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The Natural Element Method In Solid Mechanics
, 1998
"... The application of the Natural Element Method (NEM) (Traversoni, 1994; Braun and Sambridge, 1995) to boundary value problems in twodimensional small displacement elastostatics is presented. The discrete model of the domain \Omega consists of a set of distinct nodes N , and a polygonal descripti ..."
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Cited by 27 (11 self)
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The application of the Natural Element Method (NEM) (Traversoni, 1994; Braun and Sambridge, 1995) to boundary value problems in twodimensional small displacement elastostatics is presented. The discrete model of the domain \Omega consists of a set of distinct nodes N , and a polygonal description of the boundary @ In the Natural Element Method, the trial and test functions are constructed using natural neighbor interpolants. These interpolants are based on the Voronoi tessellation of the set of nodes N . The interpolants are smooth (C NEM is identical to linear finite elements. The NEM interpolant is strictly linear between adjacent nodes on the boundary of the convex hull, which facilitates imposition of essential boundary conditions. A methodology to model material discontinuities and nonconvex bodies (cracks) using NEM is also described.
Performance Modeling of Interactive, Immersive Virtual Environments for Finite Element Simulations
, 1996
"... Interactive, immersive virtual environments allows observers to move freely about computer generated 3D objects and to explore new environments. The effectiveness of these environments is dependent upon the graphics used to model reality and the endtoend lag time (i.e., the delay between a user's ..."
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Cited by 6 (6 self)
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Interactive, immersive virtual environments allows observers to move freely about computer generated 3D objects and to explore new environments. The effectiveness of these environments is dependent upon the graphics used to model reality and the endtoend lag time (i.e., the delay between a user's action and the display of the result of that action). In this paper we focus on the latter issue, which has been found to be equally important as frame rate for interactive displays. In particular, we analyze the components of lag time resulting from executing a finite element simulation on a multiprocessor system located in Argonne, Illinois connected via ATM to the interactive visualization display located in San Diego, California. The primary application involves the analysis of a disk brake system that was demonstrated at the Supercomputing 1995 conference as part of the Information Wide Area Year (IWAY) project, which entailed the interconnection of various supercomputing centers via a ...
Analysis of Power Magnetic Components With Nonlinear Static Hysteresis: FiniteElement Formulation
"... We present a new systematic methodology to efficiently solve coupled electromagnetic problems with nonlinear hysteresis at low frequency (10 kHz), called static hysteresis, by the finiteelement method. The methodology integrates a new domainwallmotion hysteresis model for power magnetic component ..."
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Cited by 1 (0 self)
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We present a new systematic methodology to efficiently solve coupled electromagnetic problems with nonlinear hysteresis at low frequency (10 kHz), called static hysteresis, by the finiteelement method. The methodology integrates a new domainwallmotion hysteresis model for power magnetic components (POMACs) into a finiteelement potential formulation via an implicitinverse model calculation. It uses a novel twolevel iterative algorithm incorporating the efficient implicitinverse model calculation to solve the complete Maxwell equations after the finiteelement discretization. Our formulation does not require an explicit inversion of the hysteresis model as usually done in previous work. The efficient and accurate fullorder model simulations applied to POMAC examples show that the proposed procedure can be applied to other electromagnetic problems with nonlinear static hysteresis. Index Terms—Converters, finite element, hysteresis, power electronics, power magnetic component. I.
Found Comput Math DOI 10.1007/s1020801190873 The Serendipity Family of Finite Elements
, 2010
"... Abstract We give a new, simple, dimensionindependent definition of the serendipity finite element family. The shape functions are the span of all monomials which are linear in at least s − r of the variables where s is the degree of the monomial or, equivalently, whose superlinear degree (total deg ..."
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Abstract We give a new, simple, dimensionindependent definition of the serendipity finite element family. The shape functions are the span of all monomials which are linear in at least s − r of the variables where s is the degree of the monomial or, equivalently, whose superlinear degree (total degree with respect to variables entering at least quadratically) is at most r. The degrees of freedom are given by moments of degree at most r − 2d on each face of dimension d. We establish unisolvence and a geometric decomposition of the space.
Found Comput Math (2011) 11: 337–344 DOI 10.1007/s1020801190873 The Serendipity Family of Finite Elements
"... Abstract We give a new, simple, dimensionindependent definition of the serendipity finite element family. The shape functions are the span of all monomials which are linear in at least s − r of the variables where s is the degree of the monomial or, equivalently, whose superlinear degree (total deg ..."
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Abstract We give a new, simple, dimensionindependent definition of the serendipity finite element family. The shape functions are the span of all monomials which are linear in at least s − r of the variables where s is the degree of the monomial or, equivalently, whose superlinear degree (total degree with respect to variables entering at least quadratically) is at most r. The degrees of freedom are given by moments of degree at most r − 2d on each face of dimension d. We establish unisolvence and a geometric decomposition of the space.
EFFICIENCY OF MULTIBODY SIMULATIONS Approved by:
"... iii ACKNOWLEDGEMENTS This thesis is dedicated to my parents, Horst and Isolde Epple. From an early age, they educated me to ask questions, think critically, and strive for excellence. Their encouragement and support are the foundation on which this thesis was built. I am deeply grateful to my advise ..."
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iii ACKNOWLEDGEMENTS This thesis is dedicated to my parents, Horst and Isolde Epple. From an early age, they educated me to ask questions, think critically, and strive for excellence. Their encouragement and support are the foundation on which this thesis was built. I am deeply grateful to my adviser, Professor Olivier A. Bauchau, for his guidance and support. He was always open to my ideas and patiently answered my numerous questions. I learned a tremendous amount during the last three years, not only about dynamics, but also about tenacity, perseverance, and thinking for oneself. Professor Bauchau provided the best possible environment for my research. I was lucky to be educated by several outstanding teachers and researchers at