Stress constrained compliance minimization by means of the small amplitude homogenization method

2014 ◽  
Vol 49 (6) ◽  
pp. 1025-1036 ◽  
Author(s):  
Sergio Gutiérrez ◽  
Esteban Zegpi
Keyword(s):  
Small Amplitude ◽  
Homogenization Method ◽  
Compliance Minimization

scholarly journals Stress minimization for lattice structures. Part I: Micro-structure design

2021 ◽  
Vol 379 (2201) ◽  
pp. 20200109 ◽  
Author(s):  
A. Ferrer ◽  
P. Geoffroy-Donders ◽  
G. Allaire
Keyword(s):  
Orientation Angle ◽  
Homogenization Method ◽  
Structure Design ◽  
Smoothing Parameter ◽  
Periodicity Cell ◽  
Lattice Structures ◽  
Compliance Minimization ◽  
Macroscopic Stress ◽  
Special Cases ◽  
Stress Minimization

Lattice structures are periodic porous bodies which are becoming popular since they are a good compromise between rigidity and weight and can be built by additive manufacturing techniques. Their optimization has recently attracted some attention, based on the homogenization method, mostly for compliance minimization. The goal of our two-part work is to extend lattice optimization to stress minimization problems two-dimensionally. The present first part is devoted to the choice of a parametrized periodicity cell that will be used for structural optimization in the second part of our work. In order to avoid stress concentration, we propose a square cell microstructure with a super-ellipsoidal hole instead of the standard rectangular hole often used for compliance minimization. This type of cell is parametrized two-dimensionally by one orientation angle, two semi-axis and a corner smoothing parameter. We first analyse their influence on the stress amplification factor by performing some numerical experiments. Second, we compute the optimal corner smoothing parameter for each possible microstructure and macroscopic stress. Then, we average (with specific weights) the optimal smoothing exponent with respect to the macroscopic stress. Finally, to validate the results, we compare our optimal super-ellipsoidal hole with the Vigdergauz microstructure which is known to be optimal for stress minimization in some special cases. This article is part of the theme issue ‘Topics in mathematical design of complex materials’.

On nearly-commensurable periods in the restricted problem of three bodies, with calculations of the long-period variations in the interior 2:1 case

1966 ◽  
Vol 25 ◽  
pp. 197-222 ◽  
Author(s):  
P. J. Message
Keyword(s):  
Periodic Solution ◽  
Periodic Solutions ◽  
Large Amplitude ◽  
Restricted Problem ◽  
Small Amplitude ◽  
Minor Planets ◽  
Long Period ◽  
Numerical Integrations ◽  
Period Variations ◽  
The Mean

An analytical discussion of that case of motion in the restricted problem, in which the mean motions of the infinitesimal, and smaller-massed, bodies about the larger one are nearly in the ratio of two small integers displays the existence of a series of periodic solutions which, for commensurabilities of the typep+ 1:p, includes solutions of Poincaré'sdeuxième sortewhen the commensurability is very close, and of thepremière sortewhen it is less close. A linear treatment of the long-period variations of the elements, valid for motions in which the elements remain close to a particular periodic solution of this type, shows the continuity of near-commensurable motion with other motion, and some of the properties of long-period librations of small amplitude.To extend the investigation to other types of motion near commensurability, numerical integrations of the equations for the long-period variations of the elements were carried out for the 2:1 interior case (of which the planet 108 “Hecuba” is an example) to survey those motions in which the eccentricity takes values less than 0·1. An investigation of the effect of the large amplitude perturbations near commensurability on a distribution of minor planets, which is originally uniform over mean motion, shows a “draining off” effect from the vicinity of exact commensurability of a magnitude large enough to account for the observed gap in the distribution at the 2:1 commensurability.

RSCVn Stars in the Southern Hemisphere

1979 ◽  
Vol 46 ◽  
pp. 371-384 ◽  
Author(s):  
J.B. Hearnshaw
Keyword(s):  
Light Curve ◽  
Southern Hemisphere ◽  
Orbital Period ◽  
Binary Stars ◽  
Small Amplitude ◽  
Light Variation ◽  
Orbital Phase

RSCVn stars are fully detached binary stars which show intrinsic small amplitude (up to 0.3 amplitude peak-to-peak) light variations, as well as, in most of the known cases, eclipses. The spectra are F to G, IV to V for the hotter component and usually KOIV for the cooler. They are also characterised by abnormally strong H and K emission from the cooler star, or, occasionally, from both components. The orbital and light curve periods are in the range 1 day to 2 weeks. An interesting feature is the migration of the light variations to earlier orbital phase, as the light variation period is shorter than the orbital period by a few parts in 10+4to a few parts in 10+3.

Amplitude Distributions of Cochlear Microphonic Response to an Acoustic Sinusoid in Noise

1968 ◽  
Vol 11 (1) ◽  
pp. 63-76
Author(s):  
Donald C. Teas ◽  
Gretchen B. Henry
Keyword(s):  
Small Amplitude ◽  
Basilar Membrane ◽  
Spectral Composition ◽  
Pass Band ◽  
Cochlear Microphonic ◽  
Filter Output ◽  
Electronic Filter ◽  
Low Pass ◽  
Band Pass ◽  
Instantaneous Voltage

The distributions of instantaneous voltage amplitudes in the cochlear microphonic response recorded from a small segment along the basilar membrane are described by computing amplitude histograms. Comparisons are made between the distributions for noise and for those after the addition to the noise of successively stronger sinusoids. The amplitudes of the cochlear microphonic response to 5000 Hz low-pass noise are normally distributed in both Turn I and Turn III of the guinea pig’s cochlea. The spectral composition of the microphonic from Turn I and from Turn III resembles the output of band-pass filters set at about 4000 Hz, and about 500 Hz, respectively. The normal distribution of cochlear microphonic amplitudes for noise is systematically altered by increasing the strength of the added sinusoid. A decrease of three percent in the number of small amplitude events (±1 standard deviation) in the cochlear microphonic from Turn III is seen when the rms voltage of a 500 Hz sinusoid is at −18 dB re the rms voltage of the noise (at the earphone). When the rms of the sinusoid and noise are equal, the decrease in small voltages is about 25%, but there is also an increase in the number of large voltage amplitudes. Histograms were also computed for the output of an electronic filter with a pass-band similar to Turn III of the cochlea. Strong 500 Hz sinusoids showed a greater proportion of large amplitudes in the filter output than in CM III . The data are interpreted in terms of an anatomical substrate.

Homogenization Method Based on Eigenvector Expansions

2006 ◽  
Vol 4 (1) ◽  
pp. 197-206 ◽  
Author(s):  
Yufeng Xing ◽  
Jinmei Tian ◽  
Dechao Zhu ◽  
Wenjian Xie
Keyword(s):  
Homogenization Method

scholarly journals Stellar magnetic imaging from spectropolarimetric data

1996 ◽  
Vol 176 ◽  
pp. 53-60 ◽  
Author(s):  
J.-F. Donati
Keyword(s):  
Small Amplitude ◽  
High Accuracy ◽  
Spectral Lines ◽  
New Method ◽  
Doppler Imaging ◽  
Magnetic Imaging ◽  
Active Stars ◽  
Surface Fields ◽  
Very High

In this paper, I will review the capabilities of magnetic imaging (also called Zeeman-Doppler imaging) to reconstruct spot distributions of surface fields from sets of rotationnally modulated Zeeman signatures in circularly polarised spectral lines. I will then outline a new method to measure small amplitude magnetic signals (typically 0.1% for cool active stars) with very high accuracy. Finally, I will present and comment new magnetic images reconstructed from data collected in 1993 December at the Anglo-Australian Telescope (AAT).

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