- Title
- Mesh optimisation methods for large deformation analysis of geomechanics problems
- Creator
- Moavenian, Mohammad Hesam
- Relation
- University of Newcastle Research Higher Degree Thesis
- Resource Type
- thesis
- Date
- 2017
- Description
- Research Doctorate - Doctor of Philosophy (PhD)
- Description
- The Finite Element Method (FEM) is an analytical tool used extensively in nonlinear geotechnical problems. Problems with complex boundary conditions and constitutive soil models can be analysed by the FEM with reasonably accurate results. The geometry of a problem remains unchanged when deformations are small. Therefore, the initial finite element mesh can be used throughout the analysis. On the other hand, in problems involving large deformations, the geometry of the problem changes in such a way that the initial mesh will no longer be usable. The Total Lagrangian (TL), the Updated Lagrangian (UL) and the Arbitrary Lagrangian–Eulerian (ALE) methods are among those methods used to analyse large deformation problems. Mesh distortion and entanglement of elements in regions with high stress/strain gradients are the main drawbacks of common finite element solutions, such as the UL method. Moreover, the accuracy and convergence degrade when using Lagrangian methods for large deformation problems. The ALE method, based on the operator split technique in which mesh and material displacements are separated, can be used to eliminate mesh distortion. In the ALE method, material displacements are obtained in the UL stage by solving the governing equations. The UL stage is followed by an Eulerian stage, in which mesh refinement techniques are used to improve mesh quality. An updated mesh is used for the UL analysis in next increment, after mapping all state variables from the old mesh to the new mesh. In this study, different re-meshing techniques are developed and implemented to enhance the capability of the ALE method in reducing the mesh distortion in a finite element domain involving large deformations. These techniques include the Spring Analogy Method (SAM), the Radial Basis Functions based method (RBF), and the Reference Jacobian Method (RJM) which have been recently used to solve simple geotechnical problems. In this study the application of these remeshing techniques in complex geotechnical problems is addressed. This study shows that the alternative methods outperform the EA method in eliminating mesh distortion in the geotechnical problems solved in this thesis. Although these remeshing methods work well in many penetration problems, they may fail to optimise the mesh adjacent to penetrating objects where elements generally experience the largest deformations in the finite element mesh. To overcome this drawback, in this research, the Elastic Hardening method is developed in which the stiffness of an element increases proportional to the element deformation. This stiffness is used in the relocation phase to obtain the new locations of the nodes of the interior domain. In this way elements which are about to distort in the next UL analysis, preserve their optimum shape in the relocation stage. This new mesh optimisation technique is found to be effective in regions where the elements face relatively high values of stresses and strains. Analysing penetration problems is computationally expensive, especially when high accuracy is intended or deep penetrations are simulated. In order to develop an approximate but closed-form equation summarising the penetration behaviour, a parametric study was conducted in this research, using more than 2,300 numerical simulations of the dynamic penetration of soil. The outcomes include two mathematical expressions relating the soil and penetrometer properties to the embedment depth and the predicted soil resistance. The h-adaptive FEM is another adaptive method that tackles mesh distortion by coarsening or refining meshes where the interpolation must be improved in order to avoid mesh distortion and enhance the accuracy of the analysis. In this study, the re-meshing methods used in the ALE framework are also used in combination with the h-adaptive methods, forming the so-called rh-adaptive method. The finite element mesh in the rh-adaptive scheme can either be optimised using re-meshing methods or coarsened and refined by applying the h-adaptive technique. The performance of the alternative remeshing methods in rh-adaptivity framework are studied for large deformation problems. It is shown that the RBF is an efficient method within the rh-adaptive framework. Moreover, the RJM method also proves to work well as a re-meshing method with the rh-adaptive technique. In order to verify and inspect the quality of elements in a domain, four mesh metrics for 6-noded elements are developed. The effect of the relocation of the middle nodes can be modelled by the introduced mesh metrics when evaluating the quality of a FE mesh. Moreover, a curve-fitting scheme based on B-spline formulation is implemented into the finite element framework.
- Subject
- finite element method (FEM); geomechanics; geotechnical problems; mesh optimisation methods
- Identifier
- http://hdl.handle.net/1959.13/1333777
- Identifier
- uon:27152
- Rights
- Copyright 2017 Mohammad Hesam Moavenian
- Language
- eng
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| Thumbnail | File | Description | Size | Format | |||
|---|---|---|---|---|---|---|---|
| View Details Download | ATTACHMENT01 | Thesis | 8 MB | Adobe Acrobat PDF | View Details Download | ||
| View Details Download | ATTACHMENT02 | Abstract | 180 KB | Adobe Acrobat PDF | View Details Download |