inclusion pairs satisfying eshelby s uniformity property eshelby conjectured that if for a given uniform loading the field inside an inclusion is uniform then the inclusion must be an ellipse or an ellipsoid this conjecture has been proved to be true in two and three dimensions provided that the inclusion is simply connected in this paper we provide an alternative proof of cherepanov s result that an inclusion with two components can be constructed inside which the field is uniform for any given uniform loading for two dimensional conductivity or for antiplane elasticity for planar elasticity we show that the field inside the inclusion pair is uniform for certain loadings and not for others we also show that the polarization tensor associated with the inclusion pair lies on the lower hashin shtrikman bound and hence the conjecture of polya and szego is not true among nonsimply connected inclusions as a consequence we construct a simply connected inclusion which is nothing close to an ellipse but in which the field is almost uniform

optimal estimates and asymptotics for the stress concentration between closely located stiff inclusions if stiff inclusions are closely located then the stress which is the gradient of the solution may become arbitrarily large as the distance between two inclusions tends to zero in this paper we investigate the asymptotic behavior of the stress concentration factor which is the normalized magnitude of the stress concentration as the distance between two inclusions tends to zero for that purpose we show that the gradient of the solution to the case when two inclusions are touching decays exponentially fast near the touching point we also prove a similar result when two inclusions are closely located and there is no potential difference on boundaries of two inclusions we then use these facts to show that the stress concentration factor converges to a certain integral of the solution to the touching case as the distance between two inclusions tends to zero we then present an efficient way to compute this integral

reconstruction of closely spaced small inclusions in this paper we establish an explicit asymptotic formula for the steady state voltage perturbations caused by closely spaced small conductivity inhomogeneities based on this new formula we design a very effective numerical method to identify the location and some geometric features of these inhomogeneities from a finite number of boundary measurements the viability of our approach is documented by numerical examples

gradient estimates for solutions to the conductivity problem in this paper we derive very precise gradient estimates for solutions to the conductivity problem in the case where two circular conductivity inclusions are very close but not touching the novelty of these estimates is that they give very specific information about the blow up of the gradient as the conductivities of the inclusions degenerate

determination of the insulated inclusion in conductivity problem and related eshelby conjecture abstract in the study of composites it is important to determine the shape of inclusions there is an interesting case in conductivity problem that the inclusion is insulated in present paper we first obtain the representation formula of the solution to an exterior problem and then prove that for any uniform loading such solution can be extended into the inclusion as an affine function if and only if the insulated inclusion is an ellipse or an ellipsoid we also show that an analogous result holds for the elasticity problem which is related to eshelby conjecture the main results in this paper are motivated by ammari kang kim and lee 2013 ammari kang and lim 2005 kang and milton 2008 and liu 2008

an optimal estimate for electric fields on the shortest line segment between two spherical insulators in three dimensions abstract we consider a gradient estimate for a conductivity problem whose inclusions are two neighboring insulators in three dimensions when inclusions with an extreme conductivity insulators or perfect conductors are closely located the gradient can be concentrated in between inclusions and then becomes arbitrarily large as the distance between inclusions approaches zero the gradient estimate in between insulators in three dimensions has been regarded as a challenging problem while the optimal blow up rates in terms of the distance were successfully obtained for the other extreme conductivity problems in two and three dimensions and are attained on the shortest line segment between inclusions in this paper we establish upper and lower bounds of gradients on the shortest line segment between two insulating unit spheres in three dimensions these bounds present the optimal blow up rate of gradient on the line segment which is substantially different from the rates in the other problems

consistent infinitesimal finite element cell method for diffusion equation in unbounded medium abstract to calculate the unit step response matrix of an unbounded medium for use in a time domain analysis of unbounded medium structure interaction for the diffusion equation the consistent infinitesimal finite element cell method is developed for the three dimensional case its derivation is based on the finite element formulation and on similarity the discretization is only performed on the structure medium interface yielding a reduction of the spatial dimension by 1 the procedure is rigorous in the radial direction and exact in the finite element sense in the circumferential directions in contrast to the boundary element procedure the consistent infinitesimal finite element cell method does not require a fundamental solution and incorporates interfaces extending from the structure medium interface to infinity compatible with similarity without any additional computational effort a general anisotropic material can be processed

quantitative estimates for enhancement of the field excited by an emitter due to presence of two closely located spherical inclusions abstract a field in a homogeneous medium can be amplified or enhanced by inserting closely located perfectly conducting inclusions into the medium in this paper precise quantitative estimates for such enhancement are derived when the given field is the one excited by an emitter of a dipole type and inclusions are spheres of the same radii in three dimensions derived estimates reveal the difference as well as the similarity between enhancement of the field excited by the emitter and that of the smooth back ground field in particular an estimate shows that when the enhancement occurs the factor of enhancement is log 1 which is different from that for the smooth background field which is known to be log 1 is the distance between two inclusions

boundary integral formulation for composite laminates in torsion the three dimensional elastic stress state in a general composite laminate under twisting load is given the analysis is carried out through an integral equation formulation that is numerically solved by the boundary element method the integral representation of the elastic behavior is deduced by means of the reciprocity theorem applied to the actual response of each ply and the problem s analytical singular fundamental solutions the interface continuity conditions due to perfect bonding are considered to complete the laminate mathematical model the method permits the analysis for generally stacked laminates having general shape of the cross section by virtue of the formulation characteristics the stress distributions calculated are not affected by a priori assumptions about their nature numerical applications are presented and the results obtained show that the proposed method allows an accurate prediction of the complete elastic response coupled with meaningful computational advantages

an h hierarchical adaptive procedure for the scaled boundary finite element method note 374 reference lch article 2002 012view record in web of science record created on 2007 04 24 modified on 2016 08 08

interior regularity estimates in high conductivity homogenization and application in this paper uniform pointwise regularity estimates for the solutions of conductivity equations are obtained in a unit conductivity medium reinforced by an e periodic lattice of highly conducting thin rods the estimates are derived only at a distance e1 for some 0 away from the fibres this distance constraint is rather sharp since the gradients of the solutions are shown to be unbounded locally in lp as soon as p 2 one key ingredient is the derivation in dimension two of regularity estimates to the solutions of the equations deduced from a fourier series expansion with respect to the fibres direction and weighted by the high contrast conductivity the dependence on powers of e of these two dimensional estimates is shown to be sharp the initial motivation for this work comes from imaging and enhanced resolution phenomena observed experimentally in the presence of micro structures lerosey et al science 315 1120 1124 2007 we use these regularity estimates to characterize the signature of low volume fraction heterogeneities in the fibred reinforced medium assuming that the heterogeneities stay at a distance e1 away from the fibres

on the spectrum of the poincare variational problem for two close to touching inclusions in 2d we study the spectrum of the poincare variational problem for two close to touching inclusions in r2 we derive the asymptotics of its eigenvalues as the distance between the inclusions tends to zero

boundary layers in wedges of laminated composite strips under generalized plane deformation part i asymptotic solutions abstract based upon lekhnitskii s formulation and the stroh formalism the structure of the asymptotic solutions has been examined for the boundary layer on the wedge type cross section of a laminated composite strip the composite strip is assumed under the so called generalized plane deformation which includes tension bending and or torsion by the terminal tractions as well as the generalized plane strain problem the solution structures are obtained with the aid of numerical calculation for various kinds of wedge geometry including the free edge and the delamination cracks with the crack faces opened or closed finally the nature of the asymptotic solutions is discussed including the mode mixity of singular stress field ahead of the wedge tip it is found that for a free edge problem the mode mixity of the singular asymptotic traction vector on the interfacial plane near the free edge remains invariant under varying types of remote loadings once a pair of adjacent materials or ply orientations is given and that accordingly one single scaling parameter governs the near field response

generalized polarization tensors for shape description with each domain an infinite number of tensors called the generalized polarization tensors gpts is associated the gpts contain significant information on the shape of the domain in the recent paper ammari et al in math comput 81 367 386 2012 a recursive optimal control scheme to recover fine shape details of a given domain using gpts is proposed in this paper we show that the gpts can be used for shape description we also show that high frequency oscillations of the boundary of a domain are only contained in its high order gpts indeed we provide an original stability and resolution analysis for the reconstruction of small shape changes from the gpts by developing a level set version of the recursive optimization scheme we make the change of topology possible and show that the gpts can capture the topology of the domain we also propose an indicator of topology which could be used in some particular cases to test whether we have the correct number of connected components in the reconstructed image we provide analytical and numerical evidence that gpts can capture topology and high frequency shape oscillations the results of this paper clearly show that the concept of gpts is a very promising new tool for shape description

optimal shape design by partial spectral data in this paper we are concerned with a shape design problem in which our target is to design up to rigid transformations and scaling the shape of an object given either its polarization tensor at multiple contrasts or the partial eigenvalues of its neumann poincare operator which are known as the fredholm eigenvalues we begin by proposing to recover the eigenvalues of the neumann poincare operator from the polarization tensor by means of the holomorphic functional calculus then we develop a regularized gauss newton optimization method for the shape reconstruction process we present numerical results to demonstrate the effectiveness of the proposed methods and to illustrate important properties of the fredholm eigenvalues and their associated eigenfunctions our results are expected to have important applications in the design of plasmon resonances in nanoparticles as well as in the multifrequency or pulsed imaging of small anomalies

criterion for determining clustering versus reentrant melting behavior for bounded interaction potentials we examine in full generality the phase behavior of systems whose constituent particles interact by means of potentials that do not diverge at the origin are free of attractive parts and decay fast enough to zero as the interparticle separation r goes to infinity by employing a mean field density functional theory which is shown to become exact at high temperatures and or densities we establish a criterion that determines whether a given system will freeze at all temperatures or it will display reentrant melting and an upper freezing temperature

characterization of electric fields between two spherical perfect conductors with general radii in 3d abstract in composite materials the inclusions are frequently spaced very closely the electric field concentrated in the narrow regions between two adjacent perfectly conducting inclusions will always become arbitrarily large in this paper we establish an asymptotic formula of the electric field in the zone between two spherical inclusions with different radii in three dimensions an explicit blowup factor relying on radii is obtained which also involves the digamma function and euler mascheroni constant and so the role of inclusions radii played in such blowup analysis is identified

strong influence of a small fiber on shear stress in fiber reinforced composites abstract in stiff fiber reinforced composites it has been known that the shear stress increases at the rate of 1 as the distance between adjacent fibers approaches 0 this paper reveals a strong influence of a combination of a triple fiber as well as the distance between a pair of fibers on the blow up so that the stress concentration can be significantly accelerated by adding a small fiber in between fibers specifically if a fiber f 2 with a small diameter is located in between fibers f 1 and f 3 1 dist f 1 f 2 and 2 dist f 2 f 3 then the stress blows up at the exact rates of 1 1 and 1 2 between f 1 and f 2 and between f 2 and f 3 respectively this estimate still holds even when a part of f 2 overlaps with f 3 the magnification factor 1 yields the enormous increase in the stress that greatly surpasses the expectancy by previous methods

efficient computation of order and mode of corner singularities in 3d elasticity a general numerical procedure is presented for the efficient computation of corner singularities which appear in the case of non smooth domains in three dimensional linear elasticity for obtaining the order and mode of singularity a neighbourhood of the singular point is considered with only local boundary conditions the weak formulation of the problem is approximated by a galerkin petrov finite element method a quadratic eigenvalue problem p q 2r u 0 is obtained with explicitly analytically defined matrices p q r moreover the three matrices are found to have optimal structure so that p r are symmetric and q is skew symmetric which can serve as an advantage in the following solution process on this foundation a powerful iterative solution technique based on the arnoldi method is submitted for not too large systems this technique needs only one direct factorization of the banded matrix p for finding all eigenvalues in the interval e 0 5 1 0 no eigenpairs can be lost as well as the corresponding eigenvectors which is a great improvement in comparison with the normally used determinant method for large systems a variant of the algorithm with an incomplete factorization of p is implemented to avoid the appearance of too much fill in to illustrate the effectiveness of the present method several new numerical results are presented in general they show the dependence of the singular exponent on different geometrical parameters and the material properties copyright 2001 john wiley sons ltd

consistent infinitesimal finite element cell method three dimensional vector wave equation to calculate the unit impulse response matrix of an unbounded medium for use in a time domain analysis of unbounded medium structure interaction the consistent infinitesimal finite element cell method is developed for the three dimensional vector wave equation this is a boundary finite element procedure the discretization is only performed on the structure medium interface yielding a reduction of the spatial dimension by 1 the procedure is rigorous in the radial direction and exact in the finite element sense in the circumferential directions in contrast to the boundary element procedure the consistent infinitesimal finite element cell method does not require a fundamental solution and incorporates interfaces extending from the structure medium interface to infinity compatible with similarity without any additional computational effort a general anisotropic material can be processed the derivation is based on the finite element formulation and on similarity

variable kinematic modelling of laminated composite plates a displacement based variable kinematic global local finite element model is developed using hierarchical multiple assumed displacement fields at two different levels 1 at the element level and 2 at the mesh level the displacement field hierarchy contains both a conventional plate expansion 2 d and a full layerwise 3 d expansion depending on the accuracy desired the variable kinematic element can use various terms from the composite displacement field thus creating a hierarchy of different elements having a wide range of kinematic complexity and representing a number of different mathematical models the vkfe is then combined with the mesh superposition technique to further increase the computational efficiency and robustness of the computational algorithm these models are used to analyse a number of laminated composite plate problems that contain localized subregions where significant 3 d stress fields exist e g free edge effects

a numerical study of stress singularities in a two material wedge abstract a general numerical procedure for determining the stress singularity at the vertex of a two material wedge is presented using an eigenfunction expansion technique and assuming the asymptotic displacement field or stress potential to be of the form r f a finite element approach is constructed the dominant order of stress singularity is determined by solving the eigenvalue equation obtained from the finite element model numerical results for some specific problems are given these results include the order of stress singularities at the free edge of an interface between adjacent layers in a laminated composite as well as the case of an interface crack in a composite laminate results are also obtained by a spectral overlay on a finite element mesh through a least square procedure and show that if high resolution is used near the free edge a good estimate of singularity can be obtained

asymptotics of the solution to the conductivity equation in the presence of adjacent circular inclusions with finite conductivities abstract we consider the conductivity problem in the presence of adjacent circular inclusions with constant conductivities when two inclusions get closer and their conductivities degenerate to zero or infinity the gradient of the solution can be arbitrary large in this paper we derive an asymptotic formula of the solution which characterizes the gradient blow up of the solution in terms of conductivities of inclusions as well as the distance between inclusions the asymptotic formula is expressed in bipolar coordinates in terms of the lerch transcendent function and it is valid for inclusions with arbitrary constant conductivities we illustrate our results with numerical calculations

efficient computation of order and mode of three dimensional stress singularities in linear elasticity by the boundary finite element method the boundary finite element method bfem a novel semi analytical boundary element procedure solely relying on standard finite element formulations is employed for the investigation of the orders and modes of three dimensional stress singularities which occur at notches and cracks in isotropic halfspaces as well as at free edges and free corners of layered plates after a comprehensive literature review and a concise introduction to the standard three dimensional bfem formulation for the static analysis of general unbounded structures we demonstrate the application of the bfem for the computation of the orders and modes of two dimensional and three dimensional stress singularities for several classes of problems within the framework of linear elasticity special emphasis is placed upon the investigation of stress concentration phenomena as they occur at straight free edges and at free corners of arbitrary opening angles in composite laminates in all cases the bfem computations agree excellently with available reference results the required computational effort is found to be considerably lower compared to e g standard finite element method fem computations in the case of free laminate corners numerous new results on the occurring stress singularities are presented it is found that free corner problems generally seem to involve a more pronounced criticality than the corresponding free edge situations

gradient estimates for parabolic and elliptic systems from linear laminates we establish several gradient estimates for second order divergence type parabolic and elliptic systems the coefficients and data are assumed to be holder or dini continuous in the time variable and all but one spatial variable this type of system arises from the problems of linearly elastic laminates and composite materials for the proof we use campanato s approach in a novel way non divergence type equations under similar conditions are also discussed

gradient estimates for solutions of the lame system with partially infinite coefficients we establish upper bounds on the blow up rate of the gradients of solutions of the lame system with partially infinite coefficients in dimension two as the distance between the surfaces of discontinuity of the coefficients of the system tends to zero

interlaminar stresses in laminated composite beam type structures under shear bending a boundary integral model for composite laminates under out of plane shear bending is presented the formulation proposed allows one to determine the elastic response of generally stacked composite laminates having general shape of the cross section the integral equations governing the ply behavior within the laminate are deduced starting from the reciprocity theorem for beam type structures the ply integral equations are obtained by employing the analytical expression of the fundamental solution of generalized plane strain anisotropic problems the laminate model is completed by imposing the displacement and stress continuity along the interfaces and the external boundary conditions the formulation is numerically solved by the boundary element method proposing a solution strategy for standard laminate configurations the solution of the linear algebraic resolving system provides the displacements and tractions on the boundary of each ply of the laminate once this boundary elastic response is known the displacements and stresses at any internal point of the laminate section are computed using their boundary integral representations some applications are presented to demonstrate the accuracy and effectiveness of the method proposed

a unified 3d based technique for plate bending analysis using scaled boundary finite element method summary this paper presents a unified technique for solving the plate bending problems by extending the scaled boundary finite element method the formulation is based on the three dimensional governing equation without enforcing the kinematics of plate theory only the in plane dimensions are discretised into finite elements any two dimensional displacement based elements can be employed the solution along the thickness is expressed analytically by using a matrix function the proposed technique is consistent with the three dimensional theory and applicable to both thick and thin plates without exhibiting the numerical locking phenomenon moreover the use of higher order spectral elements allows the proposed technique to better represent curved boundaries and to achieve high accuracy and fast convergence numerical examples of various plate structures with different thickness to length ratios demonstrate the applicability and accuracy of the proposed technique copyright 2012 john wiley sons ltd

unit impulse response of unbounded medium by scaled boundary finite element method to perform a dynamic analysis of a nonlinear structure interacting with an unbounded medium in the time domain it is desirable to formulate the interaction forces of the unbounded medium on the structure medium interface using displacements the corresponding response matrix to a unit impulse of displacements is calculated using the scaled boundary finite element method this method based solely on finite elements is very suitable to model an unbounded medium as the radiation condition at infinity is rigorously satisfied and the discretization is limited to the structure medium interface

phase separation of a multiple occupancy lattice gas a binary lattice gas model that allows for multiple occupancy of lattice sites inspired by recent coarse grained descriptions of solutions of interacting polymers is investigated by combining the steepest descent approximation with an exploration of the multidimensional energy landscape and by gibbs ensemble monte carlo simulations the one component version of the model involving on site and nearest neighbour interactions is shown to exhibit microphase separation into two sub lattices with different mean occupation numbers the symmetric two component version of the multiple occupancy lattice gas is shown to exhibit a demixing transition into two phases above a critical mean occupation number

strong convergence of the solutions of the linear elasticity and uniformity of asymptotic expansions in the presence of small inclusions abstract we consider the lame system of linear elasticity when the inclusion has the extreme elastic constants we show that the solutions to the lame system converge in appropriate h 1 norms when the shear modulus tends to infinity the other modulus the compressional modulus is fixed and when the bulk modulus and the shear modulus tend to zero using this result we show that the asymptotic expansion of the displacement vector in the presence of small inclusion is uniform with respect to lame parameters

stress singularity analysis in three dimensional bonded structure abstract stress analysis for joints between two isotropic materials is performed using three dimensional boundary element method with rongved s fundamental solution rongved l 1955 force interior to one of two joined semi infinite solids in second midwestern conf on solid mechanics pp 1 13 which satisfies boundary conditions at the interface the stress distribution around the vertex of the joint is precisely examined and the order of stress singularity obtained in three dimensional analysis is compared with that in two dimensional analysis it is shown that the order of the stress singularity along the stress singularity line which is the intersection of the interface with the free surface varies from the value in plane strain to that in plane stress as the opposite side free surface is approached the order of stress singularity in the spherical coordinates centered at the vertex is next investigated when singularity lines with a singularity order meet with each other at the vertex the order of stress singularity is larger than that for plane strain and plane stress when the vertex angle between two side free surfaces is varied the order of stress singularity is also altered in particular a bound at which singularity disappears at the plane for dundurs composite parameters is examined for a cubic dissimilar material it is demonstrated that the bound varies little in comparison with the one obtained from the two dimensional theory

gradient estimates for the perfect conductivity problem we establish both upper and lower bounds of the gradient estimates for the perfect conductivity problem in the case where perfect stiff conductors are closely spaced inside an open bounded domain and away from the boundary these results give the optimal blow up rates of the stress for conductors with arbitrary shape and in all dimensions

general theory for cross ply laminated beams we present a general formulation of the elasticity theory of the cross ply composite laminated beam subjected to various loadings such as axial load bending moment shear bending and torsion the formulation is based on the integral equation theory and a direct approach is employed to obtain the boundary integral equations for the analysis of the laminated beam the integral equations governing the elasticity problem are directly deduced from the reciprocity theorem by using the singular solutions of the orthotropic elasticity explicitly derived the numerical solution is achieved by the boundary element method which gives once the traction free boundary conditions and the interfacial continuity conditions are enforced a linear system of algebraic equations the theoretical approach does not require any a priori assumption and it is absolutely general with regard to the section properties the method of analysis provides efficient computation and accurate solutions for many applications four ply symmetric cross ply laminates under uniform axial strain and shear bending loading are examined in detail numerical results are presented and compared with existing data

decomposition theorems and fine estimates for electrical fields in the presence of closely located circular inclusions abstract when two inclusions get closer and their conductivities degenerate to zero or infinity the gradient of the solution to the conductivity equation blows up in general in this paper we show that the solution to the conductivity equation can be decomposed into two parts in an explicit form one of them has a bounded gradient and the gradient of the other part blows up using the decomposition we derive the best possible estimates for the blow up of the gradient we then consider the case when the inclusions have positive permittivities we show quantitatively that in this case the size of the blow up is reduced

consistent infinitesimal finite element cell method in plane motion note 189 reference lch article 1995 005 record created on 2007 04 24 modified on 2016 08 08

optimal estimates of the field enhancement in presence of a bow tie structure of perfectly conducting inclusions in two dimensions abstract this paper deals with the field enhancement due to insertion of a bow tie structure of perfectly conducting inclusions into the two dimensional space with a given field the field enhancement is represented by the gradient blow up of a solution to the conductivity problem the bow tie structure consists of two disjoint bounded domains which have corners with possibly different aperture angles the domains are parts of cones near the vertices which are nearly touching to each other we construct functions explicitly which characterize the field enhancement as consequences we derive optimal estimates of the gradient in terms of the distance between two inclusions and aperture angles of the corners the estimates show in quantitatively precise way that the field is enhanced beyond the corner singularities due to the interaction between two inclusions and the blow up rate is much higher than the one for the case of inclusions with smooth boundaries

gradient estimates for solutions of the lame system with partially infinite coefficients in dimensions greater than two abstract we establish upper bounds on the blow up rate of the gradients of solutions of the lame system with partially infinite coefficients in dimensions greater than two as the distance between the surfaces of discontinuity of the coefficients of the system tends to zero

stress fields in general composite laminates a direct approach is employed to obtain a general boundary integral formulation for the analysis of composite laminates subjected to uniform axial strain the integral equations governing the problem are directly deduced from the reciprocity theorem employing the generalized orthotropic elasticity fundamental solutions expressly inferred the solution is achieved by the boundary element method which gives once the traction free boundary conditions and the interfacial continuity conditions are enforced a linear system of algebraic equations the formulation does not present restrictions with regard to the laminate stacking sequence and it does not require any aprioristic assumption the interlaminar stress field near the free edge of generally stacked composite laminates subjected to uniaxial extension is investigated through this boundary integral equation formulation the numerical applications show good agreement with those already available in literature and they demonstrate the accuracy and the efficiency of the proposed method approach where a complete three dimensional analysis is performed was presented by pipes and pagano 1 who employed the finite dif ference technique to obtain the solution of the governing elastic ity equations many solutions obtained by using the finite element method are available 2 1 these differ from each other in the formu lation in the kind of employed elements and in the discretization schemes in the literature analytical solutions of approximate the ories are also present the techniques employed to achieve these solutions include the perturbation method 11 series solution 12 13 lekhintskii s complex stress potentials coupled with an eigenfunc tion expansion14 15 or a polynomial expansion 16 ll the extension of reissner s variational principle 18 19 and the force balance method coupled with the minimum complementary energy principle 20 21 the stress distributions obtained with these approaches show good agreement between them for points away from the free edge con siderable disagreement exists instead for points near the free edge location among the various numerical and analytical solutions this is to be expected as a result of a priori assumptions or because the boundary conditions of the continuum problem have been trans formed into conditions on the generalized data actually the numer ical solution techniques are not able to predict the singular trend in the stress field at the free edge and hence to achieve satisfactory solutions a lengthy extrapolation procedure is required on the other hand the analytical approximate solutions often rest on assumptions about the problem unknowns that enforce the free edge stress field structure in the present paper the stress field in multilayered composite laminates under uniform axial extension is analyzed on the basis of the integral equation theory 22 23 the laminate is considered as composed by prismatic elements having different elastic proper ties the generic element or ply is treated as homogeneous and in terms of constitutive equations it is described by a generalized orthotropic law the integral equations governing the exact elastic ity solution of the problem are directly obtained by applying the reciprocity theorem with the fundamental solutions of the general ized orthotropic elasticity 24 27 the

the scaled boundary finite element method analytical solution in frequency domain the scaled boundary finite element equation a system of ordinary differential equations in the radial coordinate is solved analytically applying a series expansion an eigenvalue problem of a hamiltonian matrix is solved when the difference of two eigenvalues is an even number besides the power series logarithmic functions occur two sets of independent solutions are obtained the scaled boundary finite element method is thus a semi analytical procedure to solve partial differential equations with the polynomial approximation of finite elements in the two circumferential directions and a closed form solution in the radial direction applications to bounded and unbounded domains demonstrate excellent accuracy

edge singularities in anisotropic composites abstract the stress singularity at the vertex of an anistropic wedge has the form r f r as r 0 where 0 f is a real function of the polar coordinates r in many cases f is independent of r the explicit form of f r depends on the eigenvalues of the elasticity constants called p here and on the order of singularity k when k is real k if k is complex is the real part of k the p s are all complex and consist of 3 pairs of complex conjugates which reduce to i when the material is isotropic the function f depends not only on p and k it also depends on whether p and k are distinct roots of the corresponding determinants in this paper we present the function f r in terms of p and k for the cases when p and k are single roots as well as when they are multiple roots the relationship between the complex variable z introduced in the analysis and the polar coordinates r is interpreted geometrically after presenting the form of f for individual cases a general form of f is given in eqn 74 we also show that the stress singularity at the crack tip of general anisotropic materials has the order of singularity 1 2 which is at least a multiple root of order 3 the implication of this on the form f r is discussed

gradient estimates for solutions to divergence form elliptic equations with discontinuous coefficients in this paper we derive global w1 and piecewise c1 estimates for solutions to divergence form elliptic equations with piecewise holder continuous coefficients the novelty of these estimates is that even though they depend on the shape and on the size of the surfaces of discontinuity of the coefficients they are independent of the distance between these surfaces

spectral analysis of the neumann poincare operator and characterization of the stress concentration in anti plane elasticity when holes or hard elastic inclusions are closely located stress which is the gradient of the solution to the anti plane elasticity equation can be arbitrarily large as the distance between two inclusions tends to zero it is important to precisely characterize the blow up of the gradient of such an equation in this paper we show that the blow up of the gradient can be characterized by a singular function defined by the single layer potential of an eigenfunction corresponding to the eigenvalue 1 2 of a neumann poincare type operator defined on the boundaries of the inclusions by comparing the singular function with the one corresponding to two disks osculating to the inclusions we quantitatively characterize the blow up of the gradient in terms of explicit functions in electrostatics our results apply to the electric field which is the gradient of the solution to the conductivity equation in the case where perfectly conducting or insulating inclusions are closely located

fast and reliable analysis of free edge stress fields in a thermally loaded composite strip by a layerwise laminate theory a layerwise theory for the analysis of free edge effects in thermally loaded symmetric laminates with arbitrary layups is developed the laminate under investigation is decomposed into an arbitrary number of mathematical layers through the thickness the theory approach employs displacement terms according to classical laminate plate theory which are upgraded by layerwise displacement functions the additional layerwise displacement functions consist of unknown inplane functions and linear thickness terms the principle of minimum potential energy yields the governing euler lagrange equations which allow for a closed form analytical solution for the inplane functions thus characterizing this method as a semi analytical one the underlying boundary conditions of traction free edges are fulfilled in an integral sense the present results are in excellent agreement with accompanying finite element computations copyright 2006 john wiley sons ltd

optimal bound on high stresses occurring between stiff fibers with arbitrary shaped cross sections abstract we consider high stresses in stiff fiber reinforced materials which increase rapidly as fibers approximate to one another this paper presents the optimal blow up rate of the stresses with respect to the distance between a pair of stiff fibers in r 3 the blow up result plays an important role in our understanding of low strengths of fiber reinforced composites referring to a problem of anti plane shear the stresses can be interpreted as the electric fields outside closely spaced perfect conductors in r 2 under the action of applied electric field h it has been shown by ammari kang et al that in the particular case of circular inclusions the electric field blows up at the optimal rate 1 2 as 0 where is the distance between conductors recently yun has extended the blow up result to pairs of conductors associated with a large class of shapes whose complements can be transformed conformally to the outside of a circle with c 2 mapping however it presented a suboptimal result that only for a special uniform field h 1 0 the electric fields blow up at the exact rate 1 2 in this paper an upper bound with the rate 1 2 of electric field for any harmonic function h is established this yields the optimal blow up rate 1 2 for the inclusions in the same class of shapes as yun

low temperature and high temperature approximations for penetrable sphere fluids comparison with monte carlo simulations and integral equation theories the two body interaction in dilute solutions of polymer chains in good solvents can be modeled by means of effective bounded potentials the simplest of which being that of penetrable spheres pss in this paper we construct two simple analytical theories for the structural properties of ps fluids a low temperature lt approximation that can be seen as an extension to pss of the well known solution of the percus yevick py equation for hard spheres and a high temperature ht approximation based on the exact asymptotic behavior in the limit of infinite temperature monte carlo simulations for a wide range of temperatures and densities are performed to assess the validity of both theories it is found that despite their simplicity the ht and lt approximations exhibit a fair agreement with the simulation data within their respective domains of applicability so that they complement each other a comparison with numerical solutions of the py and the hypernetted chain approximations is also carried out the latter showing a very good performance except inside the core at low temperatures

boundary layers in wedges of laminated composite strips under generalized plane deformation part ii complete numerical solutions abstract a procedure for finding complete numerical solutions for the elastic boundary layer field in wedges of a laminated composite strip under the generic loadings of generalized plane deformation is discussed together with numerical examples for free edge problems and delamination crack problems the procedure yields the solution in terms of loading parameters and is applicable to an arbitrary wedge angle and ply orientation and any type of loadings within the range of generalized plane deformation for the free edge problem the so called free edge stress intensity and the mode vector are defined and the free edge stress intensity is found to be a single parameter governing the fracture or failure behaviour near the free edge for a given pair of adjacent materials plies the effect of relative ply thickness upon the stress intensity and the energy release rate is also discussed for various types of loadings

mathematical analysis of plasmonic resonances for nanoparticles the full maxwell equations abstract in this paper we use the full maxwell equations for light propagation in order to analyze plasmonic resonances for nanoparticles we mathematically define the notion of plasmonic resonance and analyze its shift and broadening with respect to changes in size shape and arrangement of the nanoparticles using the layer potential techniques associated with the full maxwell equations we present an effective medium theory for resonant plasmonic systems and derive a condition on the volume fraction under which the maxwell garnett theory is valid at plasmonic resonances

asymptotic studies of closely spaced highly conducting cylinders we consider the solution of the scalar transport problem for a pair of nearly touching cylinders of high conductivity we obtain an expression for the set of multipole moments of the potential distribution for this problem in terms of the hypergeometric function we apply this expression in the estimation of truncation errors occurring in the matrix solution of the corresponding transport problem for the square array of cylinders consequently we are able to calculate the array transport coefficient for arbitrarily high cylinder conductivities and arbitrarily small cylinder separations we derive and verify an expression for this coefficient which is uniformly valid throughout the whole asymptotic region when highly conducting cylinders approach touching

precise estimates of the field excited by an emitter in presence of closely located inclusions of a bow tie shape abstract this paper studies in a quantitatively precise manner the field enhancement due to presence of an emitter of the dipole type near the bow tie structure of perfectly conducting inclusions in the two dimensional space we put special emphasis on field enhancement near vertices of the bow tie structure and derive upper and lower bounds of the gradient blow up there all three different kinds of symmetries are considered by varying locations and directions of the emitter and a different estimate is derived for each case

poincare s variational problem in potential theory one of the earliest attempts to rigorously prove the solvability of dirichlet s boundary value problem was based on seeking the solution in the form of a potential of double layer and this leads to an integral equation whose kernel is in general both singular and non symmetric c neumann succeeded with this approach for smoothly bounded convex domains and h poincare by a tremendous tour de force showed how to push through the analysis for domains with sufficiently smooth boundaries but no hypothesis of convexity in this work he was according to his own account guided by consideration of a variational problem involving the partition of energy of an electrostatic field induced by charges placed on the boundary of a domain more precisely the charge distributions which render stationary the energy of the field inside the domain divided by the energy of the field outside the domain unfortunately a rigorous treatment of this problem was not possible with the tools available at that time as poincare was well aware so far as we know the only one to propose a rigorous treatment of poincare s problem was t carleman in the two dimensional case in his doctoral dissertation thanks to later developments especially concerning sobolev spaces and spectral theory of operators on hilbert space we can now give a complete general and rigorous account of poincare s variational problem and that is the main object of the present paper as a by product we refine some technical aspects in the theory of symmetrizable operators and prove in any number of dimensions the basic properties of the analogue of the planar bergman schiffer singular integral equation we interpret poincare s variational principle as a non selfadjoint eigenvalue problem for the angle operator between two distinct pairs of subspaces of potentials we also prove a series of novel spectral analysis facts some of them conjectured by poincare related to the poincare neumann integral operator

the scaled boundary finite element method a fundamental solution less boundary element method in this boundary element method based on finite elements only the boundary is discretized with surface finite elements yielding a reduction of the spatial dimension by one no fundamental solution is necessary and thus no singular integrals must be evaluated and general anisotropic material can be analysed for an unbounded semi infinite or infinite medium the radiation condition at infinity is satisfied exactly no discretization of free and fixed boundaries and interfaces between different materials is required the semi analytical solution inside the domain leads to an efficient procedure to calculate the stress intensity factors accurately without any discretization in the vicinity of the crack tip body loads are included without discretization of the domain thus the scaled boundary finite element method not only combines the advantages of the finite element and boundary element methods but also presents appealing features of its own after discretizing the boundary with finite elements the governing partial differential equations of linear elastodynamics are transformed to the scaled boundary finite element equation in displacement a system of linear second order ordinary differential equations with the radial coordinate as independent variable which can be solved analytically introducing the definition of the dynamic stiffness a system of nonlinear first order ordinary differential equations in dynamic stiffness with the frequency as independent variable is obtained besides the displacements in the interior the static stiffness and mass matrices of a bounded medium and the dynamic stiffness and unit impulse response matrices of an unbounded medium are calculated

quantitative characterization of stress concentration in the presence of closely spaced hard inclusions in two dimensional linear elasticity in the region between close to touching hard inclusions stress may be arbitrarily large as the inclusions get closer this stress is represented by the gradient of a solution to the lame system of linear elasticity we consider the problem of characterizing the gradient blow up of the solution in the narrow region between two inclusions and estimating its magnitude we introduce singular functions which are constructed in terms of nuclei of strain and hence are solutions of the lame system and then show that the singular behavior of the gradient in the narrow region can be precisely captured by singular functions as a consequence of the characterization we are able to regain the existing upper bound on the blow up rate of the gradient namely 1 2 where is the distance between two inclusions we then show that it is in fact an optimal bound by showing that there are cases where 1 2 is also a lower bound this work is the first to completely reveal the singular nature of the gradient blow up and to obtain the optimal blow up rate in the context of the lame system with hard inclusions the singular functions introduced in this paper play essential roles in overcoming the difficulties in applying the methods of previous works the main tools of this paper are the layer potential techniques and the variational principle the variational principle can be applied because the singular functions of this paper are solutions of the lame system

electric field concentration in the presence of an inclusion with eccentric core shell geometry in this paper we analyze the gradient blow up of the solution to the conductivity problem in two dimensions in the presence of an inclusion with eccentric core shell geometry assuming that the core and shell have circular boundaries that are nearly touching we derive an asymptotic formula for the solution in terms of the single and double layer potentials with image line charges we also deduce an integral formula with image line charges for the problem relating to two nearly touching separated conductors

network approximation in the limit of small interparticle distance of the effective properties of a high contrast random dispersed composite we consider a high contrast two phase composite such as a ceramic polymer composite or a fiberglass composite our objective is to determine the dependence of the effective conductivity or the effective dielectric constant or the effective shear modulus of the composite on the random locations of the inclusions ceramic particles or fibers when the concentration of the inclusions is high we consider a two dimensional model and show that the continuum problem can be approximated by a discrete random network graph we use variational techniques to provide rigorous mathematical justification for this approximation in particular we have shown asymptotic equivalence of the effective constant for the discrete and continuum models in the limit when the relative interparticle distance goes to zero we introduce the geometrical interparticle distance parameter using voronoi tessellation and emphasize the relevance of this parameter due to the fact that for irregular non periodic geometries it is not uniquely determined by the volume fraction of the inclusions we use the discrete network to compute numerically for this purpose we employ a computer program which generates a random distribution of disks on the plane using this distribution we obtain the corresponding discrete network furthermore the computer program provides the distribution of fluxes in the network which is based on keller s formula for two closely spaced disks we compute the dependence of on the volume fraction of the inclusions v for monodispersed composites and obtaine results which are consistent with the percolation theory predictions for polydispersed composites random inclusions of two different sizes the dependence is not simple and is determined by the relative volume fraction v r of large and small particles we found some special values of v r for which the effective coefficient is significantly decreased the computer program which is based on our network model is very efficient and it allows us to collect the statistical data for a large number of random configurations

spectral resolution of the neumann poincare operator on intersecting disks and analysis of plasmon resonance the purpose of this paper is to investigate the spectral nature of the neumann poincare operator on the intersecting disks which is a domain with the lipschitz boundary the complete spectral resolution of the operator is derived which shows in particular that it admits only the absolutely continuous spectrum no singularly continuous spectrum and no pure point spectrum we then quantitatively analyze using the spectral resolution the plasmon resonance at the absolutely continuous spectrum

stress concentration for closely located inclusions in nonlinear perfect conductivity problems abstract we study the stress concentration which is the gradient of the solution when two smooth inclusions are closely located in a possibly anisotropic medium r n n 2 the governing equation may be degenerate of p laplace type with 1 p n we prove optimal l estimates for the blow up of the gradient of the solution as the distance between the inclusions tends to zero

the scaled boundary finite element method alias consistent infinitesimal finite element cell method for diffusion note 264 reference lch article 1999 008doi 10 1002 sici 1097 0207 19990810 45 10 3 0 co 2 eview record in web of science record created on 2007 04 24 modified on 2016 08 08

optimal estimates for the conductivity problem by green s function method we study a class of second order elliptic equations of divergence form with discontinuous coefficients and data which models the conductivity problem in composite materials we establish optimal gradient estimates by showing the explicit dependence of the elliptic coefficients and the distance between interfacial boundaries of inclusions these extend the known results in the literature and answer open problem b proposed by li and vogelius 2000 for the isotropic conductivity problem we also obtain more interesting higher order derivative estimates which answers open problem c of li and vogelius 2000 it is worth pointing out that the equations under consideration in this paper are non homogeneous

the scaled boundary finite element method alias consistent infinitesimal finite element cell method for elastodynamics the scaled boundary finite element method alias the consistent infinitesimal finite element cell method is developed starting from the governing equations of linear elastodynamics only the boundary of the medium is discretized with surface finite elements yielding a reduction of the spatial dimension by one no fundamental solution is necessary and thus no singular integrals must be evaluated general anisotropic material is analysed without any increase in computational effort boundary conditions on free and fixed surfaces and on interfaces between different materials are enforced exactly without any discretization this method is exact in the radial direction and converges to the exact solution in the finite element sense in the circumferential directions for a bounded medium symmetric static stiffness and mass matrices with respect to the degrees of freedom on the boundary result without any additional assumption a stress singularity is represented very accurately as the condition on the boundary in the vicinity of the point of singularity is satisfied without spatial discretization

iterative free edge stress analysis of composite laminates under extension bending twisting and thermal loadings an iterative method has been applied to analyze free edge interlaminar stresses of composite laminates which are subject to extension bending twisting and thermal loads the stresses which satisfy the traction free conditions not only at the free edges but also at the top and bottom surfaces of laminates are obtained by using the complementary virtual work and the extended kantorovich method in order to obtain accurate interlaminar stresses static and kinematic continuity conditions are applied at the interfaces between plies through iterations to demonstrate the validity of the proposed method cross ply angle ply and quasi isotropic laminates are considered through the iteration processes the convergence of the solutions is demonstrated the present method provides accurate stresses in the interior and near the free edges of laminates it can be utilized as an analytical tool to predict interlaminar stresses under the loads of mechanical and thermal combined

body loads in scaled boundary finite element method the solution of the scaled boundary finite element equation in displacement with body loads is derived the non homogeneous term caused by the body loads is processed using the technique of variation of parameters integrals in the radial direction arise which can however be evaluated explicitly for concentrated loads and loads varying as power functions in the radial coordinate in these cases no additional approximations are introduced the scaled boundary finite element method thus remains a semi analytical fundamental solution less boundary element method based on finite elements

optimal boundary gradient estimates for lame systems with partially infinite coefficients abstract in this paper we derive the pointwise upper bounds and lower bounds on the gradients of solutions to the lame systems with partially infinite coefficients as the surface of discontinuity of the coefficients of the system is located very close to the boundary when the distance tends to zero the optimal blow up rates of the gradients are established for inclusions with arbitrary shapes and in all dimensions

stress recovery and error estimation for the scaled boundary finite element method note 373 reference lch article 2002 011view record in web of science record created on 2007 04 24 modified on 2016 08 08