3,335 research outputs found
Space-time editing of elastic motion through material optimization and reduction
We present a novel method for elastic animation editing with space-time constraints. In a sharp departure from previous approaches, we not only optimize control forces added to a linearized dynamic model, but also optimize material properties to better match user constraints and provide plausible and consistent motion. Our approach achieves efficiency and scalability by performing all computations in a reduced rotation-strain (RS) space constructed with both cubature and geometric reduction, leading to two orders of magnitude improvement over the original RS method. We demonstrate the utility and versatility of our method in various applications, including motion editing, pose interpolation, and estimation of material parameters from existing animation sequences
Fast Complementary Dynamics via Skinning Eigenmodes
We propose a reduced-space elasto-dynamic solver that is well suited for
augmenting rigged character animations with secondary motion. At the core of
our method is a novel deformation subspace based on Linear Blend Skinning that
overcomes many of the shortcomings prior subspace methods face. Our skinning
subspace is parameterized entirely by a set of scalar weights, which we can
obtain through a small, material-aware and rig-sensitive generalized eigenvalue
problem. The resulting subspace can easily capture rotational motion and
guarantees that the resulting simulation is rotation equivariant. We further
propose a simple local-global solver for linear co-rotational elasticity and
propose a clustering method to aggregate per-tetrahedra non-linear energetic
quantities. The result is a compact simulation that is fully decoupled from the
complexity of the mesh.Comment: 20 pages, 24 figure
Cyclic Density Functional Theory : A route to the first principles simulation of bending in nanostructures
We formulate and implement Cyclic Density Functional Theory (Cyclic DFT) -- a
self-consistent first principles simulation method for nanostructures with
cyclic symmetries. Using arguments based on Group Representation Theory, we
rigorously demonstrate that the Kohn-Sham eigenvalue problem for such systems
can be reduced to a fundamental domain (or cyclic unit cell) augmented with
cyclic-Bloch boundary conditions. Analogously, the equations of electrostatics
appearing in Kohn-Sham theory can be reduced to the fundamental domain
augmented with cyclic boundary conditions. By making use of this symmetry cell
reduction, we show that the electronic ground-state energy and the
Hellmann-Feynman forces on the atoms can be calculated using quantities defined
over the fundamental domain. We develop a symmetry-adapted finite-difference
discretization scheme to obtain a fully functional numerical realization of the
proposed approach. We verify that our formulation and implementation of Cyclic
DFT is both accurate and efficient through selected examples.
The connection of cyclic symmetries with uniform bending deformations
provides an elegant route to the ab-initio study of bending in nanostructures
using Cyclic DFT. As a demonstration of this capability, we simulate the
uniform bending of a silicene nanoribbon and obtain its energy-curvature
relationship from first principles. A self-consistent ab-initio simulation of
this nature is unprecedented and well outside the scope of any other systematic
first principles method in existence. Our simulations reveal that the bending
stiffness of the silicene nanoribbon is intermediate between that of graphene
and molybdenum disulphide. We describe several future avenues and applications
of Cyclic DFT, including its extension to the study of non-uniform bending
deformations and its possible use in the study of the nanoscale flexoelectric
effect.Comment: Version 3 of the manuscript, Accepted for publication in Journal of
the Mechanics and Physics of Solids,
http://www.sciencedirect.com/science/article/pii/S002250961630368
Essential dynamics of proteins using geometrical simulations and subspace analysis
Essential dynamics is the application of principal component analysis to a dynamic trajectory derived from a simulation protocol in order to extract biologically relevant information contained in the high dimensional data. In this work, we apply the methodology of essential dynamics to protein trajectories derived from geometrical simulations, which are based on the perturbation of geometrical constraints inherent in a protein. Specifically, we show that the geometrical simulation model is highly efficient for the determination of native state dynamics. Furthermore, by the application of subspace analysis to the essential subspaces of multiple sets of proteins that were simulated under multiple modeling paradigms, we show that the geometrical modeling paradigm is internally consistent and provides results that are qualitatively and quantitatively similar to results obtained from the more commonly employed methods of elastic network models and molecular dynamics. The geometrical paradigm is therefore established as a viable alternative or co-model for the investigation of native state protein dynamics with application to both small, single domain proteins as well as large, multi domain systems
MODEL UPDATING AND STRUCTURAL HEALTH MONITORING OF HORIZONTAL AXIS WIND TURBINES VIA ADVANCED SPINNING FINITE ELEMENTS AND STOCHASTIC SUBSPACE IDENTIFICATION METHODS
Wind energy has been one of the most growing sectors of the nation’s renewable energy portfolio for the past decade, and the same tendency is being projected for the upcoming years given the aggressive governmental policies for the reduction of fossil fuel dependency. Great technological expectation and outstanding commercial penetration has shown the so called Horizontal Axis Wind Turbines (HAWT) technologies. Given its great acceptance, size evolution of wind turbines over time has increased exponentially. However, safety and economical concerns have emerged as a result of the newly design tendencies for massive scale wind turbine structures presenting high slenderness ratios and complex shapes, typically located in remote areas (e.g. offshore wind farms). In this regard, safety operation requires not only having first-hand information regarding actual structural dynamic conditions under aerodynamic action, but also a deep understanding of the environmental factors in which these multibody rotating structures operate. Given the cyclo-stochastic patterns of the wind loading exerting pressure on a HAWT, a probabilistic framework is appropriate to characterize the risk of failure in terms of resistance and serviceability conditions, at any given time. Furthermore, sources of uncertainty such as material imperfections, buffeting and flutter, aeroelastic damping, gyroscopic effects, turbulence, among others, have pleaded for the use of a more sophisticated mathematical framework that could properly handle all these sources of indetermination. The attainable modeling complexity that arises as a result of these characterizations demands a data-driven experimental validation methodology to calibrate and corroborate the model. For this aim, System Identification (SI) techniques offer a spectrum of well-established numerical methods appropriated for stationary, deterministic, and data-driven numerical schemes, capable of predicting actual dynamic states (eigenrealizations) of traditional time-invariant dynamic systems. As a consequence, it is proposed a modified data-driven SI metric based on the so called Subspace Realization Theory, now adapted for stochastic non-stationary and timevarying systems, as is the case of HAWT’s complex aerodynamics. Simultaneously, this investigation explores the characterization of the turbine loading and response envelopes for critical failure modes of the structural components the wind turbine is made of. In the long run, both aerodynamic framework (theoretical model) and system identification (experimental model) will be merged in a numerical engine formulated as a search algorithm for model updating, also known as Adaptive Simulated Annealing (ASA) process. This iterative engine is based on a set of function minimizations computed by a metric called Modal Assurance Criterion (MAC). In summary, the Thesis is composed of four major parts: (1) development of an analytical aerodynamic framework that predicts interacted wind-structure stochastic loads on wind turbine components; (2) development of a novel tapered-swept-corved Spinning Finite Element (SFE) that includes dampedgyroscopic effects and axial-flexural-torsional coupling; (3) a novel data-driven structural health monitoring (SHM) algorithm via stochastic subspace identification methods; and (4) a numerical search (optimization) engine based on ASA and MAC capable of updating the SFE aerodynamic model
An Eulerian projection method for quasi-static elastoplasticity
A well-established numerical approach to solve the Navier--Stokes equations
for incompressible fluids is Chorin's projection method, whereby the fluid
velocity is explicitly updated, and then an elliptic problem for the pressure
is solved, which is used to orthogonally project the velocity field to maintain
the incompressibility constraint. In this paper, we develop a mathematical
correspondence between Newtonian fluids in the incompressible limit and
hypo-elastoplastic solids in the slow, quasi-static limit. Using this
correspondence, we formulate a new fixed-grid, Eulerian numerical method for
simulating quasi-static hypo-elastoplastic solids, whereby the stress is
explicitly updated, and then an elliptic problem for the velocity is solved,
which is used to orthogonally project the stress to maintain the
quasi-staticity constraint. We develop a finite-difference implementation of
the method and apply it to an elasto-viscoplastic model of a bulk metallic
glass based on the shear transformation zone theory. We show that in a
two-dimensional plane strain simple shear simulation, the method is in
quantitative agreement with an explicit method. Like the fluid projection
method, it is efficient and numerically robust, making it practical for a wide
variety of applications. We also demonstrate that the method can be extended to
simulate objects with evolving boundaries. We highlight a number of
correspondences between incompressible fluid mechanics and quasi-static
elastoplasticity, creating possibilities for translating other numerical
methods between the two classes of physical problems.Comment: 49 pages, 20 figure
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