literature reviee composite

7/30/2019 Literature Reviee Composite

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1. D S Sharma, Stress Concentration around Circular/Elliptical/Triangular Cutouts

in Infinite Composite Plate, Proceedings of the World Congress on Engineering

2011 Vol III , WCE 2011, July 6 - 8, 2011, London, U.K

General stress functions for determining the stress concentration around circular,

elliptical and triangular cutouts in laminated composite infinite plate subjected toarbitrary biaxial loading at infinity are obtained using Muskhelishvilis complex variablemethod. The generalized stress functions are coded using MATLAB 7.0 and the effect of

fiber orientation, stacking sequence, loading factor, loading angle and cutout geometry on

stress concentration around cutouts in orthotropic/anisotropic plates is studied

2. Chyanbin HWU and Haoyi HUANG, Prediction of Sharp Notch Fracture by

Critical Principal Stress Intensity Factor, 5th International Symposium on

Advanced Science and Technology in Experimental Mechanics, 4-7 November, 2010,

Kyoto, Japan

Recently, a new definition of stress intensity factor for sharp notched is proposed. Likethe principal stress defined in elasticity for the maximum normal stress, the principal

stress intensity factor is introduced in this study. The notch fracture initiation is predicted

to be propagated along the principal angle when the critical principal stress intensity

factor is reached. The value of the critical principal stress intensity factor is calculated bythe path-independent H-integral in which the field data of stresses and displacements is

input from the finite element modeling with the critical load obtained in the experiment.

Through the use of Arcan test fixture, the critical principal stress intensity factor is shownto be a material property independent of the geometry and loading conditions

3. J. Molimard, R. Le Riche, A. Vautrin, and J. R. Lee, Identification of Orthotropic

Plate Stiffness Using Open Hole Tensile Test, SMS/MeM, GDR CNRS 2519, ENSM-

SE, 158 Cours Fauriel, 42023 Saint Etienne, France

Identification of mechanical parameters is still a challenge on real structures. With theimprovement of optical full field measurement techniques, it becomes easier, but in spite

of many publications showing the feasibility of such methods, experimental results are

still scarce. We present here a first step towards a global approach of mechanicalidentification for composite materials. The chosen mechanical test is an open hole tensile

test according to standard recommendations. For the moment, experimental data are

provided by a moir interferometry set-up. The global principle of the identification

developed here is a minimization procedure, based on Levenverg-Marquardt agorithm.This approach has the advantage to have a high adaptability. In particular, the optical

system and the signal processing can be modelized as well as the mechanical aspects. In

the paper, different kind of cost functions are tested by using an identifiability criterion.

Even if some mechanical considerations can be made, the simpler mathematical form isthe more efficient. The used model is an analytical one based on Lekhnitskii approach.

Identified values are similar to values from classical mechanical tests within 5 % except

for the Poissons ratio (15 %).


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4. Chyanbin Hwu and M.C. Hsieh, Bending Analysis For Holes In Laminates,

I nstitute of Aeronautics and Astronautics, National Cheng Kung Uni versity Tainan,

Taiwan, 70101, R.O.C.

The problems of anisotropic plates containing holes have been studied extensively for

two-dimensional deformations. Although the correspondence between the two-dimensional problems and the plate bending problems has been observed long time ago,without clarifying the involved mathematical details one still cannot get the solutions of

the plate bending problems directly from the solutions of the corresponding two-

dimensional problems. Based upon the correspondence relation, recently we developed aStroh-like formalism for the bending theory of anisotropic plates. By this newly

developed formalism, most of the relations for bending problems can be organized into

the forms for two-dimensional problems. In this paper, this formalism is further extended

to the bending analysis for the symmetric composite laminates. By using this extendedStroh-like formalism, the analytical solutions for symmetric laminates containing

elliptical holes subjected to out-of-plane bending moments have been obtained directly

from the solutions of the corresponding two-dimensional problems. The bendingmoments around the hole boundary are also given explicitly in this paper.

5. M. Yasar Kaltakci,and H. M. Arslan, Stress Concentrations Of Symmetrically

Laminated Composite Plates Containing Circular Holes, Iranian Journal of

Science & Technology, Transaction B,Engineering, Vol. 30, No. B4, Printed in The

Islamic Republic of Iran, 2006

Shiraz University

AbstractIn this study, an analysis of fiber reinforced, symmetrically laminated

composite plates containing circular holes has been carried out. First, the stress state of a

layer in a laminated plate is studied. After obtaining the stress state for each layer due tothe un-iaxial loading of a plate, the stress concentrations around a circular hole are

studied. A number of diagrams are drawn to show the stress concentrations around a hole

for layers having different oriented fibers using different material pairs with differentE1/E2 ratios (ratio of elasticity modulus of fiber direction to that of transverse direction).

Graphs are given for various E1/E2 values for the circumferential stress values around

the hole versus angular location of points for two different fiber orientation angles.Second, the failure of the laminated composite plate is studied. To determine the first

ply failureof a laminated plate, Tsai-Hill failure criterion is employed to find minimum

bearing circumferential stresses and where they occur as a function of the fiber

orientation angle.

6. Rodney S. Thomson and Murray L. Scott, Design And Optimization of Composite

Plates With Cutouts, GPO Box 2476V, Melbourne, Victoria, 3001, Australia.

The optimization of cutouts in laminated composite plates under a variety of loading

conditions has been investigated using the design sensitivity method of

MSC/NASTRAN. Two approaches were investigated: optimization of the cutout shapeand optimization of local cutout reinforcement. For the shape optimization, a least


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squares objective function was shown to successfully produce a constant failure index

around the hole boundary under biaxial loading. The shape optimization of holes in

laminated composite plates showed that the optimum shape depends on the degree oforthotropy. Quasi-isotropic laminates produced holes of similar shape to the isotropic

case while laminates without fibres in the primary loading direction could produce

unexpected shapes. A minimum weight objective was used to introduce local holereinforcement which reduced the failure index in the panel to that of a panel without ahole. Significant weight savings were demonstrated

7. V.I. Kushch,S.V. Shmegera, V.A. Buryachenko, Elastic equilibrium of a half

plane containing a finite array of elliptic inclusions, International Journal of Solids

and Structures 43 (2006) 34593483

An accurate analytical method has been proposed to solve for stress in a half planecontaining a finite array of ellip-tic inclusions, the last being a model of near-surface

zone of the fibrous composite part. The method combines the Muskhelishvilis method of

complex potentials with the Fourier integral transform technique. By accurate satisfactionof all the boundary conditions, a primary boundary-value elastostatics problem for a

piece-homogeneous domain has been reduced to an ordinary well-posed set of linear

algebraic equations. A properly chosen form of potentials provides a remarkably simple

form of equations and thus an efficient computational algorithm. The theory developed israther general and can be applied to solve a variety of elastostatics problems. Up to

several hundred interacting inclusions can be considered in this way in practical

simulations which makes the model of composite half plane realistic and flexible enoughto account for the microstructure statistics. The stress concentration factors and effective

thermo-elastic properties of random structure composites with dilute concentration of

fibers are estimated in the vicinity of a free edge. The numerical examples are given

showing accuracy and numerical efficiency of the developed method and disclosing theway and extent to which the nearby free or loaded boundary influences the local and

mean stress concentration in the fibrous composite

8. Manoharan R. and Jeevanantham A. K. Stress And Load-Displacement Analysis

Of Fiber-Reinforced Composite Laminates With A Circular Hole Under

Compressive Load, ARPN Journal of Engineering and Applied Sciences, VOL. 6,

NO. 4, APRIL 2011

This paper is focused on the analysis of stress-strain and displacement for compressive

load on the fibre-reinforced composite laminates. Three different orientations of fibersare analyzed with and without the circular cut-outs. Also different dimensions of circular

cut-outs are applied on the laminates at different compressive loading conditions. This

analysis is carried out using the finite element software ANSYS. From the result, it is

identified that cross-ply composite laminates posses the highest strength as compared toother types of angle orientations. Also it is concluded that the maximum load bearing

capacity decreases as the cut-out size increases..


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9. X.W. Xu, H.C. Man, T.M. Yue, Strength prediction of composite laminates with

multiple elliptical holes, International Journal of Solids and Structures 37 (2000)

2887-2900

Based on the classical laminated plate theory, a nite composite plate with multiple

elliptical holes is treated as ananisotropic multiple connected plate. Using the complexpotential method in the plane theory of elasticity of ananisotropic body, a series solutionto the title problem is obtained by means of the Faber series expansion, the conformal

mapping and the least squares boundary collocation techniques. Laminate strength is

predicted by using the concept of characteristic curve and the Yamada-Sun failurecriterion. The effects of the lay-ups, the hole sizes, the ellipticity of the holes, the loading

conditions, the relative distance between holes, the total number of holes and their

locations on the strength of laminates are studied in detail. Some useful conclusions are

drawn.

10. Werner Hufenbach, Lothar Kroll, Martin Lepper, PaweKostka, Marta Czulak,

Enhanced Strength Models For Notched Laminates With Finite Outer Boundaries,Institut fr Leichtbau und Kunststofftechnik (ILK), Technische Universitt

Dresden, 01062 Dresden, Germany

For the practical design of notched fibre reinforced components, methods that considerfinite anisotropic plates with a cutout are of special interest. The notch-induced stress

concentrations lead to critical strains and frequently initiate catastro-phic failure of the

component. By selective fibre reinforcement of the matrix, a redistribution of the stresspeaks relevant to failure can be achieved. In the course of this, the fibre orientation,

besides the notch geometry, plays a decisive role. An anisotropic plate with finite

dimensions and a hole in its center will be used here to analytically model stress

concentrations. Unlike the infinite plate, this problem comprises a doubly connectedouter area. A solution method has been developed for stress concentration problems of

fibre-reinforced compounds based on the method of complex-valued stress functions

combined with conformal mappings. Using the solution methods developed here, thewhole calculation procedure was modified and extended in such a way, that even the

influence of a finite outer boundary of the plate can be described. The consideration of

the outer boundary is of high importance for practical problems, because then theessential influence of the notch size in dependence of the material, geometry and loading

parameters can be also determined.

11. R. T. Edmondson and Y. B. Fu, Stroh formulation for a generally constrained

and pre-stressed elastic material, I nternational Journal of Non-L inear Mechanics,

Version 1 - 4 Nov, 2008

The Stroh formalism is essentially a spatial Hamiltonian formulation and has beenrecognized to be a powerful tool for solving elasticity problems involving generally

anisotropic elastic materials for which conventional methods developed for isotropic

materials become intractable. In this paper we develop the Stroh/Hamiltonian formulationfor a generally constrained and pre-stressed elastic material. We derive the corresponding


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integral representation for the surface-impedance tensor and ex-plain how it can be used,

together with a matrix Riccati equation, to calculate the surface-wave speed. The

proposed algorithm can deal with any form of constraint, pre-stress, and direction ofwave propagation. As an illustration, previously known results are reproduced for surface

waves in a pre-stressed incompressible elastic material and an unstressed inextensible

fibre-reinforced composite, and an additional example is included analyzing the effects ofpre-stress upon surface waves in an inextensible material.

12. Chyanbin Hwu, C.J. Tan, In-plane/out-of-plane concentrated forces and

moments on composite laminates with elliptical elastic inclusions, International

Journal of Solids and Structures 44 (2007) 65846606

The problems of composite laminates containing elliptical elastic inclusions subjected to

concentrated forces and moments are considered in this paper. By employing Stroh-likeformalism for the coupled stretchingbending analysis, analytical closed form solutions

are obtained explicitly. The generality of the solutions provided in this paper can be

shown as follows: (1) The laminates include any kinds of laminate lay-ups, symmetric orunsymmetric, which allow the stretching and bending deformations couple each other. (2)

The concentrated forces and moments can be applied in in-plane and/or out-of-plane

directions, located inside and/or outside the inclusions. (3) The elliptical elastic

inclusions can be any kinds of elastic materials including the limiting cases such as holes,rigid inclusions, cracks, line inclusions, etc. Since no such general solution has been

found in the literature, the solutions are checked and verified by the special cases that no

inclusions are embedded in the laminates, and that the inclusions are replaced by holes.Moreover, with various hardness ratios of inclusion and matrix some numerical examples

showing the stress resultants along the interface are presented. Like the Greens functions

for the infinite laminates and those containing holes/cracks, the present solutions

associated with the in-plane concentrated forces and out-of-plane concentrated momentshave exactly the same mathematical form as those of the corresponding two-dimensional

problems, in which the only difference is the contents of the symbols. While for the other

loading cases, new types of solutions are obtained explicitly..

13. Chyanbin Hwu, Cracks in Laminates Subjected to Concentrated Forces and

Moments, Key Engineering Materials Vols. 306-308 (2006) pp. 1-6

The crack problems are important not only in macro-mechanics but also in

micromechanics. Because of its importance a lot of analytical, numerical and

experimental studies have been published in journals and books. Among them, the studyof Greens function attracts many researchers attention because analytically it may

provide solutions for arbitrary loading through superposition and numerically it can be

employed as the fundamental solutions for boundary element method and as the kernel

functions of integral equations to consider crack interaction problems. Although a lot ofGreens functions have been presented in the literature, due to mathematical infeasibility

most of them are restricted to two-dimensional problems and very few of them consider

possible coupled stretching-bending analysis which may occur for general un-symmetriccomposite laminates subjected in-plane and/or out-of-plane forces and moments. In this


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paper we consider an infinite composite laminate containing a traction-free crack

subjected to concentrated forces and moments at an arbitrary point of the laminate. By

employing Stroh-like formalism for the coupled stretching-bending analysis, recently the

Greens functions for the infinite laminates (without holes) were obtained in closed-form.

Based upon the non-hole Greens functions, through the use of analytical continuation

method the Greens functions for cracks are now obtained in explicit closed-form and arevalid for the full fields. By proper differentiation, the associated stress intensity factorsare also solved explicitly.

14. Zhongrong Niu,Changzheng Cheng, Jianqiao Ye, Naman Recho, A new

boundary element approach of modeling singular stress fields of plane V-notch

problems, I nternational Journal of Solids and Structures,on October 13, 2008

In this paper, a new boundary element (BE) approach is proposed to determine thesingular stress field in plane V-notch structures. The method is based on an asymptotic

expansion of the stresses in a small region around a notch tip and application of the

conventional BE in the remaining region of the structure. The evaluation of stresssingularities at a notch tip is transformed into an eigenvalue problem of ordinary

differential equations that is solved by the interpolating matrix method in order to obtain

singularity orders (degrees) and associated eigen-functions of the V-notch. The

combination of the eigen-analysis for the small region and the conventional BE analysisfor the remaining part of the structure results in both the singular stress field near the

notch tip and the notch stress intensity factors (SIFs).Examples are given for V-notch

plates made of isotropic materials. Comparisons and parametric studies on stresses andnotch SIFs are carried out for various V-notch plates. The studies show that the new

approach is accurate and effective in simulating singular stress fields in V-notch/crack

structures.

15. D. W. A. Rees, H. Bahai, S. Taylor, Stress Concentrations for Slotted Plates in

Bi-Axial Stress, Engineering, 2012, 4, 69-75

The photo-elastic method has been employed to determine stress concentration factor

(SCF) for square plates containing holes and inclined slots when the plate edges are

subjected to in-plane tension combined with compression. Analyses given of theisochromatic fringe pattern surrounding the hole provides the SCF conveniently. The

model material is calibrated from the known solution to the stress raiser arising from a

small circular hole ina plate placed under biaxial tension-compression. These results also

compare well with a plane stress FE analysis. Consequently, photo-elasticity has enabledSCFs to be determined experimentally for a biaxial stress ratio, nominally equal to4, in

plates containing a long, thin slot arranged to be in alignment with each stress axis. The

two, principal stresses lying along axes of symmetry in the region surrounding the notch

are separated within each isochromatic fringe by the Kuske method [1]. FE provides acomparable full-field view in which contours of maximum shear stress may be identified

with the isochromatic fringe pattern directly. The principal stress distributions referred to

the plate axes show their maximum concentrations at the notch boundary. Here up to afourfold magnification occurs in the greater of the two nominal stresses under loads


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applied to the plate edges. Thus, it is of importance to establish the manner in which the

tangential stress is distributed around the slot boundary. Conveniently, it is shown how

this distribution is also revealed from an isochromatic fringe pattern, within which lie thepoints of maximum tension and maximum compression

16. Ferdinand Bodnr, Marek Jablonski, Stress distribution along the contour of acircular opening in wooden plate loaded by in-plane bending moment, Ann.WULS-

SGGW, Forestry and Wood Technology 73, 2011

Stress distribution along the contour of a circular opening in wooden plate loaded by in-plane bending moment. The analytical solution of stresses around the circular hole

boundary in two-dimensional wooden plate modelled as orthotropic linear elastic material

is presented here. The orthotropic plate with the circular hole is subjected to an in-plane

bending loading. The aim is to know the influence of the circular hole and of theprincipal directions of elasticity on concentration of stresses. Realized computations of

the hoop stress on the opening boundary and of the stress concentration factor are based

on the linear theory of anisotropic bodies with using of a complex variable method

17. Nicolas Leconte, Bertrand Langrand, Eric Markiewicz, On some features of a

plate hybrid-Trefftz displacement element containing a hole, F ini te Elements in

Analysis and Design46 (2010) 819828

The paper deals with the modeling of riveted assemblies for full-scale complete aircraft

crashworthiness. To perform computations aiming at locating rupture initiation in astructure featuring more than100,000 rivets, it is necessary to model the assembly areas

using super-elements. If rivet elements have been developed, perforated plate super-

elements are still lacking. Thus, the paper focuses on plates uper-finite element

formulations featuring defects, in particular holes. An original 8-node plate elementcontaining a hole has been selected to discuss on the possibility to extend its formulation

from linear (elasticity) to non-linear problems (impact). However, since little is known

about the features of super-elements containing a hole, it is first attempted to clarify theproperties of the selected existing super-element. This kind of element is defined

according to the introduced nomenclature, and the features of its interpolation functions

are highlighted. The location of stress fields computed by this super-element is proved tobe in close agreement with results provided by standard FE calculations. This super-

element exhibits also computational efficiency. These features encourage one to pursue

the extension of this super-element formulation to large high plastic strains and strain

rates, aiming at localising rupture initiation when performing crashworthinesscomputations of structures with many rivets and holes.

18. Fu Mo Chen, Ching Kong Chao, Chin Kun Chen, Interaction of an edge

dislocation with a coated elliptic inclusion, International Journal of Solids and

Structures 48 (2011) 14511465

This paper presents an analytical solution for plane elasticity problems of an ellipticallycylindrical lay-ered media subject to an arbitrary edge dislocation. Based on the


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technique of conformal mapping and the method of analytical continuation in conjunction

with the alternating technique, the general expressions of the displacements and stresses,

where an edge dislocation is located in matrix, coating layer and inclusion are obtained.The numerical results of image forces exerted on a generalized edge dislocation are

carried out by using the generalized PeachKoehler equation. As a numerical illustration,

both the image forces and equilibrium positions are presented for different materialcombinations and relative thickness of a coating layer. The result shows that the thicknessand the shear modulus of the coating layer have a strong influence on the stability of

dislocation

19. Chyanbin Hwu, Boundary element formulation for the coupled stretching

bending analysis of thin laminated plates, Engineering Analysis with Boundary

Elements 36 (2012) 10271039

The boundary integral equations for the coupled stretchingbending analysis of thin

laminated plates involve an integral which will be singular when the field point

approaches the source point. To avoid the singular problem occurring in the numericalprogramming, the boundary integral equations are modified in which the integrals of

singular part are integrated analytically. The analytical solutions for the free term

coefficients and singular integrals are obtained in explicit closed-form. By dividing the

boundary into elements and using suitable interpolation polynomials for basic functions,the set of equations necessary for boundary element programming are written explicitly

for regular nodes and corner nodes. The equations for the determination of displacements

and stresses at internal points are also presented in this paper.

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