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Showing 1 to 17 of 17 for “"Enrichment Functions"”.
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The Generalized Finite Element Method With Global-Local Enrichment Functions
In this work, we propose a procedure to build enrichment functions to overcome this limitation. It involves the solution of local boundary value problems using boundary conditions from a global problem defined on a coarse discretization. The local solutions are in turn used to enrich the global …
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Generalized finite element methods for three-dimensional crack growth simulations
… of the volume mesh, coupled with suitable enrichment functions. As a result, volume meshes need not fit crack surfaces. This work proposes an hp-version of the GFEM (hp-GFEM) for crack growth simulations. This method provides enough flexibility to build high-order discretizations for crack …
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Improved conditioning and accuracy of a two-scale generalized finite element method for fracture mechanics
… of the GFEM/XFEM rely on the use of preselected enrichment functions that are known to ap- proximate the solution of a problem well. However, closed-form analytical enrichment functions are not always available. This research work focuses on advances of a two-scale GFEM for the accurate and …
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Developments in Extended Finite Element Methods for Extraction of Strain Energy Release Rates and Computational Nanomechanics for SWCNT Aggregates
… directly from Irwin's integral. Crack tip enrichment functions in XFEM allow for evaluation of integral quantities in closed form (for some crack configurations studied) and therefore results in an accurate and efficient method. The effects of high order enrichments, mesh refinement and the …
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A three dimensional generalized finite element method for thin fibers embedded in a continuum
… Finite Element Method (GFEM) using global-local enrichment functions (GFEM^{gl}) to overcome these limitations. The methodology is verified by comparing the solution to specific linear elastic problems obtained by using GFEM^{gl} against solutions from the traditional FEM approach. In addition, …
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Analysis of Three-Dimensional Fracture Mechanics Problems: A Non-Intrusive Approach Using ABAQUS and a Generalized Finite Element Method
… finite element method with global-local enrichment functions (GFEM g-l ) can be implemented non-intrusively in existing closed-source FEM software as an add-on module. The GFEM g-l is based on the solution of interdependent global (structural) and local (crack) scale problems. In the …
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A generalized finite element method for three-dimensional fractures in fiber-reinforced composites
… the GFEM where fractures are represented using enrichment functions instead of meshes fitting the crack surface. Matrix cracks are described using discontinuous and singular functions as in the GFEM for homogeneous materials. This procedure can address some of the limitations of existing FEMs by …
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An interface-enriched generalized finite element method for the design of actively-cooled microvascular composites
… type of the coolant. Minimizing three objective functions are considered during the design process: the maximum temperature of the material, the void volume fraction of the microchannels, and the pressure drop needed to circulate the coolant in the network. One of the main challenges in …
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Dimensionally reduced modeling and gradient-based design of microchannel cooling networks
… materials with the ability to perform multiple functions such as dynamic tuning of electromagnetic properties, self-healing and thermal management depending on the fluid circulated in the embedded microchannels. Recent breakthroughs in the vaporization of sacrificial component (VaSC) …
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A multiscale computational framework for the simulation of local features in large structures
… Finite Element Method with global--local enrichments (GFEMgl) and the iterative global—local (IGL) method aiming at capturing localized responses with high accuracy and computational efficiency. In this framework, the GFEMgl is capable of capturing localized thermomechanical responses on …
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Computational modeling and simulation of composite materials based on tomographic images
… discretized solution space is then augmented by enrichment functions associated with points of intersection with material interfaces, thereby enabling the accurate capture of discontinuities in the solution gradient along material interfaces. An important feature of our approach is the use of 2D …
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A multi-scale generalized finite element method for sharp, transient thermal gradients
… difficult. A generalized FEM with global-local enrichments is proposed for the class of problems investigated in this research. In this procedure, a global solution space defined on a coarse mesh is enriched through the partition of unity framework of the generalized FEM with solutions of local …
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A variational multiscale computational framework for reaction-dominated thermo-chemo-mechanical process modeling in multi-constituent material systems
… The proposed fine-scale basis consists of enrichment functions that may be nonzero at element edges. The method captures sharp boundary and internal layers, suppresses spurious oscillations, and better satisfies the maximum principle as compared to other existing methods. A priori …
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Multiscale analysis of localized, nonlinear, three-dimensional thermo-structural effects
… method is based on the GFEM with global–local enrichment functions (GFEMgl), which involves the solution of interdependent coarse- (global) and fine-scale (local) problems. The global problem captures coarse-scale behavior, while local problems resolve sharp solution features in regions where …
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Three-dimensional modeling of failure in quasi-brittle materials and structures
… in the local problem domains. The GFEMg-l enrichment functions allow the kinematics to be represented in the global domain through enrichment function from the local problems rather than explicitly modeling each crack discretely in the global domain. This research effort also proposes an …
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Multiscale Peridynamics Analysis of Nanocomposites and Energetic Materials Using Nonlocal and Local Interface Models
… deletion, adaptive mesh refinement, using enrichment functions and so on, which are commonly used in other numerical methods. Peridynamics is a particle-based method where the particles are allowed to interact with other particles within their horizon which serves as a cut-off distance for …
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The real space finite element Hartree-Fock method and the thermo-mechanical properties of carbon nanotubes
This thesis consists of two parts. The first part aims to explore the application of the popular method of the finite element method (FEM) in the electronic structure theory. The finite element method is a very general numerical technique in mathematics for solving partial differential equations …