30,423 research outputs found
Guidance, flight mechanics and trajectory optimization. Volume 11 - Guidance equations for orbital operations
Mathematical formulation of guidance equations and solutions for orbital space mission
A monolithic fluid-structure interaction formulation for solid and liquid membranes including free-surface contact
A unified fluid-structure interaction (FSI) formulation is presented for
solid, liquid and mixed membranes. Nonlinear finite elements (FE) and the
generalized-alpha scheme are used for the spatial and temporal discretization.
The membrane discretization is based on curvilinear surface elements that can
describe large deformations and rotations, and also provide a straightforward
description for contact. The fluid is described by the incompressible
Navier-Stokes equations, and its discretization is based on stabilized
Petrov-Galerkin FE. The coupling between fluid and structure uses a conforming
sharp interface discretization, and the resulting non-linear FE equations are
solved monolithically within the Newton-Raphson scheme. An arbitrary
Lagrangian-Eulerian formulation is used for the fluid in order to account for
the mesh motion around the structure. The formulation is very general and
admits diverse applications that include contact at free surfaces. This is
demonstrated by two analytical and three numerical examples exhibiting strong
coupling between fluid and structure. The examples include balloon inflation,
droplet rolling and flapping flags. They span a Reynolds-number range from
0.001 to 2000. One of the examples considers the extension to rotation-free
shells using isogeometric FE.Comment: 38 pages, 17 figure
Should one compute the Temporal Difference fix point or minimize the Bellman Residual? The unified oblique projection view
We investigate projection methods, for evaluating a linear approximation of
the value function of a policy in a Markov Decision Process context. We
consider two popular approaches, the one-step Temporal Difference fix-point
computation (TD(0)) and the Bellman Residual (BR) minimization. We describe
examples, where each method outperforms the other. We highlight a simple
relation between the objective function they minimize, and show that while BR
enjoys a performance guarantee, TD(0) does not in general. We then propose a
unified view in terms of oblique projections of the Bellman equation, which
substantially simplifies and extends the characterization of (schoknecht,2002)
and the recent analysis of (Yu & Bertsekas, 2008). Eventually, we describe some
simulations that suggest that if the TD(0) solution is usually slightly better
than the BR solution, its inherent numerical instability makes it very bad in
some cases, and thus worse on average
An efficient numerical method for shakedown analysis
The algorithm proposed in [9] for incremental elastoplasticity is extended and applied to shakedown analysis. Using the three field mixed finite element proposed in [22] a series of mathematical programming problems or steps, obtained from the application of the proximal point algorithm to the static shakedown theorem, are obtained. Each step is solved by an Equality Constrained Sequential Quadratic Programming (EC-SQP) tech- nique that allows a consistent linearization of the equations improving the computational efficiency
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