-scale
anisotropic h-adaptive
penalty method
Lagrange multiplier - Abstract:
- Using a static mesh in a multi-scale simulation, such as welding, requires many fine elements from the start of the analysis. The mesh needs to be fine throughout the entire simulation in both transverse and longitudinal directions to capture high gradients. Isotropic adaptive meshing performs simultaneous coarsening, and refining, in all spatial dimensions. Application of isotropic adaptive meshing allows the use of a coarse mesh as the analysis begins and it refines as needed in all directions during the simulation. However, because of the nature of isotropic refinement, elements need to remain fine in all dimensions even if the gradient is high in only one direction. In this work, an efficient Anisotropic h-Adaptive (abbreviated AH-adaptive) FEA method is developed that performs independent refining and coarsening among all spatial dimensions. Application of the anisotropic h-adaptive meshing allows the use of a coarse mesh as the analysis starts. If there is one direction in which the gradient is much smoother than the others, the mesh coarsens in the corresponding direction, thus reducing the number of DOFs by n^{1/2} in 2D analyses, and n^{1/3} in 3D analyses. Dependent (also referred to as "constraint") nodes occur when h-adaptive refinement strategy is applied. The DOFs (degrees of freedom) on these dependent nodes must be separated from the original system of algebraic equations. Only the unconstrained (also referred to as "free") DOFs can exist in the real equation system to solve and therefore yield accurate solution fileds. To deal with the dependent DOFs, several methods can be applied for the numerical computations. A comparison between Condensation and Recovery Method, Lagrange Multiplier, and Penalty Method is performed. And the Condensation and Recovery Method is chosen to be applied in the AH-adaptive FEA scheme to maximize the computational efficiency. Highlights from this research include important contributions such as: 1) simplified gradient calculations for each element, 2) nonzero fill-in effects induced by condensing the original algebraic equation systems, 3) moving forced refinements of anticipated high gradients, 4) procedures which assist meshes with neatly coarsening elements to the allowed maximum, and 5) comparisons among possible approaches for the original system equations from a mesh which has constrained nodes.