A popular version of optimal control problems is discussed and a nonlinear two point boundary value problem embedded in the optimal control problem is then converted into an initial-value problem according to the boun...
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A popular version of optimal control problems is discussed and a nonlinear two point boundary value problem embedded in the optimal control problem is then converted into an initial-value problem according to the boundary value sensitivity differential equations. An integration method for matrix differential equations is also presented. In this novel way, the exact solutions are obtained for the linear optimal control problems. Two illustrative numerical examples are given to show the power and efficiency.
Wave localization in randomly disordered multiwave structures is investigated. The smallest localization factor is of particular interest and is related to the smallest positive Lyapunov exponent. The numerical algori...
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Wave localization in randomly disordered multiwave structures is investigated. The smallest localization factor is of particular interest and is related to the smallest positive Lyapunov exponent. The numerical algorithm by Wolf et al. is modified to determine all of the Lyapunov exponents. The wave localization in a large beamlike lattice truss modeled as an equivalent continuous Timoshenko beam is studied.
A transient, two-dimensional, finite element shock-capturing scheme on unstructured grids was applied to the study of a shock interacting with a box suspended above a rigid elevated surface. The area between the box a...
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A transient, two-dimensional, finite element shock-capturing scheme on unstructured grids was applied to the study of a shock interacting with a box suspended above a rigid elevated surface. The area between the box and the surface was partially blocked by the box support beams, resulting in complex shock diffraction processes. The results demonstrate the capability of the developed adaptive refinement/coarsening algorithm to properly adapt to weak shocks, expansions, and contact discontinuities, and highlight the resulting excellent resolution of the captured flow features. In addition to interesting shock diffraction and propagation phenomena, the results demonstrate the capability of the new code to capture, and define in great detail, vortex sheets shed from sharp corners. We show that the baroclinic effect, an inviscid process, controls the shedding phenomenon during the diffraction phase. Hence, the Eulerian model is able to correctly predict this process.
We show how to exploit the structure inherent in the linear algebra for constrained nonlinear optimization problems when inequality constraints have been converted to equations by adding slack variables and the proble...
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We show how to exploit the structure inherent in the linear algebra for constrained nonlinear optimization problems when inequality constraints have been converted to equations by adding slack variables and the problem is solved using an augmented Lagrangian method.
This paper discusses the numerical solution of eigenvalue problems for Hamiltonian systems of ordinary differential equations. Two new codes are presented which incorporate the algorithms described here;to the best of...
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Composites have inherent scatter in elastic and strength properties. A probabilistic model utilizing random material characteristics to predict damage evolution in orthotropic laminated composites is presented in this...
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Composites have inherent scatter in elastic and strength properties. A probabilistic model utilizing random material characteristics to predict damage evolution in orthotropic laminated composites is presented in this paper. The proposed model is based on the division of laminated composites into a statistically large number of mesoelements (mesovolumes). The mesovolume is assumed to be large enough to be structurally homogeneous, and at the same time it has to be comparatively small to satisfy the condition of stochastic homogeneity of stress and strain fields. Three modes of mesovolume failure, i.e., fibre breakage and matrix failure in the transverse direction as well as matrix shear cracking, are taken into account. Damage formation in a ply and in a laminate as a whole for a given plane stress state is calculated from the probabilities of mesovolume failure. These probabilities are directly utilized in reducing ply material constants. A numerical algorithm for damage accumulation and deformation history predictions for orthotropic laminated composites are developed. The behavior of a laminated orthotropic composite is presented as an illustrative example. Analysis of angle-ply Kevlar/epoxy laminates subjected to tension, compression, and shear loading is performed. The effect of scatters in elastic and strength characteristics on damage evolution is shown.
Continuous- and discrete-time differential dynamic programming (DDP) approaches to solve general optimal control problems are described and analysed. A comparison of the two approaches shows the continuous-time approa...
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Continuous- and discrete-time differential dynamic programming (DDP) approaches to solve general optimal control problems are described and analysed. A comparison of the two approaches shows the continuous-time approach to be more general and flexible compared with the discrete-time approach, since it is not tied to any discretization scheme. A comparison of DDP with the non-linear programming (NLP) approach is also given. Three structural control problems - a linear model of a space structure, a single degree of freedom non-linear impact absorber and a non-linear flexible beam subjected to an impulsive load - are used to numerically evaluate the continuous- and discrete-time DDP approaches. Several grid sizes are used to show that the continuous-time approach with a reasonable number of grid points is more accurate and efficient (in most cases) than the discrete-time approach. It is therefore recommended to fully develop and evaluate the technique for the optimal control of large-scale systems.
In this paper we develop an approach to designing reduced-order multirate estimators. A discrete-time model that accounts for the multirate timing sequence of measurements is presented and is shown to have periodicall...
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In this paper we develop an approach to designing reduced-order multirate estimators. A discrete-time model that accounts for the multirate timing sequence of measurements is presented and is shown to have periodically time-varying dynamics. Using discrete-time stability theory, the optimal projection approach to fixed-order (i.e, full- and reduced-order) estimation is generalized to obtain reduced-order periodic estimators that account for the multirate architecture. It is shown that the optimal reduced-order filter is characterized by means of a periodically time-varying system of equations consisting of coupled Riccati and Lyapunov equations. A novel homotopy algorithm, based on a Newton correction scheme, is also presented which allows solutions to periodic difference Riccati equations.
We present a new algorithm which computes dot-products of arbitrary length with minimal rounding errors, independent of the number of addends. The algorithm has an O(n) time and O(1) memory complexity and does not nee...
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We present a new algorithm which computes dot-products of arbitrary length with minimal rounding errors, independent of the number of addends. The algorithm has an O(n) time and O(1) memory complexity and does not need extensions of the arithmetic kernel, i.e., usual floating-point operations. A slight modification yields an algorithm which computes the dot-product in machine precision. Due to its simplicity, the algorithm can easily be implemented in hardware.
The hypersonic flow over a cavity is investigated. The time-dependent compressible Navier-Stokes equations are numerically sloved. An implicit algorithm, with a subiteration procedure to recover time accuracy, is used...
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The hypersonic flow over a cavity is investigated. The time-dependent compressible Navier-Stokes equations are numerically sloved. An implicit algorithm, with a subiteration procedure to recover time accuracy, is used to perform the time-accurate computations. The objective of the study is to investigate the effects of Reynolds number and cavity dimensions. The comparison of the computations with available experimental data, in terms of time mean static pressure, heat transfer, and Mach number, show good agreement. In the computations large vortex structures, which adversely affect the cavity flow characteristics, are observed at the rear of the cavity. A self-sustained oscillatory motion occurs within the cavity over a range of Reynolds number and cavity dimensions. The frequency spectra of the oscillations show good agreement with a modified semiempirical relation.
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