central limit theorem for linear eigenvalue statistics of random matrices with independent entries we consider n x n real symmetric and hermitian wigner random matrices n 1 2 w with independent modulo symmetry condition entries and the null sample covariance matrices n 1 x x with independent entries of m x n matrix x assuming first that the 4th cumulant excess 4 of entries of w and x is zero and that their 4th moments satisfy a lindeberg type condition we prove that linear statistics of eigenvalues of the above matrices satisfy the central limit theorem clt as n m m n c 0 oo with the same variance as for gaussian matrices if the test functions of statistics are smooth enough essentially of the class c 5 this is done by using a simple interpolation trick from the known results for the gaussian matrices and the integration by parts presented in the form of certain differentiation formulas then by using a more elaborated version of the techniques we prove the clt in the case of nonzero excess of entries again for essentially 5 test function here the variance of statistics contains an additional term proportional to 4 the proofs of all limit theorems follow essentially the same scheme

a stabilized conforming nodal integration for galerkin mesh free methods domain integration by gauss quadrature in the galerkin mesh free methods adds considerable complexity to solution procedures direct nodal integration on the other hand leads to a numerical instability due to under integration and vanishing derivatives of shape functions at the nodes a strain smoothing stabilization for nodal integration is proposed to eliminate spatial instability in nodal integration for convergence an integration constraint ic is introduced as a necessary condition for a linear exactness in the mesh free galerkin approximation the gradient matrix of strain smoothing is shown to satisfy ic using a divergence theorem no numerical control parameter is involved in the proposed strain smoothing stabilization the numerical results show that the accuracy and convergent rates in the mesh free method with a direct nodal integration are improved considerably by the proposed stabilized conforming nodal integration method it is also demonstrated that the gauss integration method fails to meet ic in mesh free discretization for this reason the proposed method provides even better accuracy than gauss integration for galerkin mesh free method as presented in several numerical examples copyright 2001 john wiley sons ltd

a g space theory and a weakened weak w2 form for a unified formulation of compatible and incompatible methods part ii applications to solid mechanics problems in part i of this paper we have established the g space theory and fundamentals for w 2 formulation part ii focuses on the applications of the g space theory to formulate w 2 models for solid mechanics problems we first define a bilinear form prove some of the important properties and prove that the w 2 formulation will be spatially stable and convergent to exact solutions we then present examples of some of the possible w 2 models including the sfem ns fem es fem ns pim es pim and cs pim we show the major properties of these models 1 they are variationally consistent in a conventional sense if the solution is sought in a proper h space compatible cases 2 they pass the standard patch test when the solution is sought in a proper g space with discontinuous functions incompatible cases 3 the stiffness of the discretized model is reduced compared with the finite element method fem model and possibly to the exact model allowing us to obtain upper bound solutions with respect to both the fem and the exact solutions and 4 the w 2 models are less sensitive to the quality of the mesh and triangular meshes can be used without any accuracy problems these properties and theories have been confirmed numerically via examples solved using a number of w 2 models including compatible and incompatible cases we shall see that the g space theory and the w 2 forms can formulate a variety of stable and convergent numerical methods with the fem as one special case

patterns in eigenvalues the 70th josiah willard gibbs lecture typical large unitary matrices show remarkable patterns in their eigenvalue distribution these same patterns appear in telephone encryption the zeros of riemann s zeta function a variety of physics problems and in the study of toeplitz operators this paper surveys these applications and what is currently known about the patterns

a novel alpha finite element method αfem for exact solution to mechanics problems using triangular and tetrahedral elements abstract the paper presents an alpha finite element method fem for computing nearly exact solution in energy norm for mechanics problems using meshes that can be generated automatically for arbitrarily complicated domains three node triangular fem t3 and four node tetrahedral fem t4 elements with a scale factor are formulated for two dimensional 2d and three dimensional 3d problems respectively the essential idea of the method is the use of a scale factor 0 1 to obtain a combined model of the standard fully compatible model of the fem and a quasi equilibrium model of the node based smoothed fem n sfem this novel combination of the fem and n sfem makes the best use of the upper bound property of the n sfem and the lower bound property of the standard fem using meshes with the same aspect ratio a unified approach has been proposed to obtain a nearly exact solution in strain energy for linear problems the proposed elements are also applied to improve the accuracy of the solution of nonlinear problems of large deformation numerical results for 2d using fem t3 and 3d using fem t4 problems confirm that the present method gives the much more accurate solution comparing to both the standard fem and the n sfem with the same number of degrees of freedom and similar computational efforts for both linear and nonlinear problems

a g space theory and a weakened weak w2 form for a unified formulation of compatible and incompatible methods part i theory this paper introduces a g space theory and a weakened weak form w2 using the generalized gradient smoothing technique for a unified formulation of a wide class of compatible and incompatible methods the w2 formulation works for both finite element method settings and mesh free settings and w2 models can have special properties including softened behavior upper bounds and ultra accuracy part i of this paper focuses on the theory and fundamentals for w2 formulations a normed g space is first defined to include both continuous and discontinuous functions allowing the use of much more types of methods techniques to create shape functions for numerical models important properties and a set of useful inequalities for g spaces are then proven in the theory and analyzed in detail these properties ensure that a numerical method developed based on the w2 formulation will be spatially stable and convergent to the exact solutions as long as the physical problem is well posed the theory is applicable to any problems to which the standard weak formulation is applicable and can offer numerical solutions with special properties including close to exact stiffness upper bounds and ultra accuracy copyright 2009 john wiley sons ltd

meshfree and finite element nodal integration methods nodal integration can be applied to the galerkin weak form to yield a particle type method where stress and material history are located exclusively at the nodes and can be employed when using meshless or finite element shape functions this particle feature of nodal integration is desirable for large deformation settings because it avoids the remapping or advection of the state variables required in other methods to a lesser degree nodal integration can be desirable because it relies on fewer stress point evaluations than most other methods in this work aspects regarding stability consistency efficiency and explicit time integration are explored within the context of nodal integration both small and large deformation numerical examples are provided copyright 2007 john wiley sons ltd

a moving kriging interpolation based element free galerkin method for structural dynamic analysis in this paper a meshfree method based on the moving kriging interpolation is further developed for free and forced vibration analyses of two dimensional solids the shape function and its derivatives are essentially established through the moving kriging interpolation technique following this technique by possessing the kronecker delta property the method evidently makes it in a simple form and efficient in imposing the essential boundary conditions the governing elastodynamic equations are transformed into a standard weak formulation it is then discretized into a meshfree system of time dependent equations which are solved by the standard implicit newmark time integration scheme numerical examples illustrating the applicability and effectiveness of the proposed method are presented and discussed in details as a consequence it is found that the method is very efficient and accurate for dynamic analysis compared with those of other conventional methods

extended finite element method coupled with face based strain smoothing technique for three dimensional fracture problems summary in this work the extended finite element method xfem is for the first time coupled with face based strain smoothing technique to solve three dimensional fracture problems this proposed method which is called face based smoothed xfem here is expected to combine both the advantages of xfem and strain smoothing technique in xfem arbitrary crack geometry can be modeled and crack advance can be simulated without remeshing strain smoothing technique can eliminate the integration of singular term over the volume around the crack front thanks to the transformation of volume integration into area integration special smoothing scheme is implemented in the crack front smoothing domain three examples are presented to test the accuracy efficiency and convergence rate of the face based smoothed xfem from the results it is clear that smoothing technique can improve the performance of xfem for three dimensional fracture problems copyright 2015 john wiley sons ltd

regularity conditions in the clt for linear eigenvalue statistics of wigner matrices abstract we show that the variance of centred linear statistics of eigenvalues of gue matrices remains bounded for large n for some classes of test functions less regular than lipschitz functions this observation is suggested by the limiting form of the variance which has previously been computed explicitly but it does not seem to appear in the literature we combine this fact with comparison techniques following tao vu and erdos yau et al and a littlewood paley type decomposition to extend the central limit theorem for linear eigenvalue statistics to functions in the holder class c 1 2 in the case of matrices of gaussian convolution type we also give a variance bound which implies the clt for test functions in the sobolev space h 1 and c 1 for general wigner matrices satisfying moment conditions if the additional assumption of the test function being supported away from the edge of the spectrum is made we prove the clt for test functions of regularity h 1 2 l and h 1 2 for gue and johansson matrices respectively previous results on the clt impose the existence and continuity of at least one classical derivative

a node based smoothed finite element method ns fem for upper bound solution to visco elastoplastic analyses of solids using triangular and tetrahedral meshes abstract a node based smoothed finite element method ns fem was recently proposed for the solid mechanics problems in the ns fem the system stiffness matrix is computed using the smoothed strains over the smoothing domains associated with nodes of element mesh in this paper the ns fem is further extended to more complicated visco elastoplastic analyses of 2d and 3d solids using triangular and tetrahedral meshes respectively the material behavior includes perfect visco elastoplasticity and visco elastoplasticity with isotropic hardening and linear kinematic hardening a dual formulation for the ns fem with displacements and stresses as the main variables is performed the von mises yield function and the prandtl reuss flow rule are used in the numerical procedure however the stress variables are eliminated and the problem becomes only displacement dependent the numerical results show that the ns fem has higher computational cost than the fem however the ns fem is much more accurate than the fem and hence the ns fem is more efficient than the fem it is also observed from the numerical results that the ns fem possesses the upper bound property which is very meaningful for the visco elastoplastic analyses which almost have not got the analytical solutions this suggests that we can use two models ns fem and fem to bound the solution and can even estimate the global relative error of numerical solutions

on the essence and the evaluation of the shape functions for the smoothed finite element method sfem this paper is written in response to the recently published paper int j numer meth engng 2008 76 1285 1295 at ijnme entitled on the smoothed finite element method sfem by zhang hh liu sj li lx in this paper we 1 repeat briefly the important essence of the original sfem presented in comp mech 2007 39 859 877 int j numer meth engng 2007 71 902 930 int j numer meth engng 2008 74 175 208 finite elem anal des 2007 43 847 860 j sound vib 2007 301 803 820 and 2 examine further issues in the evaluation of the shape functions used in the sfem it will be shown that the sfem presented in paper int j numer meth engng 2008 76 1285 1295 is not at all our original sfem presented in comp mech 2007 39 859 877 int j numer meth engng 2007 71 902 930 int j numer meth engng 2008 74 175 208 finite elem anal des 2007 43 847 860 j sound vib 2007 301 803 820 therefore all these theorems corollaries and remarks presented in paper int j numer meth engng 2008 76 1285 1295 have nothing to do with our original sfem the properties of the original sfem stand as they were presented in our original papers comp mech 2007 39 859 877 int j numer meth engng 2007 71 902 930 int j numer meth engng 2008 74 175 208 finite elem anal des 2007 43 847 860 j sound vib 2007 301 803 820 finally we brief on our advancements made far beyond our original sfem and our visions on future numerical methods copyright 2009 john wiley sons ltd

the nevai condition and a local law of large numbers for orthogonal polynomial ensembles we consider asymptotics of orthogonal polynomial ensembles in the macroscopic and mesoscopic scales we prove both global and local laws of large numbers analogous to the recently proven local semicircle law for wigner matrices under fairly weak conditions on the underlying measure our main tools are a general concentration inequality for determinantal point processes with a kernel that is a selfadjoint projection and a strengthening of the nevai condition from the theory of orthogonal polynomials

a coupled alpha fem for dynamic analyses of 2d fluid solid interaction problems abstract an alpha finite element method using triangular elements fem t3 which combines the node based smoothed fem ns fem t3 and standard fem t3 with a scale factor 0 1 is extended to the dynamic analysis of 2d fluid solid interaction problems based on the pressure displacement formulation the gradient smoothing technique based on a part of the smoothing domains associated with the nodes of the triangles is used to smooth both the gradient of pressure and gradient of displacement this gradient smoothing technique can provide proper softening effect and thus improve significantly the accuracy of solution of coupled system some numerical examples have been presented to illustrate the effectiveness and stability of the fem t3 0 6 compared with some existing methods for 2d fluid solid interaction problems

theoretical aspects of the smoothed finite element method sfem this paper examines the theoretical bases for the smoothed finite element method sfem which was formulated by incorporating cell wise strain smoothing operation into standard compatible finite element method fem the weak form of sfem can be derived from the hu washizu three field variational principle for elastic problems it is proved that 1d linear element and 2d linear triangle element in sfem are identical to their counterparts in fem while 2d bilinear quadrilateral elements in sfem are different from that of fem when the number of smoothing cells scs of the elements equals 1 the sfem solution is proved to be variationally consistent and has the same properties with those of fem using reduced integration when sc approaches infinity the sfem solution will approach the solution of the standard displacement compatible fem model when sc is a finite number larger than 1 the sfem solutions are not variationally consistent but energy consistent and will change monotonously from the solution of sfem sc 1 to that of sfem sc it is suggested that there exists an optimal number of sc such that the sfem solution is closest to the exact solution the properties of sfem are confirmed by numerical examples copyright 2006 john wiley sons ltd

limit theorems for linear spectrum statistics of orthogonal polynomial ensembles and their applications in random matrix theory in this paper we consider the asymptotic behavior of xfn n i 1nfn xi where xi i 1 n form orthogonal polynomial ensembles and fn is a real valued bounded measurable function under the condition that varxfn n the berry esseen be bound and cramer type moderate deviation principle mdp for xfn n are obtained by using the method of cumulants as two applications we establish the be bound and cramer type mdp for linear spectrum statistics of wigner matrix and sample covariance matrix in the complex cases these results show that in the edge case which means fn has a particular form f x i x n where n is close to the right edge of equilibrium measure and f is a smooth function xfn n behaves like the eigenvalues counting function of the corresponding wigner matrix and sample covariance matrix respectively

a stabilized nodally integrated tetrahedral a stabilized nodally integrated linear tetrahedral is formulated and analysed it is well known that linear tetrahedral elements perform poorly in problems with plasticity nearly incompressible materials and acute bending for a variety of reasons low order tetrahedral elements are preferable to quadratic tetrahedral elements particularly for nonlinear problems but the severe locking problems of tetrahedrals have forced analysts to employ hexahedral formulations for most nonlinear problems on the other hand automatic mesh generation is often not feasible for building many 3d hexahedral meshes a stabilized nodally integrated linear tetrahedral is developed and shown to perform very well in problems with plasticity nearly incompressible materials and acute bending the formulation is analytically and numerically shown to be stable and optimally convergent for the compressible case provided sufficient smoothness of the exact solution u c2 h1 3 future work may extend the formulation to the incompressible regime and relax the regularity requirements nonetheless the results demonstrate that the method is not susceptible to locking and performs quite well in several standard linear and nonlinear benchmarks published in 2006 by john wiley sons ltd

the local structure of poisson manifolds varietes de poisson et applications decomposition structures de poisson lineaires approximation lineaire systemes hamiltoniens le probleme de linearisation groupes de fonction realisations et applications impulsion paires duales et groupes de jauge existence des realisations unicite des realisations les problemes des 3 corps restreints et autres exemples

a face based smoothed finite element method fs fem for 3d linear and geometrically non linear solid mechanics problems using 4 node tetrahedral elements this paper presents a novel face based smoothed finite element method fs fem to improve the accuracy of the finite element method fem for three dimensional 3d problems the fs fem uses 4 node tetrahedral elements that can be generated automatically for complicated domains in the fs fem the system stiffness matrix is computed using strains smoothed over the smoothing domains associated with the faces of the tetrahedral elements the results demonstrated that the fs fem is significantly more accurate than the fem using tetrahedral elements for both linear and geometrically non linear solid mechanics problems in addition a novel domain based selective scheme is proposed leading to a combined fs ns fem model that is immune from volumetric locking and hence works well for nearly incompressible materials the implementation of the fs fem is straightforward and no penalty parameters or additional degrees of freedom are used the computational efficiency of the fs fem is found better than that of the fem copyright 2008 john wiley sons ltd

linear smoothed polygonal and polyhedral finite elements the strain smoothing technique over higher order elements and arbitrary polytopes yields less accurate solutions than other techniques such as the conventional polygonal finite element method in this work we propose a linear strain smoothing scheme that improves the accuracy of linear and quadratic approximations over convex polytopes the main idea is to subdivide the polytope into simplicial subcells and use a linear smoothing function in each subcell to compute the strain this new strain is then used in the computation of the stiffness matrix the convergence properties and accuracy of the proposed scheme are discussed by solving a few benchmark problems numerical results show that the proposed linear strain smoothing scheme makes the approximation based on polytopes able to deliver the same optimal convergence rate as traditional quadrilateral and hexahedral approximations the accuracy is also improved and all the methods tested pass the patch test to machine precision

an edge based smoothed finite element method es fem for static free and forced vibration analyses of solids abstract this paper presents an edge based smoothed finite element method es fem to significantly improve the accuracy of the finite element method fem without much changing to the standard fem settings the es fem can use different shape of elements but prefers triangular elements that can be much easily generated automatically for complicated domains in the es fem the system stiffness matrix is computed using strains smoothed over the smoothing domains associated with the edges of the triangles intensive numerical results demonstrated that the es fem possesses the following excellent properties 1 the es fem model possesses a close to exact stiffness it is much softer than the overly stiff fem and much stiffer than the overly soft ns fem model 2 the results are often found superconvergence and ultra accurate much more accurate than the linear triangular elements of fem and even more accurate than those of the fem using quadrilateral elements with the same sets of nodes 3 there are no spurious non zeros energy modes found and hence the method is also temporally stable and works well for vibration analysis and 4 the implementation of the method is straightforward and no penalty parameter is used and the computational efficiency is better than the fem using the same sets of nodes in addition a novel domain based selective scheme is proposed leading to a combined es ns fem model that is immune from volumetric locking and hence works very well for nearly incompressible materials these properties of the es fem are confirmed using examples of static free and forced vibration analyses of solids

fluctuations of linear eigenvalues statistics for wigner matrices edge case in this note we consider the fluctuation theorem for x f n n sum i 1 n f lambda i i lambda i ge theta n where lambda i i 1 ldots n are eigenvalues from a wigner matrix and theta n rightarrow 2 we prove that in the edge case x f n n behaves like the counting function of wigner matrix our results can be viewed as a complement of bao et al j stat phys 150 1 88 129 2013

limiting laws of linear eigenvalue statistics for hermitian matrix models we study the variance and the laplace transform of the probability law of linear eigenvalue statistics of unitary invariant matrix models of n n hermitian matrices as n assuming that the test function of statistics is smooth enough and using the asymptotic formulas by deift et al commun pure appl math 52 1325 1425 1999 for orthogonal polynomials with varying weights we show first that if the support of the density of states of the model consists of q 2 intervals then in the global regime the variance of statistics is a quasiperiodic function of n as n generically in the potential determining the model we show next that the exponent of the laplace transform of the probability law is not in general 1 2 variance as it should be if the central limit theorem would be valid and we find the asymptotic form of the laplace transform of the probability law in certain cases

cohomology of symplectomorphism groups and critical values of hamiltonians let p co be a compact simply connected symplectic manifold sym p co its group of automorphisms the period group f p co c r is defined to be the image of co x h2 p z under the integration pairing h 2 p r x h2 p z r since co 4 0 the quotient g p co r f p co is either a circle or the quotient of a circle by a countable dense subgroup the purpose of this paper is to define and study a natural homomorphism a from 7h sym p co to g p co simply stated a measures the average over p with respect to the symplectic measure of the action integral around the trajectories of a loop of symplectomorphisms in terms of hamiltonians we give a formula for a which becomes especially simple when the loop is a 1 parameter subgroup in which case we can make some concrete computations these are related to the work of guillemin sternberg 9 and duistermaat heckmann 7 on momentum mappings we also give an interpretation of a in terms of lifting symplectomorphisms from p to a prequantization i e a g p co bundle over p with a connection whose curvature form is co here we extend the theory from the usual case where g p co is a circle by using the concept of diffeological structure introduced by souriau 16 in a sequel to this paper 19 taking as a starting point the observation that the graphs of symplectomorphisms are lagrangian submanifolds in a product manifold we shall study the possible extension of a to an invariant on loops in the space of lagrangian submanifolds in a symplectic manifold it turns out that this invariant should be defined as the holonomy of a connection whose definition involves choosing a probability measure on each lagrangian submanifold the connection is flat only for certain ways of choosing these measures and the curvature in the general case is closely related to the geometric phase introduced by berry 4 which is a subject of current interest among theoretical and experimental physicists as well as mathematicians 1 6 i0 11 13 173

proofs of the stability and convergence of a weakened weak method using pim shape functions recently the smoothed point interpolation method s pim regarded as a weakened weak w 2 formulation method has been developed for solving engineering mechanics problems it works well with distorted meshes the g space theory offers the theoretical base for all the w 2 methods that use smoothing operations in this paper we first prove mathematically that if a function is of lipschitz continuity and its interpolated function is established using pim shape functions then the interpolated function belongs to a g h 0 s space our proofs work for smoothing operations that are the node based cell based and a mixture of both smoothing domains in addition when mesh is refined under a given regularity condition a sufficiently smooth target function can be approximated by its interpolated function with arbitrary accuracy meaning that the interpolation error norm approaches to zero therefore the stability and convergence of a w 2 method using pim shape functions and g space theory can be ensured

the mfs for the solution of harmonic boundary value problems with non harmonic boundary conditions we investigate applications of the method of fundamental solutions mfs for the numerical solution of two dimensional boundary value problems in complex geometries governed by the laplace equation and subject to dirichlet boundary conditions which are not harmonic such problems can be very challenging because of the appearance of boundary singularities we consider several ways of choosing the boundary collocation points as well as the source points in the mfs we show that with an appropriate such choice the mfs yields highly accurate results

upper bound solution to elasticity problems a unique property of the linearly conforming point interpolation method lc pim it is well known that the displacement based fully compatible finite element method fem provides a lower bound in energy norm for the exact solution to elasticity problems it is however much more difficult to bound the solution from above for general problems in elasticity and it has been a dream of many decades to find a systematical way to obtain such an upper bound this paper presents a very important and unique property of the linearly conforming point interpolation method lc pim it provides a general means to obtain an upper bound solution in energy norm for elasticity problems this paper conducts first a thorough theoretical study on the lc pim we derive its weak form based on variational principles study a number of properties of the lc pim and prove that lc pim is variationally consistent and that it produces upper bound solutions we then demonstrate these properties through intensive numerical studies with many examples of 1d 2d and 3d problems using the lc pim together with the fem we now have a systematical way to numerically obtain both upper and lower bounds of the exact solution to elasticity problems as shown in these example problems copyright 2007 john wiley sons ltd

a cell based smoothed finite element method for multi body contact analysis using linear complementarity formulation abstract in this paper the cell based smoothed finite element using quadrilateral elements cs fem is used for 2d contact problems which are converted into linear complementarity problems lcps which can be solved efficiently using the lemke method the modified coulomb friction contact model with tangential strength and normal adhesion is considered which models sticking slipping contacting departing and bonding debonding processes in a unified formulation smoothed galerkin weak form with contact boundary is deduced in which the stiffness is implemented using the cs fem with 1 smoothing domain 1sd 2sd 3sd 4sd 8sd and 16sd for each element contact interface equations are discretized through contact point pairs that are constructed using a master slave surface algorithm intensive numerical examples are given to investigate the effects of contact parameters on contact behaviors and examine the effectiveness of the proposed approach the numerical results of cs fem models are compared with that of fem q4 model which demonstrates that all cs fem models are softer than fem q4 model the strain energy solutions obtained using several cs fem models are monotonically decreasing with the number of the sds for each element increasing the upper bound solutions in strain energy can be obtained using a cs fem 1sd model in our examples while the lower bound solutions are obtained using cs fem 16sd model or fem q4 with fem q4 solution being the lowest

a novel singular node based smoothed finite element method ns fem for upper bound solutions of fracture problems it is well known that the lower bound to exact solutions in linear fracture problems can be easily obtained by the displacement compatible finite element method fem together with the singular crack tip elements it is however much more difficult to obtain the upper bound solutions for these problems this paper aims to formulate a novel singular node based smoothed finite element method ns fem to obtain the upper bound solutions for fracture problems in the present singular ns fem the calculation of the system stiffness matrix is performed using the strain smoothing technique over the smoothing domains sds associated with nodes which leads to the line integrations using only the shape function values along the boundaries of the sds a five node singular crack tip element is used within the framework of ns fem to construct singular shape functions via direct point interpolation with proper order of fractional basis the mix mode stress intensity factors are evaluated using the domain forms of the interaction integrals the upper bound solutions of the present singular ns fem are demonstrated via benchmark examples for a wide range of material combinations and boundary conditions copyright 2010 john wiley sons ltd

computation of limit and shakedown loads using a node based smoothed finite element method summary this paper presents a novel numerical procedure for computing limit and shakedown loads of structures using a node based smoothed fem in combination with a primal dual algorithm an associated primal dual form based on the von mises yield criterion is adopted the primal dual algorithm together with a newton like iteration are then used to solve this associated primal dual form to determine simultaneously both approximate upper and quasi lower bounds of the plastic collapse limit and the shakedown limit the present formulation uses only linear approximations and its implementation into finite element programs is quite simple several numerical examples are given to show the reliability accuracy and generality of the present formulation compared with other available methods copyright 2011 john wiley sons ltd

hybrid gradient smoothing technique with discrete shear gap method for shell structures abstract in order to enhance the performance of the discrete shear gap technique dsg for shell structures the coupling of hybrid gradient smoothing technique h gst with dsg using triangular elements hs dsg3 is presented to solve the governing partial differential equations of shell structures in the formulation hs dsg3 we firstly employ the node based gradient smoothing technique n gst to obtain the node based smoothed strain field then a scale factor 0 1 is used to reconstruct a new strain field which includes both the strain components from standard dgs3 and the strain components from node based smoothed dsg3 ns dsg3 the hs dsg3 takes advantage of the overly soft ns dsg3 model and the overly stiff dsg3 model and has a relatively appropriate stiffness of the continuous system therefore the degree of the solution accuracy can be improved significantly several typical benchmark numerical examples have been investigated and it is demonstrated that the present hs dsg3 can provide better numerical solutions than the original dsg3 for shell structures

a novel node based smoothed finite element method with linear strain fields for static free and forced vibration analyses of solids abstract this paper presents a novel node based smoothed finite element method ns fem with a higher order strain field it uses piecewise linear displacements on 3 node triangular elements together with strain field which is also linear but over the node based smoothed domains this high order strain ns fem is fundamentally different from the standard fem that uses piecewise linear displacement and constants strain fields in our high order strain ns fem the smoothed strains are expressed with complete order of polynomials which have coefficients linear and high order terms this is also different from the smoothed strain used in the existing standard ns fem which is a constant obtained by a generalized smoothing technique the unknown coefficients in assumed strain functions can be uniquely determined by linearly independent weight functions this is because the smoothed strain and compatible strain within a local region are equal in an integral sense when weighted by continuous functions we present with proofs on convergence two versions of high order strain ns fems which are termed as ns fem 1 that uses 1st order smoothed strains and ns fem 2 that uses 2nd order smoothed strains the new developed high order strain ns fem is applied for static free and forced vibration analyses of solids and our numerical results support our theorems

singular boundary method for solving plane strain elastostatic problems this study documents the first attempt to apply the singular boundary method sbm a novel boundary only collocation method to two dimensional 2d elasticity problems unlike the method of fundamental solutions mfs the source points coincide with the collocation points on the physical boundary by using an inverse interpolation technique to regularize the singularity of the fundamental solution of the equation governing the problems of interest three benchmark elasticity problems are tested to demonstrate the feasibility and accuracy of the proposed method through detailed comparisons with the mfs boundary element method bem and finite element method fem

an adaptive singular es fem for mechanics problems with singular field of arbitrary order this paper presents a singular edge based smoothed finite element method ses fem for mechanics problems with singular stress fields of arbitrary order the ses fem uses a basic mesh of three noded linear triangular t3 elements and a special layer of five noded singular triangular elements st5 connected to the singular point of the stress field the st5 element has an additional node on each of the two edges connected to the singular point it allows us to represent simple and efficient enrichment with desired terms for the displacement field near the singular point with the satisfaction of partition of unity property the stiffness matrix of the discretized system is then obtained using the assumed displacement values not the derivatives over smoothing domains associated with the edges of elements an adaptive procedure for the ses fem is proposed to enhance the quality of the solution with minimized number of nodes several numerical examples are provided to validate the reliability of the present ses fem method c 2012 elsevier b v all rights reserved

upper and lower bounds for natural frequencies a property of the smoothed finite element methods node based smoothed finite element method ns fem using triangular type of elements has been found capable to produce upper bound solutions to the exact solutions for force driving static solid mechanics problems due to its monotonic soft behavior this paper aims to formulate an ns fem for lower bounds of the natural frequencies for free vibration problems to make the ns fem temporally stable an fem is devised by combining the compatible and smoothed strain fields in a partition of unity fashion controlled by 0 1 so that both the properties of stiff fem and the monotonically soft ns fem models can be properly combined for a desired purpose for temporally stabilizing ns fem is chosen small so that it acts like a regularization parameter making the ns fem stable but still with sufficient softness ensuring lower bounds for natural frequency solution our numerical studies demonstrate that 1 using a proper the spurious non zero energy modes can be removed and the ns fem becomes temporally stable 2 the stabilized ns fem becomes a general approach for solids to obtain lower bounds to the exact natural frequencies over the whole spectrum 3 fem can even be tuned for obtaining nearly exact natural frequencies

symplectic groupoids and poisson manifolds on definit la notion de groupoide symplectique on donne la variete de poisson de ce groupoide symplectique on presente une construction

stabilized conforming nodal integration in the natural element method a stabilized conforming nodal integration scheme is implemented in the natural neighbour method in conjunction with non sibsonian interpolation in this approach both the shape functions and the integration scheme are defined through use of first order voronoi diagrams the method illustrates improved performance and significant advantages over previous natural neighbour formulations the method also shows substantial promise for problems with large deformations and for the computation of higher order gradients copyright 2004 john wiley sons ltd

symplectic diffeomorphisms and the flux homomorphism let x be a connected smooth manifold without boundary we will write difff ox for the group of all compactly supported diffeomorphisms of x which preserve the symplectic form o2 topologized as usual as the direct limit of the subgroups diff x of all diffeomorphisms with support in the fixed compact set k let diff oox be its identity component the flux is locally a homomorphism from a neighbourhood of the identity in diffo ox to h x r see calabi 6 it gives rise to a global homomorphism s o from the universal cover of difffo0x to hi x f and hence to a homomorphism

classical intertwiner space and quantization given two symplectic realizations a symplectic manifold called the classical intertwiner space is introduced as a classical analogue of an intertwiner space of representations of an associative algebra we describe explicitly how a quantum data on realizations induces a quantum data on their classical intertwiner space