- Title
- Large deformation analysis in geomechanics using adaptive finite element methods
- Creator
- Kardani, Mina
- Relation
- University of Newcastle Research Higher Degree Thesis
- Resource Type
- thesis
- Date
- 2012
- Description
- Research Doctorate - Doctor of Philosophy (PhD)
- Description
- The finite element method (FEM) is extensively used in analysis of a wide range of nonlinear geotechnical problems. The finite element method can handle simple and complex constitutive soil models, and solve problems with complicated geometries and boundary conditions with reasonably accurate results. On the other hand, mesh distortion and entanglement of elements, occurring inevitably in failure zones with high stress/strain concentration, are main drawbacks of the common finite element solutions such as the Updated Lagrangian method. In addition, efficacious application of the method requires experience and a certain amount of trial and error, particularly when choosing an optimal time and spatial discretisation. Adaptive finite element methods provide a means for obtaining more reliable solutions by continuously adjusting the discretisation in time and space according to the current solution. These procedures automatically refine, coarsen, or relocate a mesh to achieve a solution with a specified accuracy in an optimal fashion. Although a significant amount of research has been devoted to adaptive finite element analysis in solid mechanics, the application of adaptive methods has been less considered in nonlinear geotechnical problems due to the complexity. Modelling of problems in geomechanics is typically sophisticated due to nonlinear constitutive laws, large deformations, changing boundary conditions and time-dependent behaviour. A variety of adaptive finite element techniques have been developed to tackle nonlinear problems in solid mechanics. However, the application of these methods to geomechanics is still a challenge. Amongst the various adaptive techniques, the r-adaptive and h-adaptive finite element methods are probably the most favoured and most established. r-adaptive finite element method attempts to eliminate the mesh distortion by refining the mesh in the finite element domain. On the other hand, h-adaptive finite element method is based on the idea of generating a new mesh by dividing the area of original elements where the interpolation should be improved to achieve higher accuracy or to avoid mesh distortion. In this Thesis, the h-adaptive finite element technique will be employed to solve some complex geotechnical problems involving material nonlinearity, large deformation, changing boundary conditions and time-dependent nonlinearity. To achieve this, the main features of the technique including advanced mesh generation algorithms, error estimation methods and a procedure for remapping of state variables will be discussed and developed in company of a robust analysis program. The performance of the h-adaptive finite element method is then represented by considering the accuracy and efficiency of the method in solving some classical geomechanics problems such as the bearing capacity of footings, expansion of cavities, and the stability of slopes. In addition, this Thesis will address the performance and the efficiency of alternative error estimation techniques for particular geotechnical applications involved with changing boundary conditions and inertia forces, such as static and dynamic penetration of an object into soil. Such problems are categorised as one of the most sophisticated problems of computational geomechanics due to their extreme nonlinearity. This Thesis will also present a new and innovative combined adaptive method for tackling geotechnical problems with relatively large deformations. This robust method is based upon an elegant combination of the Arbitrary Lagrangian-Eulerian (ALE) method and the h-adaptive finite element method developed as a part of the Thesis. The proposed method takes advantage of r-refinement as well as h-refinement finite element techniques, and yet eliminates the individual drawback of each method.
- Subject
- adaptivity; h-adaptive; large deformation; finite element
- Identifier
- http://hdl.handle.net/1959.13/928191
- Identifier
- uon:10355
- Rights
- Copyright 2012 Mina Kardani
- Language
- eng
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| View Details Download | ATTACHMENT02 | Thesis | 4 MB | Adobe Acrobat PDF | View Details Download |