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Methods for the physically based simulation of solids and fluids
, 2007
"... in my opinion, it is fully adequate ..."
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3D COMPOSITE FINITE ELEMENTS FOR ELLIPTIC BOUNDARY VALUE PROBLEMS WITH DISCONTINUOUS COEFFICIENTS
"... Abstract. For scalar and vectorvalued elliptic boundary value problems with discontinuous coefficients across geometrically complicated interfaces, a composite finite element approach is developed. Composite basis functions are constructed, mimicing the expected jump condition for the solution at t ..."
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Abstract. For scalar and vectorvalued elliptic boundary value problems with discontinuous coefficients across geometrically complicated interfaces, a composite finite element approach is developed. Composite basis functions are constructed, mimicing the expected jump condition for the solution at the interface in an approximate sense. The construction is based on a suitable local interpolation on the space of admissible functions. We study the order of approximation and the convergence properties of the method numerically. As applications, heat diffusion in an aluminium foam matrix filled with polymer and linear elasticity of microstructured materials, in particular specimens of trabecular bone, are investigated. Furthermore, a numerical homogenization approach is developed for periodic structures and real material specimens which are not strictly periodic but are considered as statistical prototypes. Thereby, effective macroscopic material properties can be computed. Key words. composite finite elements, homogenization, elliptic partial differential equations, discontinuous coefficients
Improved robustness for nearlyincompressible large deformation meshfree simulations on Delaunay tessellations
"... A displacementbased Galerkin meshfree method for large deformation analysis of nearlyincompressible elastic solids is presented. Nodal discretization of the domain is defined by a Delaunay tessellation (threenode triangles and fournode tetrahedra), which is used to form the meshfree basis functi ..."
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A displacementbased Galerkin meshfree method for large deformation analysis of nearlyincompressible elastic solids is presented. Nodal discretization of the domain is defined by a Delaunay tessellation (threenode triangles and fournode tetrahedra), which is used to form the meshfree basis functions and to numerically integrate the weak form integrals. In the proposed approach for nearlyincompressible solids, a volumeaveraged nodal projection operator is constructed to average the dilatational constraint at a node from the displacement field of surrounding nodes. The nodal dilatational constraint is then projected onto the linear approximation space. The displacement field is constructed on the linear space and enriched with bubblelike meshfree basis functions for stability. The new procedure leads to a displacementbased formulation that is similar to Fbar methodologies in finite elements and isogeometric analysis. We adopt maximumentropy meshfree basis functions, and the performance of the meshfree method is demonstrated on benchmark problems using structured and unstructured background meshes in two and three dimensions.
Acknowledgments
, 2008
"... A few years ago, I would have never thought that I could end up at one of the world’s finest academic institutions, nevertheless earn the highest attainable degree from that very same place. For that, I would like to thank God for guiding me through the adversities of life prior to my arrival at Cal ..."
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A few years ago, I would have never thought that I could end up at one of the world’s finest academic institutions, nevertheless earn the highest attainable degree from that very same place. For that, I would like to thank God for guiding me through the adversities of life prior to my arrival at Caltech. It is indeed true that whatever does not break you, only makes you stronger. On a different note, this work would not have been possible without the guidance and supervision of my advisor, Professor Michael Ortiz, whom I started to work with four years ago by mere coincidence and only later realized how lucky I was to be in such good hands. His constant support and encouragement have been a driving force in the course of this work. I want to thank Professor Guruswami Ravichandran, Professor Kaushik Bhattacharya, and Professor Chiara Daraio for agreeing to serve on my thesis committee, especially Professor Ravichandran for providing me with advice over the past four years on how to reach this point of my academic career. Many people apart from my advisor have contributed to my advancement throughout
unknown title
, 2006
"... Threedimensional fracture and fragmentation of artificial kidney stones This article has been downloaded from IOPscience. Please scroll down to see the full text article. ..."
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Threedimensional fracture and fragmentation of artificial kidney stones This article has been downloaded from IOPscience. Please scroll down to see the full text article.
Threedimensional
, 2006
"... fracture and fragmentation of artificial kidney stones ..."
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basis
"... Volumeaveraged nodal projection method for nearlyincompressible elasticity using meshfree and bubble ..."
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Volumeaveraged nodal projection method for nearlyincompressible elasticity using meshfree and bubble