a fast semi discrete kansa method to solve the two dimensional spatiotemporal fractional diffusion equation abstract fractional order diffusion equations fdes extend classical diffusion equations by quantifying anomalous diffusion frequently observed in heterogeneous media real world diffusion can be multi dimensional requiring efficient numerical solvers that can handle long term memory embedded in mass transport to address this challenge a semi discrete kansa method is developed to approximate the two dimensional spatiotemporal fde where the kansa approach first discretizes the fde then the gauss jacobi quadrature rule solves the corresponding matrix and finally the mittag leffler function provides an analytical solution for the resultant time fractional ordinary differential equation numerical experiments are then conducted to check how the accuracy and convergence rate of the numerical solution are affected by the distribution mode and number of spatial discretization nodes applications further show that the numerical method can efficiently solve two dimensional spatiotemporal fde models with either a continuous or discrete mixing measure hence this study provides an efficient and fast computational method for modeling super diffusive sub diffusive and mixed diffusive processes in large two dimensional domains with irregular shapes

direct computation of lower bound dynamic buckling loads of imperfection sensitive systems the computation of lower bound dynamic buckling loads of imperfection sensitive systems is examined under step load of ine nite duration an extended system based on the energy criterion for establishing the lower bound dynamic buckling loads without solving the highly nonlinear initial value problems is proposed the newly introduced scaling parameters are nonsingular solutions to the extended system thus standard methods can be used to compute them using the extended system one can directly obtain the lower bound dynamic buckling loads without tracing the postbuckling equilibrium paths an efe cient implementation of newton s method for solving the extended system is presented and numerical examples are given

a nodal integration and post processing technique based on voronoi diagram for galerkin meshless methods a stabilized nodal integration technique is adopted by adding the square of the residual of the equilibrium equation to the potential energy functional an approach is proposed based on voronoi diagram to evaluate nodal volumes accurately it is a key issue for nodal integration of galerkin meshless methods furthermore as the dual of voronoi diagram the corresponding delaunay triangles are at hand provided voronoi diagram construction is completed a realistic technique is proposed based on background delaunay triangles for post processing of meshless results in the whole domain of interest two elastic stress analysis problems are investigated which demonstrate the approach is realistic versatile and robust

radial spline collocation method for static analysis of beams conventional spline collocation method scm uses equally spaced knots in the computation of approximation however when load distribution geometry material property of structure are discontinuous it will greatly reduce accuracy the goal of this paper is mainly to develop unequally spaced knots to improve the disadvantage of using equally spaced knots applying the concept of radial basis functions rbf the spline function is transformed into radial spline function rsf consequently rsf can conveniently calculate the values for unequally spaced knots so that the complicated beam problems with discontinuous characteristics can be solved accurately and efficiently by the proposed radial spline collocation method rscm in this paper the proposed rscm also can be extended to solve other structural problems such as frame plate shell etc

a meshless method for axi symmetric poroelastic simulations numerical study a meshless model based on the meshless local petrov galerkin mlpg approach is developed and implemented for the solution of axi symmetric poroelastic problems the solution accuracy and the code performance are investigated on a realistic application concerning the prediction of land subsidence above a deep compacting reservoir the analysis addresses several numerical issues including the parametric selection of the optimal size of the local sub domains for the weak form and the nodal supports the appropriate integration rule and the linear system solver the results show that mlpg can be more accurate than the standard finite element fe method on coarse discretizations with its superiority decreasing as the nodal resolution increases this is due to both a slower convergence rate and a progressively higher computational cost compared to fe these drawbacks can be partially mitigated by improving the efficiency of the numerical integration and the system solver with the aid of projection techniques based on krylov subspace methods the outcome of the present analysis supports the development of coupled methods where a limited number of mlpg nodes are used to locally improve a fe solution copyright 2006 john wiley sons ltd

on stability and the worst imperfection shape in solids with nearly simultaneous eigenmodes abstract of interest here is the influence of imperfections on the stability of elastic systems discrete or continuous with nearly simultaneous modes the majority of such structures show an extreme sensitivity of their first instability load to the shape of these small amplitude but unavoidable imperfections the determination of the worst such possible shape is thus a very important issue from the design standpoint following a general analysis of the stability of arbitrary elastic systems with nearly simultaneous bifurcation eigenmodes in the presence of imperfections conditions are given for the determination of the worst imperfection shape which minimizes the first local load maximum for the case of coincident eigenmodes the answer to the worst shape problem is considerably simplified for it is determined from the equilibrium branch of the perfect structure on which the load drops more rapidly

a perturbation method for the determination of the buckling strength of imperfection sensitive structures a perturbation method for determining the buckling strength of imperfection sensitive structures is presented the method is based on an extended system which was first used by seydel in computation of limit points of nonlinear systems the effects of various possible sources of structural imperfections on perfect structures with simple buckling loads are investigated by the method the derivations and results of the present exposition are equally applicable to discrete and continuous systems in the finite element implementation of the new formulation the perturbation expansions are determined by solving numerically several linear problems with a single positive definite sub stiffness matrix the method is illustrated with its application to the analyses of imperfection sensitivity of a simply supported column on a linear elastic foundation subjected to axial compression

dynamic 3d axisymmetric problems in continuously non homogeneous piezoelectric solids the meshless local petrov galerkin mlpg method is used to analyze transient dynamic problems in 3d axisymmetric piezoelectric solids with continuously inhomogeneous material properties both mechanical and thermal loads are considered here a 3d axisymmetric body is created by rotation of a cross section around an axis of symmetry axial symmetry of geometry and boundary conditions reduces the original 3d boundary value problem into a 2d problem the cross section is covered by small circular sub domains surrounding nodes randomly spread over the analyzed domain a unit step function is chosen as test function in order to derive local integral equations on the boundaries of the chosen sub domains called local boundary integral equations lbie these integral formulations are either based on the laplace transform technique or the time difference approach the local integral equations are non singular and take a very simple form despite of inhomogeneous and anisotropic material behaviour across the analyzed structure spatial variation of all physical fields or of their laplace transforms at discrete time instants are approximated on the local boundary and in the interior of the sub domain by means of the moving least squares mls method the stehfest algorithm is applied for the numerical laplace inversion in order to retrieve the time dependent solutions

numerical solution to the unsteady two dimensional schrodinger equation using meshless local boundary integral equation method a meshless local boundary integral equation lbie method is proposed to solve the unsteady two dimensional schrodinger equation the method is based on the lbie with moving least squares mls approximation for the mls approximation nodal points spread over the analyzed domain are utilized to approximate the interior and boundary variables a time stepping method is employed to deal with the time derivative an efficient method for dealing with singular domain integrations that appear in the discretized equations is presented finally numerical results are considered for some examples to demonstrate the accuracy efficiency and high rate of convergence of this method copyright 2008 john wiley sons ltd

an adaptive finite element meshless coupled method based on local maximum entropy shape functions for linear and nonlinear problems in this paper an automatic adaptive coupling procedure is proposed for the finite element method fem and the element free galerkin method efgm for linear elasticity and for problems with both material and geometrical nonlinearities in this new procedure initially the whole of the problem domain is modelled using the fem during an analysis those finite elements which violate a predefined error measure are automatically converted to an efg zone this efg zone can be further refined by adding nodes thus avoiding computationally expensive fe remeshing local maximum entropy shape functions are used in the efg zone of the problem domain for two reasons their weak kronecker delta property at the boundaries allows straightforward imposition of essential boundary conditions and also provides a natural way to couple the efg and fe regions compared to the use of moving least squares basis functions the zienkiewicz and zhu error estimation procedure with the superconvergent patch method for strains and stresses recovery is used in the fe region of the problem domain while the chung and belytschko error estimation procedure is used in the efg region

a local point interpolation method for static and dynamic analysis of thin beams abstract the local point interpolation method lpim is a newly developed truly meshless method based on the idea of meshless local petrov galerkin mlpg approach in this paper a new lpim formulation is proposed to deal with fourth order boundary value and initial value problems for static and dynamic analysis stability free vibration and forced vibration of beams local weak forms are developed using weighted residual method locally in order to introduce the derivatives of the field variable into the interpolation scheme a technique is proposed to construct polynomial interpolation with kronecker delta function property based only on a group of arbitrarily distributed points because the shape functions so obtained possess delta function property the essential boundary conditions can be implemented with ease as in the conventional finite element method fem the validity and efficiency of the present lpim formulation are demonstrated through numerical examples of beams under various loads and boundary conditions

energy based dynamic buckling estimates for autonomous dissipative systems the dynamic buckling global response of a nonlinear 3 degree of freedom dissipative model under a step loading of infinite duration is thoroughly discussed geometrically imperfect models with symmetric or antisymmetric imperfections losing their static stability through a limit point and an asymmetric bifurcation point respectively are considered emphasis is given to the combined effect of nonlinearities geometric and or material and damping exact approximate and lower upper bound estimates based on energy criteria for establishing the dynamic buckling response of such autonomous models without solving the highly nonlinear initial value problem are assessed the reliability and efficiency of the proposed readily obtained estimates is illustrated via numerical simulation the accuracy of which is checked using energy balance considerations certain interesting byproducts associated with a postlimit point bifurcation and breakdown of the symmetry of deformation are also revealed

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

on the convergence analysis stability and implementation of meshless local radial point interpolation on a class of three dimensional wave equations summary in this article the meshless local radial point interpolation method is applied to analyze three space dimensional wave equations of the form utt ut u uxx uyy uzz f x y z t xt x y z rd d 2 3 t 0 subject to given initial and dirichlet boundary conditions the main difficulty of the great number of methods in full 3 d problems is the large computational costs in meshless local radial point interpolation method it does not require any background integration cells so that all integrations are carried out locally over small quadrature domains of regular shapes such as circles or squares in two dimensions and spheres or cubes in three dimensions the point interpolation method with the help of radial basis functions is proposed to construct shape functions that have kronecker delta function property a weak formulation with the heaviside step function converts the set of governing equations into local integral equations on local subdomains a two step time discretization method is employed to evaluate the time derivatives this suggests crank nicolson technique to be applied on the right hand side of the equation the convergence analysis and stability of the method are fully discussed three illustrative examples are presented and satisfactory agreements are achieved it is shown theoretically that the proposed method is unconditionally stable for the second example whereas it is not for the first and third ones copyright 2015 john wiley sons ltd

implementation of meshless lbie method to the 2d non linear sg problem in this paper the meshless local boundary integral equation lbie method for numerically solving the non linear two dimensional sine gordon sg equation is developed the method is based on the lbie with moving least squares mls approximation for the mls nodal points spread over the analyzed domain are utilized to approximate the interior and boundary variables the approximation functions are constructed entirely using a set of scattered nodes and no element or connectivity of the nodes is needed for either the interpolation or the integration purposes a time stepping method is employed to deal with the time derivative and a simple predictor corrector scheme is performed to eliminate the non linearity a brief discussion is outlined for numerical integrations in the proposed algorithm some examples involving line and ring solitons are demonstrated and the conservation of energy in undamped sg equation is investigated the final numerical results confirm the ability of method to deal with the unsteady non linear problems in large domains copyright 2009 john wiley sons ltd

area minimizing discs in metric spaces we solve the classical problem of plateau in the setting of proper metric spaces precisely we prove that among all disc type surfaces with prescribed jordan boundary in a proper metric space there exists an area minimizing disc which moreover has a quasi conformal parametrization if the space supports a local quadratic isoperimetric inequality for curves we prove that such a solution is locally holder continuous in the interior and continuous up to the boundary our results generalize corresponding results of douglas rado and morrey from the setting of euclidean space and riemannian manifolds to that of proper metric spaces

the natural neighbour petrov galerkin method for elasto statics in this paper an efficient and accurate meshless natural neighbour petrov galerkin method nnpg is proposed to solve elasto static problems in two dimensional space this method is derived from the generalized meshless local petrov galerkin method mlpg as a special case in the nnpg the local supported trial functions are constructed based on the non sibsonian interpolation and test functions are taken as the three node triangular fem shape functions the local weak forms of the equilibrium equation and the boundary conditions are satisfied in local polygonal sub domains these sub domains are constructed with delaunay tessellations and domain integrals are evaluated over included delaunay triangles by using gaussian quadrature scheme as this method combines the advantages of natural neighbour interpolation with petrov galerkin method together no stiffness matrix assembly is required and no special treatment is needed to impose the essential boundary conditions several numerical examples are presented and the results show the presented method is easy to implement and very accurate for these problems copyright 2005 john wiley sons ltd

enrichment and coupling of the finite element and meshless methods a mixed hierarchical approximation based on finite elements and meshless methods is presented two cases are considered the first one couples regions where finite elements or meshless methods are used to interpolate continuity and consistency is preserved the second one enriches a finite element mesh with particles thus there is no need to remesh in adaptive refinement processes in both cases the same formulation is used convergence is studied and examples are shown copyright 2000 john wiley sons ltd

treatment of material discontinuity in the element free galerkin method abstract a method is presented for application of the element free galerkin method efg to solid mechanics problems containing material discontinuities by using the efg method the trial and test functions for the weak form are constructed with moving least square interpolants in each material domain additional constraints are imposed at the variational level to ensure satisfaction of interface conditions as a result only nodal data no elemental connectivity is needed given c 1 continuity of the interpolant weighting function the dependent variable and its gradient are continuous in each material domain two linear elastic bi material examples are presented to illustrate the effectiveness of the method

sharp and rigid isoperimetric inequalities in metric measure spaces with lower ricci curvature bounds we prove that if x mathsf d mathfrak m is a metric measure space with mathfrak m x 1 having in a synthetic sense ricci curvature bounded from below by k 0 and dimension bounded above by n in 1 infty then the classic levy gromov isoperimetric inequality together with the recent sharpening counterparts proved in the smooth setting by milman for any k in mathbb r n ge 1 and upper diameter bounds holds i e the isoperimetric profile function of x mathsf d mathfrak m is bounded from below by the isoperimetric profile of the model space moreover if equality is attained for some volume v in 0 1 and k is strictly positive then the space must be a spherical suspension and in this case we completely classify the isoperimetric regions finally we also establish the almost rigidity if the equality is almost attained for some volume v in 0 1 and k is strictly positive then the space must be mgh close to a spherical suspension to our knowledge this is the first result about isoperimetric comparison for non smooth metric measure spaces satisfying ricci curvature lower bounds examples of spaces fitting our assumptions include measured gromov hausdorff limits of riemannian manifolds satisfying ricci curvature lower bounds alexandrov spaces with curvature bounded from below finsler manifolds endowed with a strongly convex norm and satisfying ricci curvature lower bounds the result seems new even in these celebrated classes of spaces

imposing essential boundary conditions in mesh free methods imposing essential boundary conditions is a key issue in mesh free methods the mesh free interpolation does not verify the kronecker delta property and therefore the imposition of prescribed values is not as straightforward as for the finite element method the aim of this paper is to present a general overview on the existing techniques to enforce essential boundary conditions in galerkin based mesh free methods special attention is paid to the mesh free coupling with finite elements for the imposition of prescribed values and to methods based on a modification of the galerkin weak form particular examples are used to analyze and compare their performance in different situations

a coupled finite element and meshless local petrov galerkin method for two dimensional potential problems a coupled finite element fe method and meshless local petrov galerkin mlpg method for analyzing two dimensional potential problems is presented in this paper the analysis domain is subdivided into two regions a finite element fe region and a meshless mm region a single weighted residual form is written for the entire domain independent trial and test functions are assumed in the fe and mm regions a transition region is created between the two regions the transition region blends the trial and test functions of the fe and mm regions the trial function blending is achieved using a technique similar to the coons patch method that is widely used in computer aided geometric design the test function blending is achieved by using either fe or mm test functions on the nodes in the transition element the technique was evaluated by applying the coupled method to two potential problems governed by the poisson equation the coupled method passed all the patch test problems and gave accurate solutions for the problems studied

existence and characterization of regions minimizing perimeter under a volume constraint inside euclidean cones we study the problem of existence of regions separating a given amount of volume with the least possible perimeter inside a euclidean cone our main result shows that nonexistence for a given volume implies that the isoperimetric profile of the cone coincides with the one of the half space this allows us to give some criteria ensuring existence of isoperimetric regions for instance local convexity of the cone at some boundary point we also characterize which are the stable regions in a convex cone i e second order minima of perimeter under a volume constraint from this it follows that the isoperimetric regions in a convex cone are the euclidean balls centered at the vertex intersected with the cone

moving particle finite element method with superconvergence nodal integration formulation and applications abstract a new approach of moving particle finite element method has been developed which is capable to gain a global superconvergence through solving particle kernel function to satisfy high order consistencies the nodal based moving particle finite element method inconjunction with the proposed superconvergence approach provides an optimized combination in numerical accuracy and computation efficiency the three dimensional engineering scale simulations demonstrate that this scheme is robust and capable to handle high speed penetration and dynamic crack propagation with intersonic and supersonic speeds

applications of compactness results for harmonic maps to stable constant mean curvature surfaces for all lipschitz functions u such that m u da 0 in the above formula and da are the gradient and the area element on m and is the square of the norm of the second fundamental form of we shall call i the index form of the immersion note that i u is the second variation formula of the area for a normal variation leaving constant the volume functional with variational vector field u where is a unit vector field normal to the immersion complete details can be found in bdce in this paper we study stable periodic surfaces i e stable immersions m r3 where is a discrete subgroup of translations in r3 these surfaces are interesting since they are good models for naturally occurring periodic phenomena such as the formation of interfaces in block copolymers see tahh and the references cited there up to now our knowledge of stable immersions in complete flat three manifolds can be resumed in the following result see rr for a sketch of the proof

enriched element free galerkin methods for crack tip fields summary the element free galerkin efg method is a meshless method for solving partial di erential equations which uses only a set of nodal points and a cad like description of the body to formulate the discrete model it has been used extensively for fracture problems and has yielded good results when adequate refinement is used near the crack tip but stresses tend to be oscillatatory near the crack tip unless substantial refinement is used an enriched efg formulation for fracture problems is proposed two methods are used 1 adding the asymptotic fields to the trial function and 2 augmenting the basis by the asymptotic fields a local mapping of the enriched fields for curved cracks is also described results show that both methods greatly reduce stress oscillations and allow the calculation of accurate stress intensity factors with far fewer degrees of freedom 1997 by john wiley sons ltd

application of radial basis functions to linear and nonlinear structural analysis problems the basic characteristic of the techniques generally known as meshless methods is the attempt to reduce or even to eliminate the need for a discretization at least not in the way normally associated with traditional finite element techniques in the context of numerical solutions for boundary and or initial value problems the interest in meshless methods is relatively new and this is why despite the existence of various applications of meshless techniques to several problems of mechanics as well as to other fields these techniques are still relatively unknown to engineers furthermore and compared to traditional finite elements it may be difficult to understand the physical meaning of the variables involved in the formulations as an attempt to clarify some aspects of the meshless techniques and simultaneously to highlight the ease of use and the ease of implementation of the algorithms applications are made in this work to structural analysis problems the technique used here consists of the definition of a global approximation for a given variable of interest in this case components of the displacement field by means of a superposition of a set of conveniently placed in the domain and on the boundary radial basis functions rbfs in this work various types of one dimensional problems are analyzed ranging from the static linear elastic case free vibration and linear stability analysis for a beam on elastic foundation to physically nonlinear damage models problems to further complement the range of problems analysed the static analysis of a plate on elastic foundation was also addressed several error measures are used to numerically establish the performance of both symmetric and nonsymmetric approaches for several global rbfs the results obtained show that rbf collocation leads to good approximations and very high convergence rates

stability of hypersurfaces with constant mean curvature soit m n compacte orientable et soit x m n r n 1 une immersion a courbure moyenne constante non nulle alors x est stable si et seulement si x m r n 1 est une sphere s n r n 1

application of hypersingular integral equation method to three dimensional crack in electromagnetothermoelastic multiphase composites a three dimensional crack problem in electromagnetothermoelastic multiphase composites emte mcs under extended loads is investigated in this paper using green s functions the extended general displacement solutions are obtained by the boundary element method this crack problem is reduced to solving a set of hypersingular integral equations coupled with boundary integral equations in which the unknown functions are the extended displacement discontinuities then the behavior of the extended displacement discontinuities around the crack front terminating at the interface is analyzed by the main part analysis method of hypersingular integral equations analytical solutions for the extended singular stresses the extended stress intensity factors sifs and the extended energy release rate near the crack front in emte mcs are provided also a numerical method of the hypersingular integral equations for a rectangular crack subjected to extended loads is put forward with the extended displacement discontinuities approximated by the product of basic density functions and polynomials in addition distributions of extended sifs varying with the shape of the crack are presented the results show that the present method accurately yields smooth variations of extended sifs along the crack front

explicit form and efficient computation of mls shape functions and their derivatives this work presents a general and efficient way of computing both diffuse and full derivatives of shape functions for meshless methods based on moving least squares approximation mls and interpolation it is an extension of the recently introduced consistency approach based on lagrange multipliers which provides a general framework for constrained mls along with robust algorithms for the computation of shape functions and their diffuse derivatives the particularity of the proposed algorithms is that they do not involve matrix inversion or linear system solving the previous approach is limited to diffuse derivatives of the shape functions and not their full derivatives which are usually much more expensive to obtain in the present paper we propose to efficiently compute the full derivatives by a new algorithm based on the formal differentiation of the previous one in this way we obtain a unified low cost consistent methodology for evaluating the shape functions and both their diffuse and full derivatives in the second part of the paper we introduce explicit forms of mls shape functions in 1d 2d and 3d for an arbitrary number of nodes these forms are especially useful for comparing finite element and mls approximations finally we present a general architecture of an mls program copyright 2000 john wiley sons ltd

elasto plasticity revisited numerical analysis via reproducing kernel particle method and parametric quadratic programming aiming to simplify the solution process of elasto plastic problems this paper proposes a reproducing kernel particle algorithm based on principles of parametric quadratic programming for elasto plasticity the parametric quadratic programming theory is useful and effective for the assessment of certain features of structural elasto plastic behaviour and can also be exploited for numerical iteration examples are presented to illustrate the essential aspects of the behaviour of the model proposed and the flexibility of the coupled parametric quadratic programming formulations with the reproducing kernel particle method copyright 2002 john wiley sons ltd

a fictitious domain method using equilibrated basis functions for harmonic and bi harmonic problems in physics abstract in this paper we present a new meshless method to solve well known problems in physics and engineering with either constant or variable material properties in 2d space harmonic and bi harmonic problems are considered in this paper the method constructs a set of basis functions called equilibrated basis functions eqbfs through a weighted residual integration over a fictitious domain embedding the main one the bases can satisfy the governing partial differential equations approximately chebyshev polynomials of the first kind are employed to construct the eqbfs and exponential functions are used as the weights in the integrals the parameters of the solution are arranged so that all the integrals can be decomposed into much simpler 1d ones over a normalized intervals this reduces the computational efforts significantly either the eqbfs or the results of the integration process may be stored for further use the validity of the results is examined through an extended patch test a set of physical sample problems with variable non variable material properties as the potential flow over a cylinder steady state heat conduction problems in an anisotropic inhomogeneous functionally graded material potential and stokes flow through a channel of finite width obstructed by periodic cylinders and the bending of thin elastic plates having constant or variable thickness are solved to demonstrate the capabilities of the method as a preliminary study we show that the method may effectively be used in a domain decomposition approach

modelling three dimensional piece wise homogeneous domains using the α shape based natural element method in this paper the application of the natural element method nem to the numerical analysis of two and three dimensional piece wise homogeneous domains is presented the nem differs from other meshless methods in its capability to accurately reproduce essential boundary conditions along convex boundaries the shape based extension of this method nem generalizes this behaviour to non convex domains enables us to construct models entirely in terms of the initial cloud of points and allows us to simulate material discontinuities in a straightforward manner in the following sections simple and effective algorithms are presented for the construction of shapes in domains composed of various materials examples are presented in two and three dimensional cases in the context of linear elastostatics showing good performance even with the simple numerical quadrature used copyright 2002 john wiley sons ltd

a meshfree method for transverse vibrations of anisotropic plates a meshfree approach called displacement boundary method for anisotropic kirchhoff plate dynamic analysis is presented this method is deduced from a variational principle which uses a modified hybrid functional involving the generalized displacements and generalized tractions on the boundary and the lateral deflection in the domain as independent variables the discretization process is based on the employment of the fundamental solutions of the static problem operator for the expression of the variables involved in the functional the stiffness and mass matrices obtained for the dynamic model are frequency independent symmetric and positive definite and their computation involves boundary integrals of regular kernels only due to its features the final resolving system can be solved with the classical approaches by using standard numerical procedures to assess the formulation the free vibrations of some anisotropic plates were calculated and the results compared with those obtained using other solution techniques the present results are in good agreement with those found in the literature showing the accuracy and effectiveness of the proposed approach

coupling three field formulation and meshless mixed galerkin methods using radial basis functions in this work we solve the elliptic partial differential equation by coupling the meshless mixed galerkin approximation using radial basis function with the three field domain decomposition method the formulation has been adopted to increase the efficiency of the numerical technique by decreasing the error and dealing with the ill conditioning of the linear system caused by the radial basis function convergence analysis of the coupled technique is treated and numerical results of some solved examples are given at the end of this paper

meshless local boundary integral equation method for 2d elastodynamic problems a new meshless method for solving transient elastodynamic boundary value problems based on the local boundary integral equation lbie method and the moving least squares approximation mls is proposed in this paper the lbie with the mls is applied to both transient and steady state laplace transformed elastodynamics applying the mls approximation for spatially dependent terms in the first approach the lbies are transformed into a system of ordinary differential equations for nodal unknowns this system of ordinary differential equations is solved by the houbolt finite difference scheme in the second formulation the time variable is eliminated by using the laplace transformation unknown laplace transforms of displacements and traction vectors are computed from the lbies with the mls approximation the time dependent values are obtained by the durbin inversion technique copyright 2003 john wiley sons ltd

isoperimetric regions in cones we consider cones c 0 m n and prove that if the ricci curvature of c is nonnegative then geodesic balls about the vertex minimize perimeter for given volume if strict inequality holds then they are the only stable regions

the computation of symmetry breaking bifurcation points we consider symmetry breaking simple singular points of a parameter dependent nonlinear equation g lambda x 0 such points are intimately connected to pitchfork bifurcation points and we sh

least squares collocation meshless method a finite point method least squares collocation meshless method is proposed except for the collocation points which are used to construct the trial functions a number of auxiliary points are also adopted unlike the direct collocation method the equilibrium conditions are satisfied not only at the collocation points but also at the auxiliary points in a least squares sense the moving least squares interpolant is used to construct the trial functions the computational effort required for the present method is in the same order as that required for the direct collocation while the present method improves the accuracy of solution significantly the proposed method does not require any mesh so that it is a truly meshless method three numerical examples are studied in detail which show that the proposed method possesses high accuracy with low computational effort copyright 2001 john wiley sons ltd

moving particle finite element method with global smoothness we describe a new version of the moving particle finite element method mpfem that provides solutions within a c 0 finite element framework the finite elements determine the weighting for the moving partition of unity a concept of general shape function is proposed which extends regular finite element shape functions to a larger domain these are combined with shepard functions to obtain a smooth approximation the moving particle finite element method combines desirable features of finite element and meshfree methods the proposed approach in fact can be interpreted as a moving partition of unity finite element method or moving kernel finite element method this method possesses the robustness and efficiency of the c 0 finite element method while providing at least c 1 continuity

enriching the finite element method with meshfree particles in structural mechanics summary the automatic generation of meshes for the finite element fe method can be an expensive computational burden especially in structural problems with localized stress peaks the use of meshless methods can address such an issue as these techniques do not require the existence of an underlying connection among the particles selected in a general domain this study advances a numerical strategy that blends the fe method with the meshless local petrov galerkin mlpg technique in structural mechanics with the aim at exploiting the most attractive features of each procedure the idea relies on the use of fes to compute a background solution that is locally improved by enriching the approximation space with the basis functions associated to a few meshless points thus taking advantage of the flexibility ensured by the use of particles disconnected from an underlying grid adding the meshless particles only where needed avoids the cost of mesh refining or even of re meshing without the prohibitive computational cost of a thoroughly meshfree approach in the present implementation an efficient integration strategy for the computation of the coefficients taking into account the mutual fe mlpg interactions is introduced moreover essential boundary conditions are enforced separately on both fes and meshless particles thus allowing for an overall accuracy improvement also when the enriched region is close to the domain boundary numerical examples in structural problems show that the proposed approach can significantly improve the solution accuracy at a local level with no re meshing effort and at a low computational cost this article is protected by copyright all rights reserved

applications of point interpolation method for spatial general shells structures the meshfree point interpolation method pim based on polynomial function is presented for the static analysis of spatial general shell structures the formulation of the discrete system equations is derived from stress resultant geometrically exact shell theory of shear flexible shells based on the cosserat surface the pim technique constructs its interpolation functions through a set of arbitrarily distributed points in the problem domain and its shape function has the delta function property hence the implementation of essential boundary conditions can be imposed with ease as in conventional finite element method an improved matrix triangularization algorithm mta is proposed to obtain proper node enclosure and basis selection in order to overcome the singularity problem in the point interpolation method using a polynomial basis it is found that the shape functions are generally not compatible to ensure the compatibility of the solution and lead to non conforming pim npim when the energy principles are used to formulate pim to obtain compatible shape functions the enforcement of compatibility is needed along the common edges of the background cells in the problem domain and a background cell based nodal selection is utilized which lead to conforming pim cpim both npim and cpim are evaluated in the paper several benchmark problems for shells are analyzed to demonstrate the validity and efficiency of the npim and cpim the phenomena of shear locking and membrane locking are illustrated by showing the membrane and shear energies as fractions of the total energy the convergences and performances are investigated for both conforming and non conforming pims it is also shown that the npim and cpim with the improved mta are very easy to implement and very efficient in constructing shape functions in comparison with the element free galerkin method

weighted isoperimetric inequalities in cones and applications abstract this paper deals with weighted isoperimetric inequalities relative to cones of r n we study the structure of measures that admit as isoperimetric sets the intersection of a cone with balls centered at the vertex of the cone for instance in case that the cone is the half space r n x r n x n 0 and the measure is factorized we prove that this phenomenon occurs if and only if the measure has the form d a x n k exp c x 2 d x for some a 0 k c 0 our results are then used to obtain isoperimetric estimates for neumann eigenvalues of a weighted laplace beltrami operator on the sphere sharp hardy type inequalities for functions defined in a quarter space and finally via symmetrization arguments a comparison result for a class of degenerate pde s

new concepts in meshless methods meshless methods have been extensively popularized in literature in recent years due to their flexibility in solving boundary value problems two kinds of truly meshless methods the meshless local boundary integral equation mlbie method and the meshless local petrov galerkin mlpg approach are presented and discussed both methods use the moving least squares approximation to interpolate the solution variables while the mlbie method uses a local boundary integral equation formulation and the mlpg employs a local symmetric weak form the two methods are truly meshless ones as both of them do not need a finite element or boundary element mesh either for purposes of interpolation of the solution variables or for the integration of the energy all integrals can be easily evaluated over regularly shaped domains in general spheres in three dimensional problems and their boundaries numerical examples presented in the paper show that high rates of convergence with mesh refinement are achievable in essence the present meshless method based on the lswf is found to be a simple efficient and attractive method with a great potential in engineering applications copyright 2000 john wiley sons ltd

element free galerkin methods in combination with finite element approaches element free galerkin efg methods are methods for solving partial differential equations with the help of shape functions coming from moving least squares approximation the efg method is more flexible than the finite element fe method since it requires only nodal data and no element connectivity is needed because the efg method is computationally expensive combinations of the efg method and the fe method are considered implementations based on several weak forms of the problem description are studied numerical examples in elastostatics and fracture mechanics show that the implementations are able to compute both displacement and stress fields accurately

meshless local petrov galerkin method for two dimensional nonlinear water wave problems in this paper the meshless local petrov galerkin mlpg method is extended to dealing with nonlinear water wave problems the formulation is based on general fluid governing equations and a time marching procedure at each time step the boundary value problem for the pressure is solved using the mlpg method and the velocity and position of nodes are updated by numerical integration the newly extended method is applied to simulating water waves generated by a wave maker and good agreement with analytical solutions and finite element results is presented

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

critical initial imperfection of structures abstract a method is introduced for determining the critical initial imperfection of discretized structures that decreases the load bearing capacity most rapidly the effects of imperfections on simple critical points such as limit points of loads and simple bifurcation points are theoretically investigated based on the idea of the lyapunov schmidt decomposition developed in bifurcation theory imperfection sensitivity varies with the types of points nonetheless critical imperfection pattern is expressed in the same formula regardless of the types among various imperfections the most influential can be found in a quantitative manner the validity and the usability of the proposed method are illustrated through its application to simple example structures

a meshless multilayer model for a coastal system by radial basis functions abstract a multilayer computational model for simulating three dimensional tidal flows in coastal waters is presented in this paper a truly meshless numerical scheme based on radial basis functions rbfs is employed to obtain an accurate approximation to the solution of the model for computational efficiency in solving large scale problems a noniterative domain decomposition method is combined with the use of the rbfs scheme to smooth the numerical simulation of the advection across each subdomain the commonly used upstream technique is also incorporated finally for numerical verification the proposed multilayer model is successfully used to obtain a stable and convergent simulation of the water flows in the pearl river estuary of the south china sea the numerical approximations exhibit good agreement with the observed tidal and current data

local radial point interpolation mlrpi method for solving time fractional diffusion wave equation with damping the purpose of the current investigation is to determine numerical solution of time fractional diffusion wave equation with damping for caputo s fractional derivative of order 1 2 a meshless local radial point interpolation mlrpi scheme based on galerkin weak form is analyzed the reason of choosing mlrpi approach is that it does not require any background integrations cells instead integrations are implemented over local quadrature domains which are further simplified for reducing the complication of computation using regular and simple shape the unconditional stability and convergence with order o 6 2 are proved where is time stepping also several numerical experiments are illustrated to verify theoretical analysis

free mesh radial basis function collocation approach for the numerical solution of system of multi ion electrolytes the main objective of this work is to show the versatility of an innovative mesh free numerical scheme which allows the solution of the coupled transport equations governing the evolution of a system of multi ion electrolytes by mean of the use of radial basis functions interpolation and a nesting approach the nesting approach is used in order to capture the detail behaviour of the solution near a solid wall i e at the diffusion reaction layer as a numerical example the problem of silver deposition on a rotating disk is analysed the versatility of the proposed numerical scheme is proved by solving the proposed electrochemical phenomena imposing three different kinds of boundary conditions at the solid wall dirichlet neumann and robin the obtained numerical results are compared with simplified analytical approximation of the corresponding problems the effect of the ligand concentration on the others species is considered and a comparison between the obtained concentration profiles for the complex ags2o and ag s2o3 when the concentration of the ligand s2o takes different values is shown copyright 2005 john wiley sons ltd

fracture analysis in continuously nonhomogeneous magneto electro elastic solids under a thermal load by the mlpg abstract a meshless method based on the local petrov galerkin approach is proposed to solve initial boundary value problems of magneto electro elastic solids with continuously varying material properties stationary and transient thermal problems are considered in this paper the mechanical 2 d fields are described by the equations of motion with an inertial term nodal points are spread on the analyzed domain and each node is surrounded by a small circle for simplicity the spatial variation of displacements electric and magnetic potentials is approximated by the moving least squares mls scheme after performing the spatial integrations one obtains a system of ordinary differential equations for certain nodal unknowns that system is solved numerically by the houbolt finite difference scheme as a time stepping method

a hybrid meshless local petrov galerkin method for unbounded domains abstract meshless methods have gained popularity in recent years however like the finite element method they do not handle unbounded domains well coupling with other techniques more suited to performing this task is problematic since nodal values on the boundary are fictitious rather than actual the scaled boundary finite element method is a semi analytical approach to computational mechanics ideally suited to modelling unbounded domains recently a meshless version of the scaled boundary method based on the local petrov galerkin approach has been developed this paper couples the meshless scaled boundary method used to model the far field with conventional meshless local petrov galerkin modelling of the near field the coupling method is general and could be applied to other techniques of modelling the far field such as the infinite element method

the meshless finite element method a meshless method is presented which has the advantages of the good meshless methods concerning the ease of introduction of node connectivity in a bounded time of order n and the condition that the shape functions depend only on the node positions furthermore the method proposed also shares several of the advantages of the finite element method such as a the simplicity of the shape functions in a large part of the domain b c0 continuity between elements which allows the treatment of material discontinuities and c ease of introduction of the boundary conditions copyright 2003 john wiley sons ltd

meshless analysis of timoshenko beams based on a locking free formulation and variational approaches abstract a meshless method is developed based on subdomain variational formulations and a local petrov galerkin approximation along with the locking free formulation for the analysis of bending of a thick beam the local point interpolation method is employed to construct both trial and test functions the present method is a truly meshless method based only on a number of randomly located nodes no global background integration mesh is needed no element matrix assembly is required and no special treatment is needed to impose the essential boundary conditions effects of the sizes of local subdomain and interpolation domain on the performance of the present method are investigated problems of thick and thin beams under various loading and boundary conditions are analysed by the proposed method and the numerical results are compared with analytical solutions the contact problem for beam by means of subdomain variational inequalities and the meshless method has also been investigated

a meshless local petrov galerkin method for the time dependent maxwell equations abstract in this paper the meshless local petrov galerkin mlpg method is employed to solve the 2 d time dependent maxwell equations the mlpg method is a truly meshless method in which the trial and test functions are chosen from totally different functional spaces in the current work the moving least square reproducing kernel mlsrk scheme is chosen to be the trial function the method is applied for the unsteady maxwell equations in different media in the local weak form by employing the difference operator for evolution in time and simultaneously in time and space the semi discrete and fully discrete schemes are obtained respectively the error estimation is discussed for both the semi discrete and fully discrete numerical schemes for modelling the time dependent maxwell equations we show that provided that the time step size is sufficiently small the proposed scheme yields an error of o 2 m 1 2 in the l 2 norm for the square of error the new scheme is implemented and the numerical results are provided to justify our theoretical analysis

stability of hypersurfaces of constant mean curvature in riemannian manifolds hypersurfaces m n with constant mean curvature in a riemannian manifold overline m n 1 display many similarities with minimal hypersurfaces of overline m n 1 they are both solutions to the variational problem of minimizing the area function for certain variations in the first case however the admissible variations are only those that leave a certain volume function fixed for precise definitions see sect 2 this isoperimetric character of the variational problem associated to hypersurfaces of constant mean curvature introduces additional complications in the treatment of stability of such hypersurfaces

numerical non linear analysis of secondary buckling in stability problems abstract in this paper we discuss the numerical calculation of secondary buckling of structures this kind of stability problem contains two parameters one is conservative load parameter the other is auxiliary one and satisfies z 2 symmetry by using the symmetry and introducing a new parameter we construct an augmented system the system avoids the singularities of usual ones adjusting the newly introduced parameter one can calculate a double buckling load and two corresponding buckling modes secondary buckling load and secondary buckling mode directly without tracing primary post buckling path here the use of the augmented system yields a quadratically convergent iteration scheme we also discuss the implementation of newton s method solving the system a partitioning procedure with this algorithm the amount of computation is largely saved