EDGE-BIPANCYCLICITY OF HYPERCUBES WITH CONDITIONAL FAULTS

2011 ◽  
Vol 12 (04) ◽  
pp. 337-343 ◽  
Author(s):  
CHAO-MING SUN
Keyword(s):  
Free Edge ◽  
Free Edges

In this paper, we consider the conditionally faulty graphs G that each vertex of G is incident with at least m fault-free edges, 2 ≤ m ≤ n - 1. We extend the limitation m ≥ 2 in all previous results of edge-bipancyclicity with faulty edges and faulty vertices. Let fe (respectively, fv) denotes the number of faulty edges (respectively, faulty vertices) in an n-dimensional hypercube Qn. For all m, we show that every fault-free edge of Qn lies on a fault-free cycle of every even length from 4 to |V| - 2fv inclusive provided fe + fv ≤ n - 2. This result is not only optimal, but also improves on the previously best known results reported in the literature.

The Effects of Inclined Free Edges on the Thermal Stresses in a Layered Beam

1993 ◽  
Vol 115 (2) ◽  
pp. 208-213 ◽  
Author(s):  
Wan-Lee Yin
Keyword(s):  
Thermal Stresses ◽  
Stress Singularity ◽  
Approximate Solutions ◽  
Free Edge ◽  
Local Concentration ◽  
Interlaminar Stresses ◽  
Beneficial Effects ◽  
Stress Functions ◽  
Layered Beam ◽  
Free Edges

A stress-function-based variational method is used to determine the thermal stresses in a layered beam with inclined free edges at the two ends. The stress functions are expressed in terms of oblique cartesian coordinates, and polynomial expansions of the stress functions with respect to the thickness coordinate are used to obtain approximate solutions. Severe interlaminar stresses act across end segments of the layer interfaces. Local concentration of such stresses may be significantly affected by the inclination angle of the end planes. Variational solutions for a two-layer beam show generally beneficial effects of free-edge inclination in dispersing the concentration of interlaminar stresses. The significance of these effects is generally not indicated by the power of the stress singularity as computed from an elasticity analysis of a bimaterial wedge.

Progressive Damage Analyses of Composite Laminates Exhibiting Free Edge Effects Using a New Micro-Meso Approach

2011 ◽  
Vol 471-472 ◽  
pp. 263-267
Author(s):  
Hossein Hosseini-Toudeshky ◽  
Amin Farrokhabadi ◽  
Bijan Mohammadi
Keyword(s):  
Edge Effects ◽  
Composite Laminates ◽  
Free Edge ◽  
Experimental Results ◽  
Progressive Damage ◽  
Stress Strain ◽  
Laminate Thickness ◽  
Stress Variations ◽  
Angle Ply Laminates ◽  
Free Edges

In this paper, the developed new micro-meso method by the authors is used for the edge-effects analyses of various angle-ply laminates such as [10/-10]2s and [30/-30]2s. It is shown that the obtained stress-strain behaviors of laminates are in well agreement with the available experimental results. The stress variations through the laminate thickness and near the free edges are also computed and compared with the available CDM results.

scholarly journals Analysis of Free Edge Stresses in Composite Laminates Using Higher Order Theories

2014 ◽  
Vol 2014 ◽  
pp. 1-15 ◽  
Author(s):  
Hamidreza Yazdani Sarvestani ◽  
Ali Naghashpour
Keyword(s):  
Composite Laminates ◽  
High Efficiency ◽  
Single Layer ◽  
Free Edge ◽  
Higher Order ◽  
Design Guidelines ◽  
Computational Time ◽  
Interlaminar Stresses ◽  
Layerwise Theory ◽  
Free Edges

This paper presents the determination of the interlaminar stresses close to the free edges of general cross-ply composite laminates based on higher order equivalent single-layer theory (HESL). The laminates with finite dimensions were subjected to a bending moment, an axial force, and/or a torque for investigation. Full three-dimensional stresses in the interior and the boundary-layer regions were determined. The computed results were compared with those obtained from Reddy’s layerwise theory. It was found that HESL theory predicts precisely the interlaminar stresses near the free edges of laminates. Besides, high efficiency in terms of computational time is obtainable when HESL theory is used as compared with layerwise theory. Finally, various numerical results were presented for the cross-ply laminates. Also design guidelines were proposed to minimize the edge-effect problems in composite laminates.

Natural Modes and Natural Frequencies of Uniform, Circular, Free-Edge Plates

1979 ◽  
Vol 46 (2) ◽  
pp. 448-453 ◽  
Author(s):  
K. Itao ◽  
S. H. Crandall
Keyword(s):  
Circular Plate ◽  
Isotropic Material ◽  
Natural Frequencies ◽  
Free Edge ◽  
Poisson's Ratio ◽  
Thin Circular Plate ◽  
Natural Modes ◽  
Modes Of Vibration ◽  
Homogeneous Isotropic Material ◽  
Free Edges

The natural modes and natural frequencies for the first 701 modes of vibration of a uniform thin circular plate with free edges are tabulated for a homogeneous isotropic material with Poisson’s ratio ν = 0.330.

Free-edge effects analysis of angle-ply laminates under transverse loading using layer-wise finite-element method with semi-analytical shear stress calculation

2008 ◽  
Vol 223 (2) ◽  
pp. 293-306
Author(s):  
B Mohammadi ◽  
H Hosseini-Toudeshky ◽  
M-H Sadr-Lahidjani
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Shear Stress ◽  
Stress Field ◽  
Edge Effects ◽  
Free Edge ◽  
Transverse Loading ◽  
Angle Ply Laminates ◽  
Element Method ◽  
Free Edges

Free-edge stress fields are of an utmost localized nature exhibiting steep stress gradients and they rapidly decay with increasing distance from the laminates’ edges. Layer-wise theory has already been used to analyse the stress field at the free edges of the laminates. In this investigation, the layer-wise theory in finite-element method (FEM) is used to analyse the stress field of the laminates’ free edges. In this study, apart from the conventional FEM in which the stresses are calculated from the constitutive laws, the shear stress components along the thickness are calculated from the equilibrium equations by employing a semi-analytical approach. It is shown that the obtained stresses from the current investigation are very close to those available from the three-dimensional elasticity solution for a square laminate under transversely double sinusoidal pressure distribution. To investigate the free edge influence on shear stress distribution of laminates under transverse loading, the analyses are performed for three angle-ply lay-ups with clustered and alternating sequences. It is shown that the free edge effects of angle-ply laminates with different stacking sequences under transverse pressure loading could be considerably different from laminates with in-plane loading conditions.

P047 Evaluation of strength against interfacial crack initiation from free-edges in micro-components : effect of free-edge shape

2016 ◽  
Vol 2016.91 (0) ◽  
pp. 421
Author(s):  
Kazuya AIHARA ◽  
Yoshimasa TAKAHASHI ◽  
Masanori TAKUMA ◽  
Ken-ichi SAITOH ◽  
Tomohiro SATOH
Keyword(s):  
Crack Initiation ◽  
Interfacial Crack ◽  
Free Edge ◽  
Free Edges

Free Edge Stress Analysis of Unidirectional CFRP Laminates Based on a Homogenization Theory for Time-Dependent Composites

2013 ◽  
Vol 535-536 ◽  
pp. 397-400 ◽  
Author(s):  
Keita Goto ◽  
Tetsuya Matsuda
Keyword(s):  
Carbon Fiber ◽  
Stress Analysis ◽  
Tensile Load ◽  
Free Edge ◽  
Time Dependent ◽  
Homogenization Theory ◽  
Uniaxial Tensile ◽  
Cfrp Laminates ◽  
Reinforced Plastic ◽  
Free Edges

In this study, distributions of microscopic stress at free edges of unidirectional carbon fiber-reinforced plastic laminates (CFRP laminates) are analyzed three-dimensionally, based on a homogenization theory for time-dependent composites. For this, the homogenization theory is reconstructed for free edge problems using a traction-free boundary condition. Then, an analysis domain is reduced using the point-symmetry of the internal structure of the unidirectional CFRP laminate. Moreover, the substructure method is newly introduced into the theory to reduce the computational costs required for the analysis. The present method is then applied to the elastic-viscoplastic microscopic stress analysis at free edges of unidirectional carbon fiber/epoxy laminates subjected to an in-plane uniaxial tensile load. It is shown that complex microscopic stress distributions occur in the vicinity of the free edge, especially around fiber/matrix interface regions.

scholarly journals Free-edge effects of corrugated laminates

2020 ◽  
Vol 7 (1) ◽  
pp. 101-124
Author(s):  
Daniel T. Filipovic ◽  
Gerald R. Kress
Keyword(s):  
Edge Effects ◽  
Free Edge ◽  
Laminated Plates ◽  
Parameter Study ◽  
Structural Stiffness ◽  
Infinite Dimensions ◽  
Out Of Plane ◽  
Validity Range ◽  
Plane Direction ◽  
Free Edges

AbstractDue to their high numerical efficiency, homogenization models are often employed in the analysis of corrugated laminates. They are usually derived assuming periodic behavior in the corrugated direction and generalized plane strain in the out-of-plane direction, which corresponds to the assumption of infinite dimensions of the structure. As a consequence, any influences of edge effects are not mapped, although they can have a significant impact on the mechanical behavior of a given structure. The objective of this manuscript is to investigate the influence of boundary conditions - a combination of free-edges and clamping - on the structural stiffness of corrugated laminates. A total of six load cases are investigated which correspond to the line loads considered in the classical theory of laminated plates. The results of this parameter study allow the identification of several critical loading situations, where free edges can significantly alter structural stiffness. The given investigations hence contribute to the investigation of the validity range of homogenization models.

The Thermoelastic Analysis of Chip-Substrate System

2004 ◽  
Vol 126 (3) ◽  
pp. 325-332 ◽  
Author(s):  
Linzhi Wu
Keyword(s):  
Temperature Field ◽  
Stress Concentration ◽  
Integrated Circuits ◽  
Thermal Stresses ◽  
Free Edge ◽  
Thermal Gradients ◽  
Substrate Structure ◽  
Thermal Stress Field ◽  
Electronic Assemblies ◽  
Free Edges

The presence of dissimilar material systems and thermal gradients introduces thermal stresses in multi-layered electronic assemblies and packages during fabrication and operation. The thermal stresses of the chip-substrate structure near free edges play an important role in determining the reliability of electronic packaging structures. Therefore, it is important to provide designers a good estimate of free edge stresses. According to the heat conduction mechanism of integrated circuits, the temperature field distribution in the chip and substrate is derived and solved when the chip works in a steady state. Taking the temperature field in the chip and substrate as the heat source, we solve the thermal stress field in the chip and substrate by using the technique of Fourier’s series expansion. The effects of geometric parameters of the chip and substrate on thermal stresses are analyzed. From the analysis of thermal stresses in the chip-substrate structure, it can be found that the stress concentration near free edges is more prominent. In the design of electronic packagings, the stress concentration near free edges which may cause cracking and delamination leading to the failure or malfunction of electronic assemblies and packages should be taken into account in details.

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