investigation of a griffith crack subject to anti plane shear by using the non local theory abstract field equations of the non local elasticity are solved to determine the state of stress in a plate with a griffith crack subject to the anti plane shear then a set of dual integral equations is solved using schmidts method contrary to the classical elasticity solution it is found that no stress singularity is present at the crack tip the significance of this result is that the fracture criteria are unified at both the macroscopic and the microscopic scales

homomorphisms representations and characteristic polynomials of digraphs the existence of a homomorphism between two digraphs often implies many structural properties we collect in this paper some characterizations of various digraph homomorphisms using matrix equations and fiber partitions we also survey the relationship among the characteristic polynomials of a digraph and its divisors this includes an introduction of the concept of branched coverings of digraphs their voltage assignment representations and a decomposition formula for the characteristic polynomial of a branched cover with branch index 1 some open problems are included

mixed finite element formulations and related limitation principles a general treatment abstract the complete set of variational principles for an elastic structural model with non homogeneous boundary conditions and inelastic strains is presented a general methodology for deriving the approximate mixed formulation and the relevant matrix form is also shown and applied the limitation principles for a structural model with a linear elastic behaviour are derived and it is shown that each principle relating two different approximate formulations depends upon the state variable interpolated in one formulation and not in the other

on some theorems in the nonlocal theory of micropolar elasticity abstract this paper is concerned with the linear nonlocal theory of micropolar elasticity we have established a work and energy theorem and a uniqueness theorem without making any definiteness assumptions about the elastic moduli a reciprocity theorem is also established

equivalence between mixed models and displacement models sing reduced integration relations between displacement models using reduced integration and hybrid mixed models based on the hellinger reissner and the herrmann principles have been investigated five different isoparametric elements are considered for the case of plane stress plane strain and plate bending elasticity problems it is proved that the following relations hold for both models provided the number of terms of a polynomial expressing the stress or strain component in the formulation of the mixed models is equal to the number of integration points of the reduced integration if the stiffness matrix of the mixed model is evaluated by the identical integration rule with the reduced integration the stiffness matrices of both models are identical thus both models are equivalent if the stiffness matrix of the mixed model is integrated exactly by the identical integration rule with the reduced integration the displacement models using uniform reduced integration and selective reduced integration are equivalent to the mixed models based on the hellinger reissner and the herrmann principles except for the 6 node element respectively

equitable switching and spectra of graphs abstract let g be a simple graph and an equitable partition of the vertex set v g it is well known that the characteristic polynomial g of a quotient graph g divides that of g the seidel swiching g of g with respect to a proper subset v of v g is called equitable if v is a union of some cells in we show that if g is equitable g g g g some applications of this theorem to generalized composition graphs isospectral graphs integral graphs and ramanujan graphs are contained

uniqueness of initial boundary value problems in nonlocal elasticity abstract in this study we have dealt with the uniqueness of the solutions of a class of initial boundary value problems in linear isotropic homogeneous nonlocal elasticity the proof of uniqueness is based on the positive definiteness of total strain energy after giving the sufficient conditions under which total strain energy is positive definite it has been shown that the solutions of the initial boundary value problems which are considered in this study are unique existence of the solutions of these problems is an a priori assumption

constructing exact significance tests with restricted randomization rules summary in a clinical trial comparing two treatments suppose that subjects are assigned sequentially to the treatment groups by a restricted randomization rule under the randomization model an efficient recursive algorithm is provided to generate the exact permutational distribution for linear rank statistics given the final imbalance between the number of patients in the two groups if only the significance level of the test is required the efficiency of the algorithm can be improved significantly in general by the time the size of the trial reaches 30 the large sample approximation to the permutation distribution wei smythe smith 1986 is satisfactory the new procedure is illustrated by censored survival data from a prostatic cancer clinical trial we show that if the study subjects are not a random sample from a well defined population then the treatment allocation rule used at the design stage should not be ignored in the analysis

a strain difference based nonlocal elasticity model abstract a two component local nonlocal constitutive model for macroscopically inhomogeneous linear elastic materials but constant internal length is proposed in which the stress is the sum of the local stress and a nonlocal type stress expressed in terms of the strain difference field hence identically vanishing in the case of uniform strain attention is focused upon the particular case of piecewise homogeneous material the proposed model is thermodynamically consistent with a suitable free energy potential it constitutes an improved form of the vermeer and brinkgreve a new effective nonlocal strain measure for softening plasticity in chambon r desrues j vardulakis i eds localization and bifurcation theory for soils and rocks balkema rotterdam 1994 pp 89 100 model and can also be considered derivable from the eringen nonlocal elasticity model through a suitable enhancement technique based on the concept of redistribution of the local stress the concept of equivalent distance is introduced to macroscopically account for the further attenuation effects produced by the inhomogeneity upon the long distance interaction forces with the aid of a piecewise homogeneous bar in tension a portion of which degrades progressively till failure it is shown that under a suitable choice of a material constant the solution procedure exhibits no pathological features numerical instability mesh sensitivity in every degraded bar condition including the limit idealized stress free condition of the failed bar

on non local and non homogeneous elastic continua abstract a thermodynamic framework endowed with the concept of non locality residual is adopted to derive non local models of integral type for non homogeneous linear elastic materials two expressions of the free energy are considered the former yields a one component non local stress the latter leads to a two component local non local stress since the stress is expressed as the sum of the classical local stress and of a non local component identically vanishing in the case of constant strains the attenuation effects are accounted for by a symmetric space weight function which guarantees the constant strain requirement as well as the dual constant stress condition everywhere in the body the non local and non homogeneous elastic structural boundary value problem under quasi static loads is addressed in a geometrically linear range the complete set of variational formulations for the structural problem is then provided in a unitary framework the solution uniqueness of the non local structural model is proved and the non local fem is addressed starting from the non local counterpart of the total potential energy numerical applications are provided with reference to a non homogeneous bar in tension using the fredholm integral equation and the non local fem the solutions show no pathological features such as numerical instability and mesh sensitivity for degraded bar conditions

extensions and applications of equitable decompositions for graphs with symmetries abstract we extend the theory of equitable decompositions introduced in 2 where it was shown that if a graph has a particular type of symmetry i e a uniform or basic automorphism it is possible to use to decompose a matrix m appropriately associated with the graph the result is a number of strictly smaller matrices whose collective eigenvalues are the same as the eigenvalues of the original matrix m we show here that a large class of automorphisms which we refer to as separable can be realized as a sequence of basic automorphisms allowing us to equitably decompose m over any such automorphism we also show that not only can a matrix m be decomposed but that the eigenvectors of m can also be equitably decomposed additionally we prove under mild conditions that if a matrix m is equitably decomposed the resulting divisor matrix which is the divisor matrix of the associated equitable partition will have the same spectral radius as the original matrix m last we describe how an equitable decomposition effects the gershgorin region m of a matrix m which can be used to localize the eigenvalues of m we show that the gershgorin region of an equitable decomposition of m is contained in the gershgorin region m of the original matrix we demonstrate on a real world network that by a sequence of equitable decompositions it is possible to significantly reduce the size of a matrix gershgorin region

randomization matching and propensity scores in the design and analysis of experimental studies with measured baseline covariates in many experimental situations researchers have information on a number of covariates prior to randomization this information can be used to balance treatment assignment with respect to these covariates as well as in the analysis of the outcome data in this paper we investigate the use of propensity scores in both of these roles we also introduce a randomization procedure in which the balance of all measured covariates is approximately indexed by the variance of the empirical propensity scores and randomization is restricted to those permutations with the least variable propensity scores this procedure is compared with recently proposed methods in terms of resulting covariate balance and estimation efficiency properties of the estimators resulting from each procedure are compared with estimates which incorporate the propensity score in the analysis stage simulation results show that analytical adjustment for the propensity score yields results on par with those obtained through restricted randomization procedures and can be used in conjunction with such procedures to further improve inferential efficiency

relations between enhanced strain methods and the hr method abstract the three field hu washizu functional is the starting point to develop a comparative analysis of approximate linear elastostatic problems in particular we will analyse the limitation phenomena concerning two mixed methods respectively denoted the strain gap method and the mixed enhanced strain method and the two field hellinger reissner hr finite element formulation accordingly two original limitation principles are contributed we provide the theoretical motivation of the numerical observations provided in computational literature on the coincidence of the displacement and stress solutions between the enhanced assumed strain method and the hr method if different choices of shape functions are made it is further shown that the hr method provides the exact stress solution and the exact nodal displacements with one element the related analytical motivation are thus given the theoretical analyses presented in the paper are supported by numerical examples on tipical benchmarks

the finite element method for the mechanically based model of non local continuum summary in this paper the finite element method fem for the mechanically based non local elastic continuum model is proposed in such a model each volume element of the domain is considered mutually interacting with the others beside classical interactions involved by the cauchy stress field by means of central body forces that are monotonically decreasing with their inter distance and proportional to the product of the interacting volume elements the constitutive relations of the long range interactions involve the product of the relative displacement of the centroids of volume elements by a proper distance decaying function which accounts for the decrement of the long range interactions as long as distance increases in this study the elastic problem involving long range central interactions for isotropic elastic continuum will be solved with the aid of the fem the accuracy of the solution obtained with the proposed fem code is compared with other solutions obtained with galerkins approximation as well as with finite difference method moreover a parametric study regarding the effect of the material length scale in the mechanically based model and in the kroner eringen non local elasticity has been investigated for a plane elasticity problem copyright 2011 john wiley sons ltd

a symmetric nonlocal damage theory abstract the paper presents a thermodynamically consistent formulation for nonlocal damage models nonlocal models have been recognized as a theoretically clean and computationally efficient approach to overcome the shortcomings arising in continuum media with softening the main features of the presented formulation are i relations derived by the free energy potential fully complying with nonlocal thermodynamic principles ii nonlocal integral operator which is self adjoint at every point of the solid including zones near to the solid s boundary iii capacity of regularizing the softening ill posed continuum problem restoring a meaningful nonlocal boundary value problem in the present approach the nonlocal integral operator is applied consistently to the damage variable and to its thermodynamic conjugate force i e nonlocality is restricted to internal variables only the present model when associative nonlocal damage flow rules are assumed allows the derivation of the continuum tangent moduli tensor and the consistent tangent stiffness matrix which are symmetric the formulation has been compared with other available nonlocal damage theories finally the theory has been implemented in a finite element program and the numerical results obtained for 1 d and 2 d problems show its capability to reproduce in every circumstance a physical meaningful solution and fully mesh independent results

variational formulations and a consistent finite element procedure for a class of nonlocal elastic continua the structural boundary value problem in the context of nonlocal integral elasticity and quasi static loads is considered in a geometrically linear range the nonlocal elastic behaviour is described by the so called eringen model in which the nonlocality lies in the constitutive relation the diffusion processes of the nonlocality are governed by an integral relation containing a recently proposed symmetric spatial weight function expressed in terms of an attenuation function a firm variational basis to the nonlocal model is given by providing the complete set of variational formulations composed by ten functionals with different combinations of the state variables in particular the nonlocal counterpart of the classical principles of the total potential energy complementary energy and mixed hu washizu principle and hellinger reissner functional are recovered some examples concerning a piecewise bar in tension are provided by using the fredholm integral equation and the proposed nonlocal fem

weighted zeta functions of digraphs abstract we define a weighted zeta function of a digraph and a weighted l function of a symmetric digraph and give determinant expressions of them furthermore we give a decomposition formula for the weighted zeta function of a g cyclic cover of a symmetric digraph for any finite group and g a decomposition formula for the weighted zeta function of an oriented line graph l g of a regular covering g of a graph g is given furthermore we define a weighted l function of an oriented line graph l g of g and present a factorization formula for the weighted zeta function of l g by weighted l functions of l g as a corollay we obtain a factorization formula for the multiedge zeta function of g given by stark and terras

on thermoelastostatics of composites with nonlocal properties of constituents i general representations for effective material and field parameters abstract a theory of thermoelastic composites with nonlocal properties of constituents is analyzed for multiphase elastic solids of arbitrary geometry and material symmetry due to their generality one uses the nonlocal integral models because the gradient models are usually derived as approximations of corresponding integral models in the immediate infinitely closed vicinity of the point being considered one explores a simplified theory for linear macroscopically elasticity which differs from the classical local theory in the stress strain constitutive relation only whereas the equilibrium and compatibility equations remain unaltered one obtains the new representation of the effective modulus and compliance through the mechanical influence function which does not explicitly depend as opposed to its local counterpart on the elastic operators of constituents the representations for the effective eigenstrains and eigenstresses through either the mechanical influence functions or transformation influence functions are presented the effective strain energy and potential energy are expressed in terms of only average values of the state variables and the effective properties representations of both the first and second statistical moments of stress and strain fields in the constituents are also performed many of the results were obtained as the straightforward generalizations of their local counterparts because the methods used for obtaining the mentioned results widely exploit the hill s 1963 condition which holds for any compatible strain field and equilibrium stress field not necessarily related to each other by a specific stress strain relation

divergence and flutter instabilities of nanobeams in moving state accounting for surface and shear effects abstract transverse vibrations of elastically rested moving beam like nanostructures accounting for surface effect are of high concern the role of nonlocality on the free dynamic response of moving nanobeams has been revealed in recent years nevertheless the influence of the surface energy on the mechanical behavior of such elements has not been explained yet in this paper equations of motion of rested nanoscaled beams in the moving state are derived carefully via surface energetic shear deformable beam models subsequently the transverse vibrations of the nanostructure are evaluated using galerkin based assumed mode method the explicit expressions of divergence velocities are obtained analytically and these are successfully verified with the results of a numerical approach the roles of crucial parameters on the first divergence velocity are addressed in some detail additionally the stable and unstable regions are determined systematically and the influence of both surface energy and shear energy on the stability of moving nanostructure is discussed

constrained randomization in a therapeutic efficacy trial the use of valid constrained randomization is presented for a therapeutic efficacy trial the construction and evaluation of randomization schemes are studied for two treatment replicates per block and for hypothesized linear gradients two different isomorphism classes of designs are compared using the variance of the mean squared error criterion the results indicate that valid constrained randomization schemes can be constructed that are superior to ordinary randomization a mastitis efficacy trial provided the specific problem to be solved

a mixed finite element for three dimensional nonlinear analysis of steel frames abstract this paper develops and demonstrates a mixed beam finite element that can represent the inelastic three dimensional stability behavior of frames composed of open walled cross section members the kinematics of deformation of the element include finite rotation and warping of the cross section due to torsion the material inelasticity is based on a two space model that includes the effect of shear stresses due to uniform torsion in addition to normal stresses due to axial force biaxial bending and bimoment initial geometric imperfections and residual stresses are accommodated the formulation is based on a two field displacement and generalized stress hellinger reissner hr variational principle the interpolation of the generalized stresses i e cross section stress resultants along the element length is based on the geometrically exact nonlinear governing differential equations of equilibrium this leads to significant improvements in the accuracy over conventional displacement based elements in problems involving highly nonlinear variations in the curvature along the member lengths due to geometric nonlinearity and or distributed plasticity effects several numerical examples involving two and three dimensional elastic and inelastic stability behavior are presented to illustrate the capabilities of the formulation

zeta functions of digraphs abstract we define a zeta function of a digraph and an l function of a symmetric digraph and give determinant expressions of them furthermore we give a decomposition formula for the zeta function of a g cyclic cover of a symmetric digraph for any finite group and g

characteristic polynomials of graph bundles having voltages in a dihedral group abstract in this paper we compute the characteristic polynomial of a graph bundle when its voltages lie in a dihedral group as the first attempt to compute the characteristic polynomial of a graph bundle also of a graph covering having voltages in a nonabelian group as a result we compute the characteristic polynomial of a graph bundle having a circulant graph as a fibre it is applied for the characteristic polynomials of a discrete torus and a discreteklein bottle

characteristic polynomials and zeta functions of equitably partitioned graphs abstract let v 1 v r be an equitable partition of the vertex set of a directed graph digraph x it is well known that the characteristic polynomial x x of a quotient graph x divides that of x but the remainder part is not well investigated in this paper we define a deletion graph x over an equitable partition which is a signed directed graph defined for a fixed set of deleting vertices v i v i i 1 r and give a similarity transformation exchanging the adjacency matrix a x which is compatible with the equitable partition for a block triangular matrix whose diagonal blocks are the adjacency matrix of the quotient graph and the deletion graph in fact we show the result for more general matrices including adjacency matrix of graphs and as corollaries we show the followings i a decomposition formula of the reciprocal of the ihara bartholdi zeta function over an equitably partitioned undirected graph into the quotient graph part and the deletion graph part and ii chen and chen s result 4 theorem 3 1 on the ihara bartholdi zeta functions on generalized join graphs and iii teranishi s result 32 theorem 3 3

nonlocal elasticity and related variational principles abstract the eringen model of nonlocal elasticity is considered and its implications in solid mechanics studied the model is refined by assuming an attenuation function depending on the geodetical distance between material particles such that in the diffusion processes of the nonlocality effects certain obstacles as holes or cracks existing in the domain can be circumvented a suitable thermodynamic framework with nonlocality is also envisaged as a firm basis of the model the nonlocal elasticity boundary value problem for infinitesimal displacements and quasi static loads is addressed and the conditions for the solution uniqueness are established three variational principles nonlocal counterparts of classical ones i e the total potential energy the complementary energy and the mixed hu washizu principles are provided the former is used to derive a nonlocal type fem nl fem in which the symmetric global stiffness matrix reflects the nonlocality features of the problem an alternative standard fem based solution method is also provided which consists in an iterative procedure of the type local prediction nonlocal correction in which the nonlocality is simulated by an imposed like correction strain the potentialities of these analysis methods are pointed out their numerical implementations being the object of an ongoing research work

the b bar method and the limitation principles abstract the generalized elastic material provides a reference model to cast in a unitary framework many structural models which are based on nonlinear monotone multivalued relations such as viscoelasticity plasticity and unilateral models the modified forms of the hu washizu and hellinger reissner principles and the displacement based variational formulation are recovered for the generalized elastic material starting from a functional in the complete set of state variables the related limitation principles are derived and their specialization to elasticity and elastoplasticity with mixed hardening are provided it is shown that the interpolating fields for the pressure and the volumetric strain usually adopted in the b bar method lead to a limitation principle accordingly the same elastic and elastoplastic solutions can be obtained by means of an approximate mixed displacement pressure variational principle a second application is concerned with the conditions ensuring the coincidence of the solutions between an approximate two field mixed formulation and the displacement based method numerical examples are provided to show the coincidence of the solutions obtained from different mixed finite element formulations in elasticity or elastoplasticity under the validity of the limitation principles

construction of multi dimensional isotropic kernels for nonlocal elasticity based on phonon dispersion data abstract kernels for non local elasticity are in general obtained from phonon dispersion relations however non local elastic kernels are in the form of three dimensional 3d functions whereas the dispersion relations are always in the form of one dimensional 1d frequency versus wave number curves corresponding to a particular wave direction in this paper an approach to build 2d and 3d kernels from 1d phonon dispersion data is presented our particular focus is on isotropic media where we show that kernels can be obtained using fourier bessel transform yielding axisymmetric kernel profiles in reciprocal and real spaces these kernel functions are designed to satisfy the necessary requirements for stable wave propagation uniformity of nonlocal stress and stress regularization the proposed concept is demonstrated by developing some physically meaningful 2d and 3d kernels that will find useful applications in nonlocal mechanics relative merits of the kernels obtained via proposed methods are explored by fitting 1d kernels to dispersion data for argon and using the kernel to understand the size effect in non local energy as seen from molecular simulations a comparison of proposed kernels is made based on their predictions of stress field around a crack tip singularity

characteristic polynomials of digraphs having a semi free action abstract let be a semi free action of a group g on a finite digraph the front divisor of has as vertex set the set of the vertex orbits of and there are t arcs going from u to v in if from any vertex u of the orbit u there are t arcs of going towards the vertices in v our main result is that the characteristic polynomial of is a product of the characteristic polynomial of its front divisor and polynomials associated with the free part of under this work extends earlier work of lee and kim characteristic polynomials of graphs having a semifree action linear algebra appl 307 2000 35 46

variational formulations convergence and stability properties in nonlocal elastoplasticity a thermodynamically consistent formulation of nonlocal plasticity in the framework of the internal variable theories of inelastic behaviors of associative type is presented a family of mixed variational formulations with different combinations of state variables is provided starting from the finite step nonlocal elastoplastic structural problem it is shown that a suitable minimum principles provides a rational basis to exploit the iterative elastic predictor plastic corrector algorithm in terms of the dissipation functional a sufficient condition is proved for the convergence of the iterative elastic predictor plastic corrector algorithm based on a suitable choice of the elastic operator in the prediction phase and a necessary and sufficient condition for the existence of a unique solution if any of the nonlocal problem at hand is then provided the nonlinear stability analysis of the nonlocal problem is carried out following the concept of nonexpansivity proposed in local plasticity

closed form solution for a nonlocal elastic bar in tension a simple mechanical one dimensional problem in the context of nonlocal integral elasticity is solved analytically the nonlocal elastic material behaviour is described by the eringen model whose nonlocality features all reside in the constitutive relation this relation of integral type contains an attenuation function usually assumed symmetric aimed to capture the diffusion process of the nonlocality effects it also exhibits a convolution format the governing equation is a fredholm integral equation of second kind whose analytical treatment even for the usual choice of a symmetric kernel is not easy to develop in the present paper assuming a specific shape for the attenuation function a closed form solution in terms of strains is alternatively obtained by solving a volterra integral equation of second kind the latter can be easily solved with standard techniques at least for the adopted kernel taking also advantage from the symmetry of the solution such a closed form solution is an essential result to validate the effectiveness of numerical procedures aimed to solve more complex mechanical problems in the context of nonlocal elasticity 2002 elsevier science ltd all rights reserved

equitable decompositions of graphs with symmetries abstract we investigate connections between the symmetries automorphisms of a graph and its spectral properties whenever a graph has a symmetry i e a nontrivial automorphism it is possible to use to decompose any matrix m c n n appropriately associated with the graph the result of this decomposition is a number of strictly smaller matrices whose collective eigenvalues are the same as the eigenvalues of the original matrix m some of the matrices that can be decomposed are the graph s adjacency matrix laplacian matrix etc because this decomposition has connections to the theory of equitable partitions it is referred to as an equitable decomposition since the graph structure of many real world networks is quite large and has a high degree of symmetry we discuss how equitable decompositions can be used to effectively bound both the network s spectral radius and spectral gap which are associated with dynamic processes on the network moreover we show that the techniques used to equitably decompose a graph can be used to bound the number of simple eigenvalues of undirected graphs where we obtain sharp results of petersdorf sachs type

a critical comparison of nonlocal and gradient enhanced softening continua continuous models of material degradation may cease to produced meaningful results in the presence of high strain gradients these gradients may occur for instance in the propagation of waves with high wave numbers and at stress concentrators adding nonlocal or gradient terms to the constitutive modelling may enhance the ability of the models to describe such situations the effect of adding nonlocal or gradient terms and the relation between these enhancements are examined in a continuum damage setting a nonlocal damage model and two different gradient damage models are considered in one of the gradient models higher order deformation gradients enter the equilibrium equations explicitly while in the other model the gradient influence follows in a more implicit way from an additional partial differential equation the latter implicit gradient formulation can be rewritten in the integral format of the nonlocal model and can therefore be regarded as truly nonlocal this is not true for the explicit formulation in which the nonlocality is limited to an infinitesimal volume this fundamental difference between the formulations results in quite different behaviour in wave propagation localisation and at crack tips this is shown for the propagation of waves in the models their localisation properties and the behaviour at a crack tip the responses of the nonlocal model and the implicit gradient model agree remarkably well in these situations while the explicit gradient formulation shows an entirely different and sometimes nonphysical response

moving least square reproducing kernel methods i methodology and convergence this paper formulates the moving least square interpolation scheme in a framework of the so called moving least square reproducing kernel mlsrk representation in this study the procedure of constructing moving least square interpolation function is facilitated by using the notion of reproducing kernel formulation which as a generalization of the early discrete approach establishes a continuous basis for a partition of unity this new formulation possesses the quality of simplicity and it is easy to implement moreover the reproducing kernel formula proposed is not only able to reproduce any mth order polynomial exactly on an irregular particle distribution but also serves as a projection operator that can approximate any smooth function globally with an optimal accuracy in this contribution a generic m consistency relation has been found which is the essential property of the mlsrk approximation an interpolation error estimate is given to assess the convergence rate of the approximation it is shown that for sufficiently smooth function the interpolant expansion in terms of sampled values will converge to the original function in the sobolev norms as a meshless method the convergence rate is measured by a new control variable dilation parameter of the window function instead of the mesh size h as usually done in the finite element analysis to illustrate the procedure convergence has been shown for the numerical solution of the second order elliptic differential equations in a galerkin procedure invoked with this interpolant in the numerical example a two point boundary problem is solved by using the method and an optimal convergence rate is observed with respect to various norms

zeta functions of finite graphs and coverings iii abstract a graph theoretical analog of brauer siegel theory for zeta functions of number fields is developed using the theory of artin l functions for galois coverings of graphs from parts i and ii in the process we discuss possible versions of the riemann hypothesis for the ihara zeta function of an irregular graph

mechanically based approach to non local elasticity variational principles abstract the mechanically based approach to non local elastic continuum will be captured through variational calculus based on the assumptions that non adjacent elements of the solid may exchange central body forces monotonically decreasing with their interdistance depending on the relative displacement and on the volume products such a mechanical model is investigated introducing primarily the dual state variables by means of the virtual work principle the constitutive relations between dual variables are introduced defining a proper convex potential energy it is proved that the solution of the elastic problem corresponds to a global minimum of the potential energy functional moreover the euler lagrange equations together with the natural boundary conditions associated to the total potential energy functional are established with variational calculus and they coincide with analogous relations already obtained by means of mechanical considerations numerical analysis of a tensile specimen has been introduced to show the capabilities of the proposed approach

wave propagation in 1d elastic solids in presence of long range central interactions abstract in this paper wave propagation in non local elastic solids is examined in the framework of the mechanically based non local elasticity theory established by the author in previous papers it is shown that such a model coincides with the well known kroner eringen integral model of non local elasticity in unbounded domains the appeal of the proposed model is that the mechanical boundary conditions may easily be imposed because the applied pressure at the boundaries of the solid must be equilibrated by the cauchy stress in fact the long range forces between different volume elements are modelled in the body domain as central body forces applied to the interacting elements it is shown that the shape change of travelling disturbances coalesces with those predicted by the non local integral theory of elasticity in unbounded domains but several differences arise in the case of bounded domains the wave propagation problem has been formulated by means of the hamiltonian functional of the proposed mechanically based model of non local elasticity introducing an additional term to the elastic potential energy that accounts for elastic long range interactions in this way the wave equation may be obtained in a weak formulation and be further used to provide approximate analytical solutions to the governing equation in the context of standing wave analysis an equivalent discrete point spring model similar to lattice type networks has also been introduced to show the mechanical equivalence of the non local elastic model as well as to provide a mechanical scheme suitable for the numerical treatment of pressure waves travelling in non local bounded domains

a unified approach for variationally consistent finite elements in elastoplasticity abstract a general variationally consistent approach for elastoplastic finite element analysis is presented a weak formulation of the finite step i e in terms of finite increments elastoplastic boundary value problem is obtained by enforcing the stationarity of a mixed functional of hu washizu type a peculiarity of the present formulation is that the constitutive equations are expressed in weak form also all fields are then independently discretized in terms of so called generalized variables the result is a set of non linear algebraic equations a subset of which can be interpreted as the backward difference time integrated constitutive law of the finite element an iterative procedure where all calculations are at the element and not at the gauss point level resting on newton raphson scheme is proposed for the solution of the governing equations it is shown how the customary displacement approach and also some other mixed formulations in elastoplasticity can be regarded as special cases of the present formulation

rectangular rigid stamp on a nonlocal elastic half plane first the solution of the problem of a rectangular rigid stamp uniformly moving on an elastic half plane is given secondly the solution is obtained for a motionless rectangular stamp on a nonlocal elastic half space the finite distribution of the stress under the stamp has been compared with the unbounded stresses of local case

mixed finite element methods reduced and selective integration techniques a unification of concepts the equivalence of certain classes of mixed finite element methods with displacement methods which employ reduced and selective integration techniques is established this enables one to obtain the accuracy of the mixed formulation without incurring the additional computational expense engendered by the auxiliary field of the mixed method applications and numerical examples are presented for problems with constraints which can be difficult to enforce in finite element approximations and have often dictated the use of mixed principles these include thin beams and plates and linear and nonlinear incompressible and nearly incompressible continuum problems in solid and fluid mechanics

fe formulation of a nonlocal plasticity theory a nonlocal continuum plasticity theory is presented the nonlocal field introduced here is defined as a certain weighted average of the corresponding local field taken over all the material points in the body hereby a quantity with the dimension of length occurs as a material parameter when this so called internal length is equal to zero the local classical plasticity theory is regained in the present model the yield function will depend on a nonlocal field the consistency condition and the integration algorithm result in integral equations for determination of the field of plastic multipliers the integral equations are classified as fredholm equations of the second kind and the existence of a solution will be commented upon after discretization a matrix equation is obtained and an algorithm for finding the solution is proposed for a generalized von mises material a plane boundary value problem is solved with a fe method since the nonlocal quantities are integrals c0 continuous elements are sufficient the solution strategy is split into a displacement estimate for equilibrium and the integration of constitutive equations in the numerical simulations shear band formation is analysed and the results display mesh insensitivity

restricted randomization a practical example abstract a method of restricted randomization which avoids bad patterns in the treatments but retains validity in the analysis is demonstrated on an example that exhibits many features of real agricultural experiments such as untidy treatment structure and uncertainty about blocking the method uses permutation groups modern farming methods force agricultural experimenters to use long thin lines of plots for blocking rather than more compact areas ordinary randomization of a long thin block can produce a plan with say all low levels of nitrogen at one end of the block the first section of the article discusses why simple rerandomization is not a satisfactory method of avoiding poor layouts restricted randomization has been developed as a method of avoiding badly patterned plans while ensuring validity of the usual analysis one method of restricted randomization uses special groups of permutations of the plots catalogs of good restricted randomizations have been given for symmetric factorial de

rational approach for assumed stress finite elements a new method for the formulation of hybrid elements by the hellinger reissner principle is established by expanding the essential terms of the assumed stresses as complete polynomials in the natural coordinates of the element the equilibrium conditions are imposed in a variational sense through the internal displacements which are also expanded in the natural co ordinates the resulting element possesses all the ideal qualities i e it is invariant it is less sensitive to geometric distortion it contains a minimum number of stress parameters and it provides accurate stress calculations for the formulation of a 4 node plane stress element a small perturbation method is used to determine the equilibrium constraint equations the element has been proved to be always rank sufficient

the mechanically based approach to 3d non local linear elasticity theory long range central interactions abstract this paper presents the generalization to a three dimensional 3d case of a mechanically based approach to non local elasticity theory recently proposed by the authors in a one dimensional 1d case the proposed model assumes that the equilibrium of a volume element is attained by contact forces between adjacent elements and by long range forces exerted by non adjacent elements specifically the long range forces are modelled as central body forces depending on the relative displacement between the centroids of the volume elements measured along the line connecting the centroids further the long range forces are assumed to be proportional to a proper material dependent distance decaying function and to the products of the interacting volumes consistently with the modelling of the long range forces as central body forces the static boundary conditions enforced on the free surface of the solid involve only local stress due to contact forces the proposed 3d formulation is developed both in a mechanical and in a variational context for this the elastic energy functionals of the solid with long range interactions are introduced based on the principle of virtual work to set the proper correspondence between the mechanical and the kinematic variables of the model numerical applications are reported for 2d solids under plane stress conditions