curvature diameter homotopy groups and cohomology rings we establish two topological results a if m is a 1 connected compact n manifold and q 2 then the minimal number of generators for the qth homotopy group q m mng q m is bounded above by a number depending only on mng h m and q where h m is the homology group c let mathscr m n y be the collection of compact orientable n manifolds whose oriented bundles admit so n invariant fibrations over y with fiber compact nilpotent manifolds such that the induced so n actions on y are equivalent then q m finitely generated m mathscr m n y contains only finite isomorphism classes depending only on n y q together with the results of cg and gr1 from a we conclude that i if m is a complete n manifold of nonnegative curvature then mng q m is bounded above by a number depending only on n and q 2 together with the results of ch and cfg from c we conclude that ii if m is a compact n manifold whose sectional curvature and diameter satisfy secm and diamm d then q m has a finite number of possible isomorphism classes depending on n d q 2 provided q m is finitely generated we also show that b if m is a compact n manifold with secm and diam m d then the cohomology ring h m may have infinitely many isomorphism classes in particular b answers some questions raised by k grove gro

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

discontinuous displacement approximation for capturing plastic localization it is proposed to capture localized plastic deformation via the inclusion of regularized displacement discontinuities at element boundaries interfaces of the finite element subdivision the regularization is based on a kinematic assumption for an interface that resembles that which is pertinent to the classical shear band concept as a by product of the regularization an intrinsic band width is introduced as a constitutive property rather than a geometric feature of the finite element mesh in this way the spurious mesh sensitivity which is obtained when the displacement approximation is continuous can be avoided another consequence is that the interfacial relation between the elements is derived directly from the conventional constitutive properties of the continuously deforming material an interesting feature is that the acoustic tensor will not only play a role for diagnosing discontinuous bifurcation but will also serve as the tangent stiffness tensor of the interface up to within a scalar factor an analytical investigation of the behaviour of the interface is carried out and it is shown that dilatation may indeed accompany slip within a shear band for a general plasticity model the significance of proper mesh alignment is demonstrated for a simple problem in plane strain and plane stress it is shown that a unique structural post peak response in accordance with non linear fracture mechanics can be achieved when the plastic softening modulus is properly related to the bandwidth the paper concludes with a numerical simulation of the gradual development of a shear band in a soil slope

minimal entropy and collapsing with curvature bounded from below we show that if a closed manifold m admits an structure not necessarily polarized possibly of rank zero then its minimal entropy vanishes in particular this is the case if m admits a non trivial s1 action as a corollary we obtain that the simplicial volume of a manifold admitting an structure is zero we also show that if m admits an structure then it collapses with curvature bounded from below this in turn implies that m collapses with bounded scalar curvature or equivalently its yamabe invariant is non negative we show that structures of rank zero appear rather frequently every compact complex elliptic surface admits one as well as any simply connected closed 5 manifold we use these results to study the minimal entropy problem we show the following two theorems suppose that m is a closed manifold obtained by taking connected sums of copies of s4 p2 overline mathbb c p 2 s2 s2and the k3 surface then m has zero minimal entropy moreover m admits a smooth riemannian metric with zero topological entropy if and only if m is diffeomorphic to s4 p2 s2 s2 p2 overline mathbb c p 2 or p2 p2 finally suppose that m is a closed simply connected 5 manifold then m has zero minimal entropy moreover m admits a smooth riemannian metric with zero topological entropy if and only if m is diffeomorphic to s5 s3 s2 then on trivial s3 bundle over s2 or the wu manifold su 3 so 3

localisation in a cosserat continuum under static and dynamic loading conditions abstract localisation studies have been carried out for an unconstrained elasto plastic strain softening cosserat continuum because of the presence of an internal length scale in this continuum model a perfect convergence is found upon mesh refinement a finite constant width of the localisation zone and a finite energy dissipation are computed under static as well as under transient loading conditions because of the existence of rotational degrees of freedom in a cosserat continuum additional wave types arise and wave propagation becomes dispersive this has been investigated analytically and numerically for an elastic cosserat continuum and an excellent agreement has been found between both solutions

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

homeomorphism classification of positively curved manifolds with almost maximal symmetry rank we show that a closed simply connected 8 manifold 9 manifold of positive sectional curvature on which a 3 torus 4 torus acts isometrically is homeomorphic to a sphere a complex projective space or a quaternionic projective plane sphere we show that a closed simply connected 2m manifold m 5 of positive sectional curvature on which an m 1 torus acts isometrically is homeomorphic to a complex projective space if and only if its euler characteristic is not 2 by wi these results imply a homeomorphism classification for positively curved n manifolds n 8 of almost maximal symmetry rank open image in new window

nilpotency almost nonnegative curvature and the gradient flow on alexandrov spaces we show that almost nonnegatively curved m manifolds are up to finite cover nilpotent spaces in the sense of homotopy theory and have c m nilpotent fundamental groups we also show that up to a finite cover almost nonnegatively curved manifolds are fiber bundles with simply connected fibers over nilmanifolds

limits and degenerations of unitary conformal field theories in the present paper degeneration phenomena in conformal field theories are studied for this purpose a notion of convergent sequences of cfts is introduced properties of the resulting limit structure are used to associate geometric degenerations to degenerating sequences of cfts which as familiar from large volume limits of non linear sigma models can be regarded as commutative degenerations of the corresponding quantum geometries as an application the large level limit of the a series of unitary virasoro minimal models is investigated in detail in particular its geometric interpretation is determined

reproducing kernel particle methods for large deformation analysis of non linear structures abstract large deformation analysis of non linear elastic and inelastic structures based on reproducing kernel particle methods rkpm is presented the method requires no explicit mesh in computation and therefore avoids mesh distortion difficulties in large deformation analysis the current formulation considers hyperelastic and elasto plastic materials since they represent path independent and path dependent material behaviors respectively in this paper a material kernel function and an rkpm material shape function are introduced for large deformation analysis the support of the rkpm material shape function covers the same set of particles during material deformation and hence no tension instability is encountered in the large deformation computation the essential boundary conditions are introduced by the use of a transformation method the transformation matrix is formed only once at the initial stage if the rkpm material shape functions are employed the appropriate integration procedures for the moment matrix and its derivative are studied from the standpoint of reproducing conditions in transient problems with an explicit time integration method the lumped mass matrices are constructed at nodal coordinate so that masses are lumped at the particles several hyperelasticity and elasto plasticity problems are studied to demonstrate the effectiveness of the method the numerical results indicated that rkpm handles large material distortion more effectively than finite elements due to its smoother shape functions and consequently provides a higher solution accuracy under large deformation unlike the conventional finite element approach the nodal spacing irregularity in rkpm does not lead to irregular mesh shape that significantly deteriorates solution accuracy no volumetric locking is observed when applying non linear rkpm to nearly incompressible hyperelasticity and perfect plasticity problems further model adaptivity in rkpm can be accomplished simply by adding more points in the highly deformed areas without remeshing

gradient enhanced damage for quasi brittle materials summary conventional continuum damage descriptions of material degeneration suffer from loss of well posedness beyond a certain level of accumulated damage as a consequence numerical solutions are obtained which are unacceptable from a physical point of view the introduction of higher order deformation gradients in the constitutive model is demonstrated to be an adequate remedy to this deficiency of standard damage models a consistent numerical solution procedure of the governing partial differential equations is presented which is shown to be capable of properly simulating localization phenomena

collapsing with a lower bound on the curvature operator cheeger and gromov showed that f structures are related to collapse with a double sided curvature bound we define fibered f structures and extend some of the cheeger gromov results to the setting of collapse with a lower bound on the curvature operator

on the upper estimate of the heat kernel of a complete riemannian manifold let m be a complete non compact riemannian manifold whose sectional curvature is bounded between two constants k and k then one expects that the heat diffusion in such a manifold behaves like the heat diffusion in euclidean space the purpose of this paper is to give a justification of such a statement in 5 j cheeger and the third author found a lower estimate of the heat kernel by comparing it with the heat kernel of the space form whose curvature is the lower bound of the curvature of the manifold this lower estimate is sharp if we insist the dependence should be on the lower bound of the ricci curvature alone it remains to give an upper estimate of the heat kernel one does not however expect to have a comparison theorem for the upper bound because it is more sensitive to the geometry of the manifold in fact the heat kernel of the upper hialf space and the heat kernel of the complete hyperbolic manifold with finite volume have quite different behavior this is reflected by the fact that the laplacian has no discrete spectrum in the first case while infinite number of discrete eigenvalues may exist in the latter case what we will prove here is that in any case the heat kernel has to decay in a manner similar to the euclidean heat kernel thus we will prove that for any constant c 4 there exists c1 depending on c t the bound of the curvature of m and x so that for all t e 0 t

a cell based smoothed finite element method for kinematic limit analysis this paper presents a new numerical procedure for kinematic limit analysis problems which incorporates the cell based smoothed finite element method with second order cone programming the application of a strain smoothing technique to the standard displacement finite element both rules out volumetric locking and also results in an efficient method that can provide accurate solutions with minimal computational effort the non smooth optimization problem is formulated as a problem of minimizing a sum of euclidean norms ensuring that the resulting optimization problem can be solved by an efficient second order cone programming algorithm plane stress and plane strain problems governed by the von mises criterion are considered but extensions to problems with other yield criteria having a similar conic quadratic form or 3d problems can be envisaged

three manifolds with many flat planes we discuss the rigidity or lack thereof imposed by dierent no tions of having an abundance of zero curvature planes on a complete riemann ian 3 manifold we prove a rank rigidity theorem for complete 3 manifolds showing that having higher rank is equivalent to having reducible universal covering we also study 3 manifolds such that every tangent vector is con tained in a at plane including examples with irreducible universal covering and discuss the eect of nite volume and real analiticity assumptions

surfaces generated by moving least squares methods an analysis of moving least squares m l s methods for smoothing and interpolating scattered data is presented in particular theorems are proved concerning the smoothness of interpolants and the description of m l s processes as projection methods some properties of compositions of the m l s projector with projectors associated with finiteelement schemes are also considered the analysis is accompanied by examples of univariate and bivariate problems

a meshfree enriched finite element method for compressible and near incompressible elasticity summary in this paper a two dimensional displacement based meshfree enriched fem me fem is presented for the linear analysis of compressible and near incompressible planar elasticity the me fem element is established by injecting a first order convex meshfree approximation into a low order finite element with an additional node the convex meshfree approximation is constructed using the generalized meshfree approximation method and it possesses the kronecker delta property on the element boundaries the gradient matrix of me fem element satisfies the integration constraint for nodal integration and the resultant me fem formulation is shown to pass the constant stress test for the compressible media the me fem interpolation is an element wise meshfree interpolation and is proven to be discrete divergence free in the incompressible limit to prevent possible pressure oscillation in the near incompressible problems an area weighted strain smoothing scheme incorporated with the divergence free me fem interpolation is introduced to provide the smoothing on strains and pressure with this smoothed strain field the discrete equations are derived based on a modified hu washizu variational principle several numerical examples are presented to demonstrate the effectiveness of the proposed method for the compressible and near incompressible problems copyright 2012 john wiley sons ltd

an efficient nesting sub domain gradient smoothing integration algorithm with quadratic exactness for galerkin meshfree methods abstract an efficient nesting sub domain gradient smoothing integration algorithm is proposed for galerkin meshfree methods with particular reference to the quadratic exactness this approach is consistently built upon the smoothed gradients of meshfree shape functions defined on two level nesting triangular sub domains where each integration cell consists of four equal area nesting sub domains first a rational measure is designed to evaluate the error of the gradient smoothing integration for the stiffness matrix thereafter through a detailed analysis of the gradient smoothing integration errors associated with the two level nesting triangular sub domains a quadratically exact algorithm for the stiffness matrix integration is established through optimally combining the contributions from the two level nesting sub domains meanwhile the integration of force terms consistent with the stiffness integration is presented in order to ensure exact quadratic solutions within the galerkin formulation it is noted that the proposed approach with quadratic exactness shares the same foundation as the well established stabilized conforming nodal integration method with linear exactness i e the smoothed derivatives of meshfree shape functions are directly built upon the values of meshfree shape functions on the boundary of the integration cells and the time consuming derivative computations are completely avoided moreover the present formulation has even less integration sampling points than the four point gauss integration numerical examples show very favorable performance regarding the accuracy and efficiency for the proposed approach

an enhanced cell based smoothed finite element method for the analysis of reissner mindlin plate bending problems involving distorted mesh summary in this work an enhanced cell based smoothed finite element method fem is presented for the reissner mindlin plate bending analysis the smoothed curvature computed by a boundary integral along the boundaries of smoothing cells in original smoothed fem is reformulated and the relationship between the original approach and the present method in curvature smoothing is established to improve the accuracy of shear strain in a distorted mesh we span the shear strain space over the adjacent element this is performed by employing an edge based smoothing technique through a simple area weighted smoothing procedure on mitc4 assumed shear strain field a three field variational principle is utilized to develop the mixed formulation the resultant element formulation is further reduced to a displacement based formulation via an assumed strain method defined by the edge smoothing technique as the result a new formulation consisting of smoothed curvature and smoothed shear strain interpolated by the standard transverse displacement rotation fields and smoothing operators can be shown to improve the solution accuracy in cell based smoothed fem for reissner mindlin plate bending analysis several numerical examples are presented to demonstrate the accuracy of the proposed formulation copyright 2013 john wiley sons ltd

limit analysis of plates and slabs using a meshless equilibrium formulation a meshless element free galerkin efg equilibrium formulation is proposed to compute the limit loads which can be sustained by plates and slabs in the formulation pure moment fields are approximated using a moving least squares technique which means that the resulting fields are smooth over the entire problem domain there is therefore no need to enforce continuity conditions at interfaces within the problem domain which would be a key part of a comparable finite element formulation the collocation method is used to enforce the strong form of the equilibrium equations and a stabilized conforming nodal integration scheme is introduced to eliminate numerical instability problems the combination of the collocation method and the smoothing technique means that equilibrium only needs to be enforced at the nodes and stable and accurate solutions can be obtained with minimal computational effort the von mises and nielsen yield criteria which are used in the analysis of plates and slabs respectively are enforced by introducing second order cone constraints ensuring that the resulting optimization problem can be solved using efficient interior point solvers finally the efficacy of the procedure is demonstrated by applying it to various benchmark plate and slab problems

a spillover phenomenon in the optimal location of actuators in this paper we are interested in finding the optimal location and shape of the actuators in a stabilization problem namely we consider the one dimensional wave equation damped by an internal feedback supported on a subdomain omega of given length the criterion we want to optimize represents the rate of decay of the total energy of the system it theoretically involves all the eigenmodes of the operator from an engineering point of view it seems more realistic to consider only a finite number of modes say the n first ones in that context we are able to prove existence and uniqueness of an optimal domain omega n it is the better possible location for the actuators we characterize this optimal domain and we point out the following strange phenomenon at least for small lengths the optimal domain omega n which is the better one for the n first modes is actually the worse one for the n 1th mode this looks like the well known spillover phenomenon in control theory at last we will give some possible extension and open problems in higher dimension

collapsing and the differential form laplacian the case of a smooth limit space we analyze the limit of the p form laplacian under a collapse with bounded sectional curvature and bounded diameter to a smooth limit space as an application we characterize when the p form laplacian has small positive eigenvalues in a collapsing sequence

splittings and cr structures for manifolds with nonpositive sectional curvature let m n denote the universal covering space of a compact riemannian manifold m n with sectional curvature 1 k mn 0 we show that a collection of deck transformations of m n satisfying certain metric dependent conditions determines an open dense subset of m n at every point of which there exists a local isometric splitting with nontrivial flat factor such a collection which we call an abelian structure also gives rise to an essentially canonical cr structure in the sense of buyalo i e an atlas for an injective f structure for which additional conditions hold it follows in particular that the minimal volume of m n vanishes we show that an abelian structure exists if the injectivity radius at all points of m n is less than e n 0 this yields a conjecture of buyalo as well as a strengthened version of the conclusion of gromov s gap conjecture in our special situation in addition we observe that abelian structures on nonpositively curved manifolds have certain stability properties under suitably controlled changes of metric

superconvergent gradient smoothing meshfree collocation method abstract a superconvergent meshfree collocation method with smoothed nodal gradients is presented in this method the first order smoothed gradients of meshfree shape function are constructed through a meshfree interpolation of the standard derivatives of meshfree shape function while the second order smoothed gradients are computed through directly differentiating the first order smoothed gradients it is noted that the second order smoothed gradients evaluated at meshfree nodes can be conveniently expressed as two successive first order gradient smoothing operations on the meshfree shape function which facilitates a trivial numerical implementation subsequently an employment of the second order smoothed gradients in the strong form of a given problem leads to the gradient smoothing meshfree collocation method purely using nodes as the collocation points based upon a local truncation error analysis it is systematically shown that the proposed meshfree collocation method yields superconvergent solutions for odd degree basis functions a key ingredient attributed to this superconvergence property is that the second order smoothed gradients meet the consistency conditions which go one order beyond the original basis degree of meshfree approximation another interesting fact is that the present formulation enables a convergent collocation scheme when the linear basis function is used in meshfree approximation which is non feasible in the conventional collocation formulation the effectiveness of the proposed methodology is validated by numerical examples for both potential and elasticity problems numerical results well demonstrate the superconvergence and higher efficiency of the present gradient smoothing meshfree collocation method

a boundary of the set of the riemannian manifolds with bounded curvatures and diameters on etudie la structure de la fermeture de l ensemble constitue par des classes d isometrie de varietes de riemann a courbures et diametres bornes

the almost cyclicity of the fundamental groups of positively curved manifolds recall that a pure f structure is a kind of generalized torus action the main result asserts that if a compact positively curved manifold mn admits an invariant pure f structure such that each orbit has positive dimension then the fundamental group has a finite cyclic subgroup with index less than wn a constant depending only on n as an application we conclude that for all 0 1 the fundamental group of a pinched n manifold either has a cyclic subgroup with index less than wn or has order less than w n a constant depending only on n and in particular this substantially improves the main result in ro1

optimizing the rate of decay of solutions of the wave equation using genetic algorithms a counterexample to the constant damping conjecture we consider the problem of optimizing the rate of decay of solutions of the linear damped wave equation on a bounded interval this corresponds to optimizing the spectral abscissa of the associated linear operator by writing the damping term as a fourier cosine series and obtaining some inequalities that the coefficients in this series have to satisfy in order that the spectral abscissa be larger than a real number alpha we are then able to use a genetic algorithm to obtain values of the spectral abscissa which are better than those given by the constant damping case this provides a counterexample to the conjecture that the best possible decay was obtained for constant damping

collapsed 5 manifolds with pinched positive sectional curvature abstract let m be a closed 5 manifold of pinched curvature 0 sec m 1 we prove that m is homeomorphic to a spherical space form if one of the following conditions holds i the center of the fundamental group has index w a constant depending on ii 1 4 1 10 6 2 and the fundamental group is a non cyclic group of order c a constant iii the volume is less than and the fundamental group is either isomorphic to a spherical 5 space group or has an odd order and it has a center of index w a constant

achieving arbitrarily large decay in the damped wave equation we exhibit a sequence of viscous dampings for the fixed string that yields arbitrarily fast attenuation of any and all initial disturbances the limit case produces extinction of all solutions in finite time

application of the quadrilateral area co ordinate method a new element for mindlin reissner plate the quadrilateral area co ordinate method is used to formulate a new quadrilateral element for mindlin reissner plate bending problem firstly an independent shear field is assumed based on the locking free timoshenko s beam formulae secondly a fourth order deflection field is assumed by introducing some generalized conforming conditions thirdly the rotation field is determined by the strain displacement relations furthermore a hybrid post processing procedure is suggested to improve the stress internal force solutions following this procedure a new 4 node 12 dof quadrilateral element named ac mq4 is successfully constructed since all formulations are expressed by the area co ordinates element ac mq4 presents some different but beneficial characters when compared with other usual models numerical examples show the new element is free of shear locking insensitive to mesh distortion and possesses excellent accuracy in the analysis of both thick and thin plates it has also been demonstrated that the area co ordinate method the generalized conforming condition method and the hybrid post processing procedure are efficient tools for developing simple effective and reliable finite element models copyright 2005 john wiley sons ltd

the rate at which energy decays in a viscously damped hinged euler bernoulli beam we study the best decay rate of the solutions of a damped euler bernoulli beam equation with a homogeneous dirichlet boundary conditions we show that the fastest decay rate is given by the supremum of the real part of the spectrum of the infinitesimal generator of the underlying semigroup if the damping coefficient is in l infty 0 1

perturbing the critically damped wave equation we consider the wave equation with viscous damping the equation is said to be critically damped when the damping is that value for which the spectral abscissa of the associated wave operator is minimized within the class of constant dampings the critically damped wave operator possesses a nonsemisimple eigenvalue we present a detailed study of the splitting of this eigenvalue under bounded perturbations of the damping and subsequently show that the critical choice is a local minimizes of the spectral abscissa over lines in the class of all bounded dampings

the second twisted betti number and the convergence of collapsing riemannian manifolds let mi overset d gh longrightarrow x denote a sequence of n manifolds converging to a compact metric space x in the gromov hausdorff topology such that the sectional curvature is bounded in absolute value and dim x n we prove the following stability result if the fundamental groups of mi are torsion groups of uniformly bounded exponents and the second twisted betti numbers of mi vanish then there is a manifold m and a sequence of diffeomorphisms from m to a subsequence of mi such that the distance functions of the pullback metrics converge to a pseudo metric in c0 norm furthermore m admits a foliation with leaves diffeomorphic to flat manifolds not necessarily compact such that a vector is tangent to a leaf if and only if its norm converges to zero with respect to the pullback metrics these results lead to a few interesting applications

gradient plasticity theory with a variable length scale parameter the definition and magnitude of the intrinsic length scale are keys to the development of the gradient plasticity theory that incorporates size effects however a fixed value of the material length scale is not always realistic and different problems could require different values moreover a linear coupling between the local and nonlocal terms in the gradient plasticity theory is not always realistic and that different problems could require different couplings this work addresses the proper modifications required for the full utility of the current gradient plasticity theories in solving the size effect problem it is shown that the current gradient plasticity theories do not give sound interpretations of the size effects in micro bending and micro torsion tests if a definite and fixed length scale parameter is used a generalized gradient plasticity model with a non fixed length scale parameter is proposed based on dislocation mechanics this model assesses the sensitivity of predictions to the way in which the local and nonlocal parts are coupled or to the way in which the statically stored and geometrically necessary dislocations are coupled in addition a physically based relation for the length scale parameter as a function of the course of deformation and the material microstructural features is proposed the proposed model gives good predictions of the size effect in micro bending tests of thin films and micro torsion tests of thin wires

on the fundamental groups of manifolds of positive sectional curvature let m be an n manifold with sectional curvature 0 6 k 1 the main result asserts that the fundamental group of m has a finite normal cyclic subgroup with index less than w n 8 oc a constant depending on n and 8

inelastic analysis of 2d solids using a weak form rpim based on deformation theory abstract a radial point interpolation method rpim is presented for inelastic analysis of 2d problems in this method the problem domain is represented by a set of scattered nodes and the field variable is interpolated using the field values of local supporting nodes radial basis function rbf augmented with polynomials is used to construct the shape functions these shape functions possess delta function property that makes the numerical procedure very efficient and many techniques used in the finite element method can be adopted easily galerkin weak form formulation is applied to derive the discrete governing equations and integration is performed using gauss quadrature and stabilized nodal integration the pseudo elastic method proposed by h jahed et al is employed for the determination of stress field and hencky s total deformation theory is used to define the effective material parameters treated as field variables these parameters are functions of the final state of stress fields that can be obtained in an iterative manner based on pseudo linear elastic analysis from one dimensional uniaxial material curve a very long thick walled cylinder and a v notched tension specimen are analyzed and their stress distributions match well with those obtained by finite element commercial software ansys or the available literature

fundamental groups of positively curved manifolds with symmetry we obtain a classification for the fundamental groups of closed n manifolds of positive sectional curvature which admit an isometric t k action with k ge frac n 6 1 n ne 11 15

a nonlocal plasticity formulation for the material point method a new multi variate fixed point iteration scheme is devised for solving the coupled dynamic integral equations governing nonlocal plasticity using the material point method mpm novel use of the mpm grid for particle particle communications results in a simple and efficient matrix free method moreover a straightforward method for deriving a convergence criterion for this method is developed and applied to two classical verification problems that are well known to be mesh dependent with a local model but are shown to be mesh independent with the new nonlocal mpm formulation

non local yield limit degradation presented is a new type of a non local continuum model which avoids problems of convergence at mesh refinement and spurious mesh sensitivity in a softening continuum characterized by degradation of the yield limit the key idea which has recently been proposed in a general context and has already been applied to softening damage due to stiffness degradation is to apply the non local concept only to those parameters which cause the degradation while keeping the definition of the strains local compared to the previously advanced fully non local continuum formulation the new approach has the advantage that the stresses are subjected to the standard differential equations of equilibrium and standard boundary or interface conditions the new formulation exhibits no zero energy periodic modes imbrication of finite elements is unnecessary and finite elements with standard continuity requirements are sufficient two dimensional finite element solutions with up to 3248 degrees of freedom are presented to document convergence and efficacy the formulation is applied to tunnel excavation in a soil stabilized by cement grouting with the objective of preventing cave in burst of the tunnel sides due to compression softening

collapsing riemannian manifolds to ones of lower dimensions on considere l effondrement d une suite de varietes de riemann mi vers un espace de dimension inferieure x on etudie le cas ou l espace limite x est une variete de riemann et les courbures sectionnelles de mi sont bornees

a sub domain smoothed galerkin method for solid mechanics problems summary a sub domain smoothed galerkin method is proposed to integrate the advantages of mesh free galerkin method and fem arbitrarily shaped sub domains are predefined in problems domain with mesh free nodes in each sub domain based on mesh free galerkin weak formulation the local discrete equation can be obtained by using the moving kriging interpolation which is similar to the discretization of the high order finite elements strain smoothing technique is subsequently applied to the nodal integration of sub domain by dividing the sub domain into several smoothing cells moreover condensation of dof can also be introduced into the local discrete equations to improve the computational efficiency the global governing equations of present method are obtained on the basis of the scheme of fem by assembling all local discrete equations of the sub domains the mesh free properties of galerkin method are retained in each sub domain several 2d elastic problems have been solved on the basis of this newly proposed method to validate its computational performance these numerical examples proved that the newly proposed sub domain smoothed galerkin method is a robust technique to solve solid mechanics problems based on its characteristics of high computational efficiency good accuracy and convergence copyright 2014 john wiley sons ltd

a new implementation of the element free galerkin method abstract element free galerkin methods efg are methods for solving partial differential equations with moving least squares interpolants efg methods require only nodal data no element connectivity is needed in a previous implementation of the efg method lagrange multipliers were used to enforce the essential boundary condition however the use of lagrange multipliers increases the cost of solving the linear algebraic equations a new implementation is developed based on a modified variational principle in which the lagrange multipliers are replaced at the outset by their physical meaning so that the discrete equations are banded in addition weighted orthogonal basis functions are constructed so the need for solving equations at each quadrature point is eliminated numerical examples show that the present implementation effectively computes stress concentrations and stress intensity factors at cracks with very irregular arrangements of nodes the latter makes it very advantageous for modelling progressive cracking

an implicit gradient model by a reproducing kernel strain regularization in strain localization problems abstract a reproducing kernel strain regularization rksr as a mathematical generalization of gradient theory and non local theory for strain localization problems is presented rksr introduces a correction of the weight function in the non local strain by imposition of gradient reproducing conditions both continuum and discrete forms of rksr are presented and they lead to an implicit representation of gradient models as such rksr provides a gradient type regularization to the localization problem without increasing the order of differentiation in the governing equations hence no additional boundary conditions are required and the need for higher order continuity for the approximation of unknowns in the governing equations is no longer an issue a von neumann spectral analysis is employed to study the spectral properties of rksr of various orders in one dimension it is shown that rksr almost duplicates the spectral properties of second and fourth order gradient theories in summary rksr reproduces the regularization properties of gradient methods without dealing with additional boundary conditions or higher order continuity issues

rationality of geometric signatures of complete 4 manifolds according to cg4 and cfg the complete manifolds with bounded sectional curvature and finite volume admit positive rank f structures near infinity in this paper we show that in dimension four if the manifolds also have bounded covering geometry near infinity then there exist f structures with special topological properties f structures with these properties cannot be constructed solely by means of the general methods in cg4 and cfg using these special properties we prove a conjecture of cheeger gromov on the rationality of the geometric signatures in the four dimensional case

a mass for alf manifolds we prove a positive mass theorem on alf manifolds i e complete noncompact manifolds that are asymptotic to a circle fibration over a euclidean base with fibers of asymptotically constant length

real analyticity of solutions of hamilton s equation il existe des constantes positives cn et sn dependant seulement de la dimension n de la variete m telles que pour une metrique initiale g 0 avec r g 0 1 l equation de hamilton a une solution jusqu a t sn et l estimation suivante est vraie pour la metrique solution en t o t sn k 0 t k k 1 12 k r 2 c n

continuous discontinuous finite element approximations of fourth order elliptic problems in structural and continuum mechanics with applications to thin beams and plates and strain gradient elasticity abstract a new finite element method for fourth order elliptic partial differential equations is presented and applied to thin bending theory problems in structural mechanics and to a strain gradient theory problem the method combines concepts from the continuous galerkin cg method the discontinuous galerkin dg method and stabilization techniques a brief review of the cg method the dg method and stabilization techniques highlights the advantages and disadvantages of these methods and suggests a new approach for the solution of fourth order elliptic problems a continuous discontinuous galerkin c dg method is proposed which uses c 0 continuous interpolation functions and is formulated in the primary variable only the advantage of this formulation over a more traditional mixed approach is that the introduction of additional unknowns and related difficulties can be avoided in the context of thin bending theory the c dg method leads to a formulation where displacements are the only degrees of freedom and no rotational degrees of freedom need to be considered the main feature of the c dg method is the weak enforcement of continuity of first and higher order derivatives through stabilizing terms on interior boundaries consistency stability and convergence of the method are shown analytically numerical experiments verify the theoretical results and applications are presented for bernoulli euler beam bending poisson kirchhoff plate bending and a shear layer problem using toupin mindlin strain gradient theory

a study of strain localization in a multiple scale framework the one dimensional problem abstract this work approaches strain localization by recognizing the multiple scales inherent in the problem a component associated with the region of localized strain typically one with high gradient is referred to as the fine scale it represents the microstructure the field obtained by removing the fine scale from the total solution is referred to as the coarse scale the aim of the multiple scale method advanced here is to derive a model for the coarse scale field that accounts for the finite scale this process eliminates the fine scale from the problem yet retains its effect in applying this framework to the nonlinear problems with which localized strains are associated a crucial step is a first order approximation of the relevant relations the fully nonlinear problem is solved by an iterative scheme by accounting directly for the microstructure the multiple scale model recovers the regularizing effects of various alternative formulations for softening strain localization it thus presents itself as a unifying framework for such models numerical solutions are shown to be invariant with respect to the discretization furthermore for cases in which the displacements assume a distinct profile within the localization band the multiple scale model provides a resolution that can be made as accurate as desired even with the coarsest mesh possible the model is applied to strain localization problems that arise in inviscid and viscoplastic solids numerical simulations are presented that demonstrate the efficacy of the approach

an adaptive wavelet galerkin method for an elastic plastic damage constitutive model 1d problem we present a wavelet galerkin method for the analysis of elastic plastic damage systems ju s model j w ju int j solids struct 25 1989 803 is explicitly considered and numerically tested but the method applies equally well to a broad range of damage mechanics models a three step elastic predictor plastic corrector damage corrector strategy is the core of the proposed approach we use a displacement approach with wavelet interpolating functions instead of classical polynomials this allows to clearly locate those sites in the system where damage is taking place thanks to the high pass filtering action operated by the wavelets this opens the way to inexpensive self adaptive strategies that are introduced and preliminary tested herein

gradient dependent plasticity formulation and algorithmic aspects a plasticity theory is proposed in which the yield strength not only depends on an equivalent plastic strain measure hardening parameter but also on the laplacian thereof the consistency condition now results in a differential equation instead of an algebraic equation as in conventional plasticity to properly solve the set of non linear differential equations the plastic multiplier is discretized in addition to the usual discretization of the displacements for appropriate boundary conditions this formulation can also be derived from a variational principle accordingly the theory is complete

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

eight node reissner mindlin plate element based on boundary interpolation using timoshenko beam function a new eight node reissner mindlin plate element is developed with a special interpolation within the element this special interpolation is an extension of the element boundary interpolation that employs timoshenko beam function for the boundary segment interpolation the element function can effectively capture the structural behaviours of thick plates and achieve high precision in the analysis of thick plates patch tests and numerical investigations are conducted it can be seen that the proposed element successfully passes all the patch tests the results of the numerical investigation show that the proposed element is free of the shear locking phenomenon and possesses a higher accuracy in the analyses as compared to the earlier research in the literature

ends of finite volume nonpositively curved manifolds we study complete finite volume n manifolds m of bounded nonpositive sectional curvature a classical theorem of m gromov says that if such m has negative curvature then it is homeomorphic to the interior of a compact manifold with boundary and we denote this boundary partial m if n ge 3 we prove that the universal cover of the boundary widetilde partial m and also the pi 1m cover of the boundary partial widetilde m have vanishing n 2 dimensional homology for n 4 the first of these recovers a result of nguy tilde hat mathrm e n phan saying that each component of the boundary partial m is aspherical for any n ge 3 the second of these implies the vanishing of the first group cohomology group with group ring coefficients h 1 b pi 1m mathbb z pi 1m 0 a consequence is that pi 1m is freely indecomposable these results extend to manifolds m of bounded nonpositive curvature if we assume that m is homeomorphic to the interior of a compact manifold with boundary our approach is a form of homological collapse for ends of finite volume manifolds of bounded nonpositive curvature this paper is very much influenced by earlier yet still unpublished work of nguy tilde hat mathrm e n phan

collapsing riemannian manifolds while keeping their curvature bounded i soit y n une variete de riemann connexe complete et p y n le rayon d injectivite i p de l application exponentielle en p est defini comme etant le plus petit r tel que exp p b r p n est pas un diffeomorphisme sur son image on etudie la situation dans laquelle la taille du rayon d injectivite est petite relativement a la courbure

a variational principle for gradient plasticity abstract we elaborate on a generalized plasticity model which belongs to the class of gradient models suggested earlier by aifantis and co workers the generalization of the conventional theory of plasticity has been accomplished by the inclusion of higher order spatial gradients of the equivalent plastic strain in the yield condition first it is shown how these gradients affect the critical condition for the onset of localization and allow for a wavelength selection analysis leading to estimates for the width and or spacing of shear bands due to the presence of higher order gradients additional boundary conditions for the equivalent plastic strain are required this question and also the associated problem of the formulation and solution of general boundary value problems were left open in the previous work we demonstrate here that upon assuming a certain type of additional boundary conditions the structural symmetries of the gradient dependent constitutive model are such that there exists a variational principle for the displacement rates and the rate of the equivalent plastic strain the variational principle can serve as a basis for the numerical solution of boundary value problems in the sense of the finite element method explicit expressions for the tangent stillness matrix and the generalized nodal point forces are given

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

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

deforming the metric on complete riemannian manifolds soit m g ij x une variete de riemann a n dimensions complete non compacte de tenseur de complexe riemannien r ijkl satisfaisant r ijkl 2 k 0 sur m ou 0 0 dependant seulement de n et de k 0 telle que l equation d evolution g ij x t t 2r ij x t sur m g ij x o g ij x x m ait une solution lisse g ij x t 0 pour un temps court 0 t t u k 0 et satisfait l estimation suivante pour un entier m 0 il existe des constantes c m 0 dependant seulement de n m et k 0 telles que sup x m v m r ijkl x t 2 c m t m 0 t t u k 0

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

nilpotent structures and invariant metrics on collapsed manifolds let mn be a complete riemannian manifold of bounded curvature say iki 0 we put mn w n c u fn c where 1n e consists of those points at which the injectivity radius of the exponential map is e the complementary set n c is called the e collapsed part of mn if x e 4 n r e then the metric ball bx r is quasi isometric with small distortion to the flat ball b0 r in the euclidean space rn after slightly

a strain constructed point interpolation method and strain field construction schemes for solid mechanics problems using triangular mesh abstract this paper presents a strain constructed point interpolation method sc pim for solid mechanics problems using three node triangular mesh in the sc pim the point interpolation method pim is used to construct both displacement and strain fields a total of 14 schemes are proposed to construct strain fields that are equivalent to the compatible strain fields in energy norm and therefore the strain constructed galerkin sc galerkin weak form can be used to form the discretized system equations in these schemes strains at critical points vertices of the triangular integration cells are first obtained using the generalized strain smoothing techniques over the node based and or edge based smoothing domains and constructed strain fields in the integration cells are then obtained using linear interpolations a sc pim model using any of the 14 schemes is stable and convergent but not necessarily to the exact solution standard numerical patch tests are conducted to find six linearly conforming schemes converging to the exact solution benchmark problems have been studied to investigate the performance and properties of the sc pim with all these six conforming schemes outstanding schemes have been identified with better accuracy and high convergence rates in terms of both displacement and energy norms

optimal shape and position of the actuators for the stabilization of a string abstract the energy in a string subject to constant viscous damping k on a subset of length l 0 decays exponentially in time we consider the problem of optimizing the decay rate for the which are the unions of at most n intervals this rate is given by the spectral abscissa of the linear operator associated to the wave equation we are interested in small values of k therefore we consider the derivative of the spectral abscissa at k 0 we prove that except for the case l 1 2 when the number of intervals is not fixed a priori an optimal domain does not exist we study numerically the case of one or two intervals using a genetic algorithm these numerical results are not intuitive in particular the optimal position of one interval is never at the middle of the string

collapsing of abelian fibered calabi yau manifolds we study the collapsing behavior of ricci flat kahler metrics on a projective calabi yau manifold which admits an abelian fibration when the volume of the fibers approaches zero we show that away from the critical locus of the fibration the metrics collapse with locally bounded curvature and along the fibers the rescaled metrics become flat in the limit the limit metric on the base minus the critical locus is locally isometric to an open dense subset of any gromov hausdorff limit space of the ricci flat metrics we then apply these results to study metric degenerations of families of polarized hyperkahler manifolds in the large complex structure limit in this setting we prove an analogue of a result of gross and wilson for k3 surfaces which is motivated by the strominger yau zaslow picture of mirror symmetry