90 research outputs found

    Adaptive finite element simulation of fracture: from plastic deformation to crack propagation

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    As engineers and scientists, we have a host of reasons to understand how structural systems fail. We may be able to improve the safety of buildings during natural disaster by designing more fracture resistant connectors, to lengthen the life span on industrial machinery by designing it to sustain very large deformation at high temperatures, or prepare evacuation procedures for populated areas in high seismic zones in the event of rupture in the earth's crust. In order to achieve a better understanding of how any of these structures fail, experimental, theoretical, and computational advances must be made. In this dissertation we will focus on computational simulation by means of the finite element method and will investigate topological and physical aspects of adaptive remeshing for two types of structural systems: quasi-brittle and ductile. For ductile systems, we are interested in modeling the large deformations that occur before rupture of the material. The deformations can be so large that element distortion can cause lack of numerical convergence. Thus, we present a remeshing and internal state variable mapping technique to enable large deformation modeling and alleviate mesh distortion. We perform detailed studies on the Lie-group interpolation and variational recovery scheme and conclude that the approach results in very limited numerical diffusions and is applicable for modeling systems with significant ductile distortion. For quasi brittle systems mesh adaptivity is the central theme as it is for the work on ductile systems. We investigate two- and three-dimensional problems on CPU and GPU systems with the main goals of either improving computational efficiency or fidelity of the final solution. We investigate quasi-brittle fracture by means of the inter-element extrinsic cohesive zone model approach in which interface elements capable of separating are adaptively inserted at bulk element facets when and where they are needed throughout the numerical simulation. The inter-element cohesive zone model approach is known to suffer from mesh bias. Thus, we utilize polygonal element meshes with adaptive splitting to improve the capability of the mesh to represent experimentally obtained fracture patterns. The fact that we utilize the efficient linear polygonal elements and only apply the adaptive element splitting where needed means that we also achieve improved computational efficiency with this approach. In the last half of the dissertation, we depart from the use of unstructured meshes and focus on the development of hierarchical mesh refinement and coarsening schemes on the structured 4k mesh in two and three dimensions. In three-dimensions, the size of the problem increases so rapidly that mesh adaptivity is critical to enable the simulation of large-scale systems. Thus, we develop the topological and physical aspects of the mesh refinement and coarsening scheme. The scheme is rigorously tested on two benchmark problems; both of which shows significant speed up over a uniform mesh implementation and demonstrate physically meaningful results. To achieve greater speed up, the adaptive mesh refinement and coarsening scheme on the 2D 4k mesh is mapped to a GPU architecture. Considerations for the numerical implementation on the massively parallel system are detailed. Further, a study on the impact of the parallelization of the dynamic fracture code is performed on a benchmark problem, and a statistical investigation reveals the validity of the approach. Finally, the benchmark example is extended to such that the speicmen dimensions matches that of the original experimental system. The speedup provided by the GPU allows us to model this large system in a pratical amount of time and ultimately allows us to investigate differences between the commonly used reduced-scale model and the actual experimental scale. This dissertation concludes with a summary of contribution and comments on potential future research directions. Appendices featuring scripts and codes are also included for the interested reader

    Curvilinear Interface Methodology for Finite-Element Applications

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    Recent trends in design and manufacturing suggest a tendency toward multiple centers of specialty which results in a need for improved integration methodology for dissimilar finite element or CFD meshes. Since a typical finite element or CFD analysis requires about 50% of an engineers effort to be devoted to modeling and input, there is a need to advance the state-of-the-art in modeling, methodology. These two trends indicate a need to for the capability to combine independently-modeled configurations in an automated and robust way without the need for global remodeling. One approach to addressing this need is the development of interfacing methodology which will automatically integrate independently modeled subdomains. The present research included the following objectives: (i) to develop and implement computational methods for automatically remodeling non-coincident finite element models having a pre-defined interface, (ii) to formulate and implement a parametric representation of general space curves and surfaces with a well-defined orientation, and (iii) to demonstrate the computational methodology with representative two- and three-dimensional finite element models. Methodology for automatically remodeling non-coincident subdomains was developed and tested for two- and three-dimensional, independently modeled subdomains. Representative classes of applications have been solved which gave good agreement with reference solutions obtained with conventional methods. The two-dimensional classes of problems solved included flat and curved membranes multiple subdomains having large gaps between the subdomains and general space curves representing an interface for re-modeling the portions of subdomains adjacent to the interface. The three-dimensional classes of problems solved includes multiple three-dimensional subdomains having large three-dimensional gap between previously modeled subdomains. The interface was represented by general surfaces with a well-defined orientation and having curvature in possibly more than one direction. The results demonstrated the re-modeling methodology to be general, flexible in use, highly automated, and robust for a diverse class of problems. The research reported represents an important advancement in the area of automated re-modeling for computational mechanics applications

    Galerkin projection of discrete fields via supermesh construction

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    Interpolation of discrete FIelds arises frequently in computational physics. This thesis focuses on the novel implementation and analysis of Galerkin projection, an interpolation technique with three principal advantages over its competitors: it is optimally accurate in the L2 norm, it is conservative, and it is well-defined in the case of spaces of discontinuous functions. While these desirable properties have been known for some time, the implementation of Galerkin projection is challenging; this thesis reports the first successful general implementation. A thorough review of the history, development and current frontiers of adaptive remeshing is given. Adaptive remeshing is the primary motivation for the development of Galerkin projection, as its use necessitates the interpolation of discrete fields. The Galerkin projection is discussed and the geometric concept necessary for its implementation, the supermesh, is introduced. The efficient local construction of the supermesh of two meshes by the intersection of the elements of the input meshes is then described. Next, the element-element association problem of identifying which elements from the input meshes intersect is analysed. With efficient algorithms for its construction in hand, applications of supermeshing other than Galerkin projections are discussed, focusing on the computation of diagnostics of simulations which employ adaptive remeshing. Examples demonstrating the effectiveness and efficiency of the presented algorithms are given throughout. The thesis closes with some conclusions and possibilities for future work

    A framework for automatic modeling of underground excavations in homogeneous rock mass

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    Determining the optimum excavation sequence in mining or civil engineering requires using stress analysis methods to repeatedly solve large models. Time consuming preparation of the model and lengthy computations, often measured in days, can have major impacts on successful ongoing operation of an underground mine, where stope failures can cost millions of dollars and perhaps result in closure of the mine. Widespread acceptance of new tunneling methods such as NATM which depend heavily on numerical stress analysis tools and the fact that the effects of excavation at the face of the tunnel are distinctively three dimensional necessitates the use of 3D numerical analysis of these problems. A framework was developed to facilitate efficient modeling of underground excavations and to create an optimal 3D mesh by reducing the number of surface and volume elements while keeping the result of stress analysis accurate enough at the region of interest, where a solution is sought. Fewer surface and volume elements means fewer degrees of freedom in the numerical model. The reduction in number of degrees of freedom directly translates to savings in computational time and resources. The mesh refinement algorithm is driven by a set of criteria that are functions of distance and visibility of points from the region of interest and the framework can be easily extended by adding new types of criteria. A software application was developed to realize the proposed framework and it was applied to a number of mining and civil engineering problems to investigate the applicability, accuracy and efficiency of the framework. The optimized mesh produced by the framework reduced the time to solution significantly and the accuracy of the results obtained from the optimized mesh is comparable to the accuracy of the input data for mining engineering problems

    Real-time stress analysis of three-dimensional boundary element problems with continuously updating geometry

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    Computational design of mechanical components is an iterative process that involves multiple stress analysis runs; this can be time consuming and expensive. Significant improvements in the efficiency of this process can be made by increasing the level of interactivity. One approach is through real-time re-analysis of models with continuously updating geometry. In this work the boundary element method is used to realise this vision. Three primary areas need to be considered to accelerate the re-solution of boundary element problems. These are re-meshing the model, updating the boundary element system of equations and re-solution of the system. Once the initial model has been constructed and solved, the user may apply geometric perturbations to parts of the model. A new re-meshing algorithm accommodates these changes in geometry whilst retaining as much of the existing mesh as possible. This allows the majority of the previous boundary element system of equations to be re-used for the new analysis. Efficiency is achieved during re-integration by applying a reusable intrinsic sample point (RISP) integration scheme with a 64-bit single precision code. Parts of the boundary element system that have not been updated are retained by the re-analysis and integrals that multiply zero boundary conditions are suppressed. For models with fewer than 10,000 degrees of freedom, the re-integration algorithm performs up to five times faster than a standard integration scheme with less than 0.15% reduction in the L_2-norm accuracy of the solution vector. The method parallelises easily and an additional six times speed-up can be achieved on eight processors over the serial implementation. The performance of a range of direct, iterative and reduction based linear solvers have been compared for solving the boundary element system with the iterative generalised minimal residual (GMRES) solver providing the fastest convergence rate and the most accurate result. Further time savings are made by preconditioning the updated system with the LU decomposition of the original system. Using these techniques, near real-time analysis can be achieved for three-dimensional simulations; for two-dimensional models such real-time performance has already been demonstrated

    Automatic mesh generation and adaptive remeshing for geological modelling

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    Development of the VHP-Female Full-Body Computational Model and Its Applications for Biomedical Electromagnetic Modeling

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    Computational modeling offers better insight into a wide range of bioelectrical and biomechanical problems with improved tools for the design of medical devices and the diagnosis of pathologies. Electromagnetic modeling at low and high frequencies is particularly necessary. Modeling electromagnetic, structural, thermal, and acoustic response of the human body to different internal and external stimuli is limited by the availability of numerically efficient computational human models. This study describes the development to date of a computational full-body human model - Visible Human Project (VHP) - Female Model. Its unique feature is full compatibility both with MATLAB and specialized FEM computational software packages such as ANSYS HFSS/Maxwell 3D. This study also describes progress made to date in using the newly developed tools for segmentation. A visualization tool is implemented within MATLAB and is based on customized version of the constrained 2D Delaunay triangulation method for intersecting objects. This thesis applies a VHP - Female Model to a specific application, transcranial Direct Current Stimulation (tDCS). Transcranial Direct Current Stimulation has been beneficial in the stimulation of cortical activity and treatment of neurological disorders in humans. The placement of electrodes, which is cephalic versus extracephalic montages, is studied for optimal targeting of currents for a given functional area. Given the difficulty of obtaining in vivo measurements of current density, modeling of conventional and alternative electrode montages via the FEM has been utilized to provide insight into the tDCS montage performance. An insight into future work and potential areas of research, such as study of bone quality have been presented too
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