Linear and Nonlinear Programming

Luenberger, David G.; Ye, Yinyu

doi:10.1007/978-3-319-18842-3

Cited by 474 publications

(404 citation statements)

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“…To this end, we observe from (2.12) that, for a submacroscopically stable pair (F 0 , G 0 ), the tensor G 0 is a solution of the constrained minimization problem: minimize G → (F 0 , G) subject to the constraint det G det F 0 . The KuhnTucker theorem ( [23], p. 314) implies that, corresponding to the given solution G 0 , there is a number λ 0 for which…”

Section: Submacroscopic Stabilitymentioning

confidence: 99%

Toward a Field Theory for Elastic Bodies Undergoing Disarrangements

Deseri

Owen

The Rational Spirit in Modern Continuum Mechanics

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Abstract. Structured deformations are used to refine the basic ingredients of continuum field theories and to derive a system of field equations for elastic bodies undergoing submacroscopically smooth geometrical changes as well as submacroscopically non-smooth geometrical changes (disarrangements). The constitutive assumptions employed in this derivation permit the body to store energy as well as to dissipate energy in smooth dynamical processes. Only one non-classical field G, the deformation without disarrangements, appears in the field equations, and a consistency relation based on a decomposition of the Piola-Kirchhoff stress circumvents the use of additional balance laws or phenomenological evolution laws to restrict G. The field equations are applied to an elastic body whose free energy depends only upon the volume fraction for the structured deformation. Existence is established of two universal phases, a spherical phase and an elongated phase, whose volume fractions are (1 − γ 0 ) 3 and (1 − γ 0 ) respectively, with γ 0 := ( √ 5 − 1)/2 the "golden mean". Mathematics Subject Classifications (2002):74A, 74B20, 74M25, 74H99, 76N99, 80A17.

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Section: Submacroscopic Stabilitymentioning

confidence: 99%

Toward a Field Theory for Elastic Bodies Undergoing Disarrangements

Deseri

Owen

The Rational Spirit in Modern Continuum Mechanics

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“…The finite derivative is a special form of a secant correction, used to obtain a special property over a finite interval, see e.g. [10]. In the present case the secant representation is used to provide a higher order correction to the fourth-order representation g q in the form…”

Section: Energy Conservationmentioning

confidence: 99%

“…This concept bears similarity with the notion of a secant representation of derivatives used in quasi Newton methods, see e.g. [10] Chapter 9. The concept was rapidly adopted within computational mechanics, see e.g.…”

Section: Introductionmentioning

confidence: 97%

Conservative fourth-order time integration of non-linear dynamic systems

Krenk

2015

Computer Methods in Applied Mechanics and Engineering

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“…Thus, LSE figures out object position by optimizing sum of squares residual between object and reference points. Linear Least Squares (LLS) and Nonlinear Least Squares (NLS) ( [26], [27], [28] and [29]) are realized and compared. Simulation and experiments have been carried out to verify these proposed methods.…”

Section: Introductionmentioning

confidence: 99%

Improvement of Ultrasound-based System Using Sine Wave Detector and CAN Network

Tan¹

2017

Preprint

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This paper presents an improved indoor localization system based on RF and ultrasonic signal which we named SNSH system. This system composes of a transmitter mounted in a mobile target, and a series of receiver nodes which are managed by a coordinator. By measuring Time Delay of Arrival (TDoA) of RF and ultrasonic signal from the transmitter, distance from target to receiver node is calculated and sent to the coordinator through CAN network, and all the information are gathered in PC to estimate 3D position of the target. Sine wave detector and dynamic threshold filter are applied to provide excellent accuracy of range measurement from TDoA result, and multilateration algorithms is realized to optimize coordinate determination accuracy. Specifically, Linear Least Square and Non-linear Least Square techniques are implemented to contrast their performances in target coordinate estimation. RF signal encoding/decoding time, time delay in CAN network and math calculating are carefully considered to ensure optimal system performance and get ready for field application. Experiments show that sine wave detector algorithm has greatly improved range measurement accuracy, with mean error at 2.2mm and maximum error at 6.7 mm, for distance below 5m. In addition, 3D position accuracy is greatly enhanced by multilateration methods, with mean error in position stay under 15mm, and 90% confident error values at 23mm for LLS, 20mm for NLS. Overall system update period has been verified in real system operation, with maximum rate at 25ms, and compared with other existing researches.

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Linear and Nonlinear Programming

Cited by 474 publications

References 0 publications

Toward a Field Theory for Elastic Bodies Undergoing Disarrangements

Toward a Field Theory for Elastic Bodies Undergoing Disarrangements

Conservative fourth-order time integration of non-linear dynamic systems

Improvement of Ultrasound-based System Using Sine Wave Detector and CAN Network

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