A Noncanonically Shape Laminated Plate Subjected to Impact Loading: Theory and Experiment

2008 ◽  
Vol 75 (5) ◽  
Author(s):  
Natalia V. Smetankina ◽  
Alexander N. Shupikov ◽  
Sergei Yu. Sotrikhin ◽  
Vladimir G. Yareshchenko
Keyword(s):  
Order Theory ◽  
Transverse Shear Strain ◽  
Laminated Plate ◽  
Immersion Method ◽  
Plan View ◽  
First Order Theory ◽  
Wide Range ◽  
Normal Element ◽  
Straight Lines ◽  
Theoretical Results

This paper suggests an analytical approach to investigating vibrations of a laminated plate with a noncanonical shape in plan view under impact with an impactor having a semispherical end. The approach suggested is based on the immersion method. The dynamic behavior of the plate is described by the first-order theory accounting for transverse shear strain, thickness reduction, and normal element rotation inertia in each layer. Impact has been analyzed for different points of the plate whose contour consists of straight lines and circle arcs. The theoretical results are consistent with experimental data obtained with the dynamic wide-range strain measurement technique.

A Higher Order Finite Element Model for the Vibration Analysis of Laminated Beams

1998 ◽  
Vol 120 (3) ◽  
pp. 822-824 ◽  
Author(s):  
S. R. Marur ◽  
T. Kant
Keyword(s):  
Axial Strain ◽  
Element Model ◽  
Order Theory ◽  
Higher Order ◽  
Transverse Shear Strain ◽  
Normal Strain ◽  
Laminated Beams ◽  
First Order Theory ◽  
Displacement Model ◽  
Transverse Normal Strain

A higher order displacement model based on a cubic axial strain, cubic transverse shear strain and quadratic transverse normal strain across the thickness of the beam, to model exactly the warping of the cross section is proposed which maintains zero stress at the top and bottom of the beam with out the aid of any shear correction factor. Numerical experiments carried out clearly bring out the efficacy of this model over the first order theory for laminated beams.

scholarly journals Simulating of Bird Strike on Aircraft Laminated Glazing

2019 ◽  
Vol 304 ◽  
pp. 01010
Author(s):  
Natalia Smetankina ◽  
Alyona Malykhina ◽  
Dmytro Merkulov
Keyword(s):  
Order Theory ◽  
Aviation Industry ◽  
Strength Analysis ◽  
Bird Strike ◽  
First Order Theory ◽  
Bird Impact ◽  
Normal Element ◽  
The Mathematical Model ◽  
Transverse Shear Strains ◽  
Good Agreement

A bird strike is a critical problem in the context of safety in the aviation industry. All modern aircraft structures are designed with account of likely collision with birds. Thus, aviation standards in force require that the aircraft construction would allow the crew to conclude the flight safely after collision with a 1.81-kg bird. A method for analysing the stress-strained state of laminated airplane glazing at different operational factors is presented. The method includes a technique for strength analysis of the laminated airplane glazing at bird impact, and a technique for analysis of excess pressure. The model of laminated glazing is based on the refined first-order theory accounting for transverse shear strains, thickness reduction and normal element rotation inertia in each layer. The mathematical model of the pressure impulse authentically reproducing the bird impact is based on experimental research. Theoretical results are in good agreement with experimental data, thus allowing to recommend the method to develop new airplane glazing elements.

On the nominal transverse shear strain to characterize the severity of creasing

TAPPI Journal ◽  
2018 ◽  
Vol 17 (04) ◽  
pp. 231-240
Author(s):  
Douglas Coffin ◽  
Joel Panek
Keyword(s):  
Shear Strain ◽  
Transverse Shear ◽  
Elastic Limit ◽  
Experimental Results ◽  
Transverse Shear Strain ◽  
Maximum Strain ◽  
Machine Direction ◽  
Engineering Approach ◽  
Wide Range ◽  
Analytic Expression

A transverse shear strain was utilized to characterize the severity of creasing for a wide range of tooling configurations. An analytic expression of transverse shear strain, which accounts for tooling geometry, correlated well with relative crease strength and springback as determined from 90° fold tests. The experimental results show a minimum strain (elastic limit) that needs to be exceeded for the relative crease strength to be reduced. The theory predicts a maximum achievable transverse shear strain, which is further limited if the tooling clearance is negative. The elastic limit and maximum strain thus describe the range of interest for effective creasing. In this range, cross direction (CD)-creased samples were more sensitive to creasing than machine direction (MD)-creased samples, but the differences were reduced as the shear strain approached the maximum. The presented development provides the foundation for a quantitative engineering approach to creasing and folding operations.

scholarly journals A first-order theory of Ulm type

Computability ◽  
2019 ◽  
Vol 8 (3-4) ◽  
pp. 347-358
Author(s):  
Matthew Harrison-Trainor
Keyword(s):  
Order Theory ◽  
First Order ◽  
First Order Theory

scholarly journals Quasi-decidability of a Fragment of the First-Order Theory of Real Numbers

2015 ◽  
Vol 57 (2) ◽  
pp. 157-185 ◽  
Author(s):  
Peter Franek ◽  
Stefan Ratschan ◽  
Piotr Zgliczynski
Keyword(s):  
Order Theory ◽  
Real Numbers ◽  
First Order ◽  
First Order Theory

scholarly journals Optimising the AR Engraved Structure on Light-Guide Facets for a Wide Range of Wavelengths

Optics ◽  
2020 ◽  
Vol 2 (1) ◽  
pp. 25-42
Author(s):  
Ioseph Gurwich ◽  
Yakov Greenberg ◽  
Kobi Harush ◽  
Yarden Tzabari
Keyword(s):  
Theoretical Analysis ◽  
Light Guide ◽  
Spectral Band ◽  
Angular Range ◽  
The Past ◽  
Input And Output ◽  
Wide Range ◽  
The Given ◽  
Theoretical Results ◽  
Shape And Size

The present study is aimed at designing anti-reflective (AR) engraving on the input–output surfaces of a rectangular light-guide. We estimate AR efficiency, by the transmittance level in the angular range, determined by the light-guide. Using nano-engraving, we achieve a uniform high transmission over a wide range of wavelengths. In the past, we used smoothed conical pins or indentations on the faces of light-guide crystal as the engraved structure. Here, we widen the class of pins under consideration, following the physical model developed in the previous paper. We analyze the smoothed pyramidal pins with different base shapes. The possible effect of randomization of the pins parameters is also examined. The results obtained demonstrate optimized engraved structure with parameters depending on the required spectral range and facet format. The predicted level of transmittance is close to 99%, and its flatness (estimated by the standard deviation) in the required wavelengths range is 0.2%. The theoretical analysis and numerical calculations indicate that the obtained results demonstrate the best transmission (reflection) we can expect for a facet with the given shape and size for the required spectral band. The approach is equally useful for any other form and of the facet. We also discuss a simple way of comparing experimental and theoretical results for a light-guide with the designed input and output features. In this study, as well as in our previous work, we restrict ourselves to rectangular facets. We also consider the limitations on maximal transmission produced by the size and shape of the light-guide facets. The theoretical analysis is performed for an infinite structure and serves as an upper bound on the transmittance for smaller-size apertures.

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