on computational shells with scale effects abstract the paper deals with the computations of so called geometrically exact shells with scale effects these type of computations are relevant to thin walled structures at small scales e g thin films nanotubes etc the shell formulation exhibits higher order gradients and is developed following some author s recent work on generalised continua the framework has been modified as to account for two dimensional surfaces as well the shell formulation reduces to a standard one upon disregarding the higher gradient terms the classical part of the formulation is a well known 7 parameter model previously developed by one of the authors which takes thickness change into account the numerical treatment is based on a meshfree formulation which provides the necessary c 1 continuity as possible applications dynamic buckling of cylindrical and spherical shells is investigated and some results for various states of loading and scale parameters are presented the examples include also nanotubes of different dimensions where scale effects matter the influence of the extra gradients is well demonstrated resulting in different buckling behaviours

pseudo divergence free element free galerkin method for incompressible fluid flow abstract incompressible modeling in finite elements has been a major concern since its early developments and has been extensively studied however incompressibility in mesh free methods is still an open topic thus instabilities or locking can preclude the use of mesh free approximations in such problems here a novel mesh free formulation is proposed for incompressible flow it is based on defining a pseudo divergence free interpolation space that is the finite dimensional interpolation space approaches a divergence free space when the discretization is refined note that such an interpolation does not include any overhead in the computations the numerical evaluations are performed using the inf sup numerical test and two well known benchmark examples for stokes flow

symmetry reductions dynamical behavior and exact explicit solutions to the gordon types of equations in this paper the combination of lie symmetry analysis and the dynamical system method is performed on the mixed second order sine gordon equation all of the geometric vector fields of the sine gordon equation the generalized nonlinear wave equation and its special case the liouville equation are presented then the symmetry reductions and exact solutions to such nonlinear wave equations are considered especially the bifurcations of the sine gordon equation are obtained and the exact explicit traveling wave solutions are investigated by the dynamical system method to guarantee the existence of the traveling wave solutions all of the parameter conditions are determined

a point interpolation method for simulating dissipation process of consolidation abstract a biot s consolidation problem in foundation engineering is numerically investigated using improved point interpolation method pim a weak form of biot s theory is first developed to consider the unbalanced forces at previous time step and thus guarantees the global equilibrium at current step two independent variables in the weak form displacement and excess pore water pressure are approximated using the same shape functions through pim technique the pim technique constructs its interpolation functions through a cluster of scattered points in problem domain and its shape function is of delta properties thus implementation of essential boundary conditions is as easy as in conventional finite element method crank nicholson s integration scheme is used to discretize time domain finally examples are studied and compared with finite element methods to demonstrate its capability

a parallelized meshfree method with boundary enrichment for large scale cfd a parallel computational implementation of a meshfree method the reproducing kernel particle method rkpm is used for 3 d implicit cfd analysis a novel procedure for implementing the essential boundary condition using the hierarchical enrichment method is presented using this enrichment along the essential boundaries produces results that more closely match experimental and analytical results for a flow past a cylinder problem than does either the finite element method or other meshfree methods that require matrix inversion for the application of essential boundary conditions this technique also allows the efficient parallelization of the algorithm and leads to higher parallel speedups than do other boundary condition implementations many of which involve inherently serial steps this is important because the expense of meshfree computations makes parallelization crucial for large size problems the performance of the parallelization technique and the accuracy of the implicit cfd algorithm are demonstrated in two example problems

group classifications optimal systems and exact solutions to the generalized thomas equations abstract in this paper the complete group classifications are performed on the types of thomas equations tes which arise in the study of chemical exchange progress etc all of the vector fields of the equations are presented then the optimal system of the general thomas equation is given and all of the symmetry reductions and exact solutions generated from the optimal system are investigated furthermore the exact analytic solutions to the thomas equations are obtained by the generalized power series method

convergence analysis of a hierarchical enrichment of dirichlet boundary conditions in a mesh free method implementation of dirichlet boundary conditions in mesh free methods is problematic in wagner and liu international journal for numerical methods in engineering 2001 50 507 a hierarchical enrichment technique is introduced that allows a simple implementation of the dirichlet boundary conditions in this paper we provide some error analysis for the hierarchical enrichment mesh free technique we derive optimal order error estimates for the hierarchical enrichment mesh free interpolants for one dimensional elliptic boundary value problems we can directly apply the interpolation error estimates to obtain error estimates for the mesh free solutions for higher dimensional problems derivation of error estimates for the mesh free solutions depends on the availability of an inverse inequality numerical examples in 1d and 2d are included showing the convergence behaviour of mesh free interpolants and mesh free solutions when the hierarchical enrichment mesh free technique is employed copyright 2001 john wiley sons ltd

symmetry reductions and exact solutions to the systems of carbon nanotubes conveying fluid abstract in this paper the systems of carbon nanotubes cnts conveying fluid are considered by the combination of lie symmetry analysis and the dynamical system method all of the geometric vector fields of the three systems are obtained then the symmetry reductions and exact solutions to the systems are investigated by the dynamical system and the power series method especially the convergence of the power series solution to the nonlinear system is shown under the condition which is easily satisfied generally

essential boundary condition enforcement in meshless methods boundary flux collocation method element free galerkin efg methods are based on a moving least squares mls approximation which has the property that shape functions do not satisfy the kronecker delta function at nodal locations and for this reason imposition of essential boundary conditions is difficult in this paper the relationship between corrected collocation and lagrange multiplier method is revealed and a new strategy that is accurate and very simple for enforcement of essential boundary conditions is presented the accuracy and implementation of this new technique is illustrated for one dimensional elasticity and two dimensional potential field problems copyright 2001 john wiley sons ltd

exact solutions via equivalence transformations of variable coefficient fifth order kdv equations abstract in this paper a family of variable coefficient fifth order kdv equations has been considered by using an infinitesimal method based on the determination of the equivalence group differential invariants and invariant equations are obtained invariants provide an alternative way to find equations from the family which may be equivalent to a specific subclass of the same family and the invertible transformation which maps both equivalent equations here differential invariants are applied to obtain exact solutions

an implicit corrected sph formulation for thermal diffusion with linear free surface boundary conditions the smoothed particle hydrodynamics sph method has proven useful for modeling large deformation of fluids including fluids with stress free surfaces because of the lagrangian nature of the method it is well suited to address the thermal evolution of these free surface flows boundary conditions at the interface of the fluid with a solid wall are usually enforced through the use of boundary particles however applying conditions at free surfaces in particular gradient boundary conditions can be problematic with traditional sph formulations due to the degradation of the gradient approximation in these regions compounding this difficulty is that traditional approximations of the laplacian operator suffer a similar degradation near free surfaces a new sph formulation of the laplacian operator is presented which improves the accuracy near free surface boundaries this new form is based on a gradient approximation commonly used in thermal viscous and pressure projection problems but includes higher order terms in the appropriate taylor series comparisons with other approximations of second order derivatives are given the discretization is tested by solving steady state and transient problems of thermal diffusion using the backward euler method with a gmres solver boundary conditions are imposed through an augmented matrix copyright 2008 john wiley sons ltd

pressure stability in fractional step finite element methods for incompressible flows abstract the objective of this paper is to analyze the pressure stability of fractional step finite element methods for incompressible flows that use a pressure poisson equation for the classical first order projection method it is shown that there is a pressure control which depends on the time step size and therefore there is a lower bound for this time step for stability reasons the situation is much worse for a second order scheme in which part of the pressure gradient is kept in the momentum equation the pressure stability in this case is extremely weak to overcome these shortcomings a stabilized fractional step finite element method is also considered and its stability is analyzed some simple numerical examples are presented to support the theoretical results

on a path following method for non linear solid mechanics with applications to structural and cardiac mechanics subject to arbitrary loading scenarios abstract in computational solid mechanics path following methods have been proven useful when dealing with non monotonously evolving loading magnitudes as encountered e g in instability or softening behaviour the present work derives from a displacement based method a cavity volume based path following method and considers its application specifically to cardiac mechanics problems both methods are able to account for an arbitrary number of simultaneously acting loading conditions when applied to the newton raphson method the corresponding loading increments are computed by means of volume increments or point wise prescribed displacement increments respectively no additional variables are required and the physics of the problem at hands is not altered both methods are implemented in an in house meshfree modelling software and successfully applied to non linear elastic and inelastic problems in structural mechanics the cavity volume control method in particular is demonstrated to accurately predict the highly non linear elastic and anisotropic material behaviour encountered when modelling the heart albeit the proposed methods can be equally used e g in finite element methods they are very well suited for meshfree methods where the kronecker delta property does not apply

an infinite horizon stochastic maximum principle for discounted control problem with lipschitz coefficients in the present work a stochastic maximum principle for discounted control of a certain class of degenerate diffusion processes with global lipschitz coefficient is investigated the value function is given by a discounted performance functional leading to a stochastic maximum principle of semi couple forward backward stochastic differential equation with non smooth coefficients the proof is based on the approximation of the lipschitz coefficients by smooth ones and the approximation of the infinite horizon adjoint process

exact travelling wave solutions for the n 1 dimensional double sine and sinh gordon equations for the n 1 dimensional double sine and sinh gordon equations by using the approach of dynamical systems to the travelling wave solutions in different regions of the parameter space all possible bounded solutions solitary wave solutions kink and anti kink wave solutions and periodic wave solutions et al are obtained explicit exact parametric representations are given

two dimensional symmetry reduction of 2 1 dimensional nonlinear klein gordon equation in this paper one dimensional optimal system of group invariant solutions of 2 1 dimensional klein gordon system is constructed then the classification of group invariant solutions is given out and the corresponding two dimensional symmetry reduced equations are obtained at last some symmetry transformations are gained in detail especially we obtain the most general solution from a given solution by use of six variable one parameter subgroups transformations

hierarchical enrichment for bridging scales and mesh free boundary conditions the finite element method when used with a basis made up of piecewise polynomials often requires the generation of a very fine computational mesh in order to capture localized solution phenomena such as boundary layers or near singularities enrichment of the basis with additional functions obtained through analytical or experimental means can allow for a coarser mesh and more accurate solution we introduce an enrichment scheme in which an interaction or bridging scale term is used to separate the basis formed by the enrichment functions from the original set of basis functions in effect making the enrichment hierarchical this separation of scales allows the simple application of essential boundary conditions it also allows a quantification of the effects of the enrichment leading to strategies for error estimation and control of the stiffness matrix condition number we also find that this formulation allows for the simple application of essential boundary conditions for mesh free shape functions which are notoriously problematic we find that for multiple dimensions care must be taken to derive a weak form which is truly consistent with the strong form on the essential boundary copyright 2001 john wiley sons ltd

a finite element formulation for the stokes problem allowing equal velocity pressure interpolation abstract in this paper we study a variational formulation of the stokes problem that accommodates the use of equal velocity pressure finite element interpolations the motivation of this method relies on the analysis of a class of fractional step methods for the navier stokes equations for which it is known that equal interpolations yield good numerical results the reason for this turns out to be the difference between two discrete laplacian operators computed in a different manner the formulation of the stokes problem considered here aims to reproduce this effect from the analysis of the finite element approximation of the problem we obtain stability and optimal error estimates using velocity pressure interpolations satisfying a compatibility condition much weaker than the inf sup condition of the standard formulation in particular this condition is fulfilled by the most common equal order interpolations

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

high re solutions for incompressible flow using the navier stokes equations and a multigrid method the vorticity stream function formulation of the two dimensional incompressible navierstokes equations is used to study the effectiveness of the coupled strongly implicit multigrid csi mg method in the determination of high re fine mesh flow solutions the driven flow in a square cavity is used as the model problem solutions are obtained for configurations with reynolds number as high as 10 000 and meshes consisting of as many as 257 x 257 points for re 1000 the 129 x 129 grid solution required 1 5 minutes of cpu time on the amdahl 470 v 6 computer because of the appearance of one or more secondary vortices in the flow field uniform mesh refinement was preferred to the use of one dimensional gridclustering coordinate transformations the past decade has witnessed a great deal of progress in the area of computational fluid dynamics developments in computer technology hardware as well as in advanced numerical algorithms have enabled attempts to be made towards analysis and numerical solution of highly complex flow problems for some of these applications the use of simple iterative techniques to solve the navier stokes equations leads to a rather slow convergence rate for the solutions the solution convergence rate can be seriously affected if the coupling among the various governing differential equations is not properly honored either in the interior of the solution domain or at its boundaries the rate of convergence is also generally strongly dependent on such problem parameters as the reynolds number the mesh size and the total number of computational points this has led several researchers to examine carefully the recently emerging multigrid mg technique as a useful means for enhancing the convergence rate of iterative numerical methods for solving discretized equations at a number of computational grid points so large as to be considered impractical previously

adaptive coupled arbitrary lagrangian eulerian finite element and meshfree method for injection molding process this paper presents an adaptive method that couples the finite element fe method and the meshfree mf method in the arbitrary lagrangian eulerian ale description for numerical simulation of injection molding processes the ale feature is used to accurately capture moving free surfaces of flow problems and meanwhile to alleviate mesh distortion and its influence on the accuracy and robustness of numerical solutions based on the continuous blending method originally presented for properly imposing the essential boundary conditions in mf methods the coupled ale fe and mf method is developed to exploit the respective advantages of both fe and mf methods but to avoid their respective weak points the method features self adaptivity in view of the fact that moving free surfaces in an injection molding process are continuously advanced the pressure stabilized fractional step algorithm in which the modified version of the finite increment calculus process is extended to the coupled ale fe and mf method is used to solve incompressible navier stokes equations governing the injected polymer flow so that equal low order u p interpolations that violate the lbb condition can be effectively used numerical experiments demonstrate the significance and ability of the proposed method for numerical simulation of injection molding processes copyright 2007 john wiley sons ltd

a shell theory with scale effects and higher order gradients abstract this works follows a generalised continuum framework developed by sansour 1998 to derive a strain gradient formulation suitable to address scale effects of structures where one dimension is very small e g thin films nano tubes etc whereas a previous strain gradient approach by sansour et al 2009 considered the fully three dimensional setting the approach here proposes a shell theory which aims to run computations of thin structures more efficiently and to include scale effects the theory features a generalised deformation description new strain and stress measures as consequence of these new quantities a corresponding generalised variational principle is formulated the approach is completed by dirichlet boundary conditions for the displacement field and its derivatives a numerical example is presented based on a meshfree formulation which provides the necessary c 1 continuity

optimality necessary conditions in singular stochastic control problems with nonsmooth data the present paper studies the stochastic maximum principle in singular optimal control where the state is governed by a stochastic differential equation with nonsmooth coefficients allowing both

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

the superconvergent patch recovery spr and adaptive finite element refinement abstract the error estimation processes which have been developed by the authors depend on the accuracy with which stresses gradients can be recovered the recovery methods available currently such as the l 2 projection and averaging are inaccurate and an improved process is needed this paper presents a very much improved recovery process yielding superconvergent values throughout the domain details of this method named the superconvergent patch recovery are presented with test results showing its efficiency examples of adaptive h based refinement are given showing high local and overall efficiency indices for error estimation

a taylor galerkin method for convective transport problems a method is described to derive finite element schemes for the scalar convection equation in one or more space dimensions to produce accurate temporal differencing the method employs forward time taylor series expansions including time derivatives of second and third order which are evaluated from the governing partial differential equation this yields a generalized time discretized equation which is successively discretized in space by means of the standard bubnov galerkin finite element method the technique is illustrated first in one space dimension with linear elements and euler leap frog and crank nicolson time stepping several interesting relations with standard galerkin and recently developed petrov galerkin methods emerge and the new taylor galerkin schemes are found to exhibit particularly high phase accuracy with minimal numerical damping the method is successively extended to deal with variable coefficient problems and multi dimensional situations

a general stochastic maximum principle for optimal control problems the maximum principle for nonlinear stochastic optimal control problems in the general case is proved the control domain need not be convex and the diffusion coefficient can contain a control variable

imposing nonlocal boundary conditions in galerkin type methods based on non interpolatory functions abstract the imposition of inhomogeneous dirichlet essential boundary conditions is a fundamental challenge in the application of galerkin type methods based on non interpolatory functions i e functions which do not possess the kronecker delta property such functions typically are used in various meshfree methods as well as methods based on the isogeometric paradigm the present paper analyses a model problem consisting of the poisson equation subject to non standard boundary conditions namely instead of classical boundary conditions the model problem involves dirichlet and neumann type nonlocal boundary conditions variational formulations with strongly and weakly imposed inhomogeneous dirichlet type nonlocal conditions are derived and compared within an extensive numerical study in the isogeometric framework based on non uniform rational b splines nurbs the attention in the numerical study is paid mainly to the influence of the nonlocal boundary conditions on the properties of the considered discretisation methods

a collocated c0 finite element method reduced quadrature perspective cost comparison with standard finite elements and explicit structural dynamics summary we demonstrate the potential of collocation methods for efficient higher order analysis on standard nodal finite element meshes we focus on a collocation method that is variationally consistent and geometrically flexible converges optimally embraces concepts of reduced quadrature and leads to symmetric stiffness and diagonal consistent mass matrices at the same time it minimizes the evaluation cost per quadrature point thus reducing formation and assembly effort significantly with respect to standard galerkin finite element methods we provide a detailed review of all components of the technology in the context of elastodynamics that is weighted residual formulation nodal basis functions on gauss lobatto quadrature points and symmetrization by averaging with the ultra weak formulation we quantify potential gains by comparing the computational efficiency of collocated and standard finite elements in terms of basic operation counts and timings our results show that collocation is significantly less expensive for problems dominated by the formation and assembly effort such as higher order elastostatic analysis furthermore we illustrate the potential of collocation for efficient higher order explicit dynamics throughout this work we advocate a straightforward implementation based on simple modifications of standard finite element codes we also point out the close connection to spectral element methods where many of the key ideas are already established copyright 2014 john wiley sons ltd

reproducing kernel element method part i theoretical formulation in this paper and its sequels we introduce and analyze a new class of methods collectively called the reproducing kernel element method rkem the central idea in the development of the new method is to combine the strengths of both finite element methods fem and meshfree methods two distinguished features of rkem are the arbitrarily high order smoothness and the interpolation property of the shape functions these properties are desirable especially in solving galerkin weak forms of higher order partial differential equations and in treating dirichlet boundary conditions so unlike the fem there is no need for special treatment with the rkem in solving high order equations compared to meshfree methods dirichlet boundary conditions do not present any difficulty in using the rkem a rigorous error analysis and convergence study of the method are presented the performance of the method is illustrated and assessed through some numerical examples

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

lie symmetry analysis and exact solutions for the short pulse equation abstract in this paper the lie symmetry analysis and the generalized symmetry method are performed for a short pulse equation spe the symmetries for this equation are given for the traveling wave solutions the exact parametric representations are investigated to guarantee the existence of the above solutions all parameter conditions are determined furthermore the exact analytic solutions are obtained by using the power series method

the unified group classification method for the generalized nonlinear wave equation and its partial difference schemes this paper is concerned with the generalized nonlinear second order equation and its discrete counterpart furnished with different lattices respectively by the unified symmetry analysis method the complete group classifications of the equations are performed in the sense of point symmetry all of the vector fields of the continuous nonlinear equation are obtained as its special cases the vector fields of some other important nonlinear equations are provided then we develop the unified group classification method for dealing with partial difference schemes p s all of the point symmetries of the difference schemes are presented with respect to the given arbitrary analytic function f u

consistent element free galerkin method an element free galerkin efg method with linear quadratic and cubic approximations which can exactly in a numerical sense pass the corresponding patch tests is proposed and is named as consistent efg cefg method the development of this method is based on the hu washizu three field variational principle numerical integration schemes with corrected nodal derivatives at quadrature points are proposed according to the satisfaction of the orthogonality condition between stress and strain difference thus the method is variationally consistent the consistency of the corrected nodal derivatives and the satisfaction of patch test conditions are theoretically proved and also numerically validated numerical results show that the proposed cefg method greatly improves the numerical performance of the efg method in terms of accuracy convergence efficiency and stability especially the proposed cubic cefg method which shows exceptional accuracy and convergence copyright 2014 john wiley sons ltd

an iterative stabilized fractional step algorithm for finite element analysis in saturated soil dynamics abstract the discretization of the u p model for saturated porous media results in the semi discrete system of mixed type in displacements and pressures the babuska brezzi condition or the simpler patch test proposed by zienkiewicz and taylor precludes the use of elements with the equal low order of interpolation for u and p unless special stabilization techniques such as the fractional step algorithms are used the purpose of this paper is to present a modified version of the fractional step algorithm which allows much larger time step sizes than those for the existing ones the method is based on introducing an iteration algorithm the numerical experiments demonstrate the effectiveness and improved performance of the proposed modified version of the fractional step algorithm

a meshless integral method based on regularized boundary integral equation a meshless integral method based on the regularized boundary integral equation is developed and applied to two dimensional linear elasticity the governing integral equation is obtained from the weak form of elasticity over a local sub domain and the moving least squares approximation is used for meshless function approximation the method is built on the lbie method proposed by atluri and co workers and several key improvements are introduced in this work that significantly enhance the accuracy and robustness of the method the most critical improvement is the use of the subtraction technique to remove the strong singularity that results in a regularized governing integral equation the technique is straightforward and efficient and is much simpler and easier compared to other singularity removal techniques a special numerical integration is employed for the calculation of integrals with weak singularity which further improves accuracy the collocation method is employed to enforce the essential boundary conditions exactly which is simple and computationally efficient the natural boundary conditions are incorporated in the system governing equation and require no special handling numerical tests show that the meshless integral method is accurate and robust the effects of weight function support domain sub domain and monomial basis are investigated and discussed

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

moving kriging interpolation and element free galerkin method a new formulation of the element free galerkin efg method is presented in this paper efg has been extensively popularized in the literature in recent years due to its flexibility and high convergence rate in solving boundary value problems however accurate imposition of essential boundary conditions in the efg method often presents difficulties because the kronecker delta property which is satisfied by finite element shape functions does not necessarily hold for the efg shape function the proposed new formulation of efg eliminates this shortcoming through the moving kriging mk interpolation two major properties of the mk interpolation the kronecker delta property i s j i j and the consistency property n i i x i and n i i x x l i x i are proved some preliminary numerical results arc given

elastoplastic meshless integral method abstract in this paper the meshless integral method based on regularized boundary integral equation a bodin j ma x j xin p krishnaswami a meshless integral method based on regularized boundary integral equation comput methods appl mech engrg 195 2006 6258 6286 has been extended to elastoplastic materials in the formulation the domain of interest is populated with a set of nodes using an automatic node generation algorithm the sub domain and support domain associated with each node are also generated automatically using algorithms that have been developed for this purpose the governing integral equation is obtained from the weak form of elastoplasticity over a local sub domain and the moving least squares approximation is used for meshless function approximation the constitutive law is the small deformation rate independent flow theory based on von mises yielding criterion with isotropic hardening the generalized collocation method is employed to enforce the essential boundary conditions exactly which is simple and computationally efficient natural boundary conditions are incorporated in the system governing equation and require no special handling the solution algorithm for elastoplastic analysis is discussed in detail the proposed method can handle any prescribed loading profile including unloading and reversed loading numerical examples show that the elastoplastic integral meshless method is accurate and robust

finite element solution of the unsteady navier stokes equations by a fractional step method abstract a finite element method is presented for the numerical simulation of time dependent incompressible viscous flows the method is based on a fractional step approach to the time integration of the navier stokes equations in which only the incompressibility condition is treated implicitly this leads to a computational scheme of extremely simple algorithmic structure that is particularly attractive for cost effective solutions of large scale problems numerical results indicate the versatility and effectiveness of the proposed method

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 point interpolation meshless method based on radial basis functions a point interpolation meshless method is proposed based on combining radial and polynomial basis functions involvement of radial basis functions overcomes possible singularity associated with the meshless methods based on only the polynomial basis this non singularity is useful in constructing well performed shape functions furthermore the interpolation function obtained passes through all scattered points in an influence domain and thus shape functions are of delta function property this makes the implementation of essential boundary conditions much easier than the meshless methods based on the moving least squares approximation in addition the partial derivatives of shape functions are easily obtained thus improving computational efficiency examples on curve surface fittings and solid mechanics problems show that the accuracy and convergence rate of the present method is high copyright 2002 john wiley sons ltd

linearized state based peridynamics for 2 d problems summary in this work the authors formulate a 2 d linearized ordinary state based peridynamic model of elastic deformations and compute the stiffness matrix for 2 d plane stress strain conditions this model is then verified by testing the recovery of elastic properties for given poisson s ratios in the range 0 1 0 45 the convergence behavior of peridynamic solutions in terms of the size of the nonlocal region by comparison with the classical local mechanics model is also discussed the degree to which the peridynamic surface effect influences the recovery of elastic properties is examined and stress strain recovery values are found to have a definite influence on the results the technique used here can provide the basis for applying 2 d peridynamic models to the study of fatigue failure and quasi static fracture problems copyright 2016 john wiley sons ltd

numerical modeling of viscoelastic flows using equal low order finite elements a mixed finite element scheme abbreviated as i ps devss cnbs scheme for modeling viscoelastic flow problems is presented the finite incremental calculus fic pressure stabilization process and the discrete elastic viscous stress splitting method devss are introduced into the general framework of the iterative version of the fractional step algorithm with the use of the crank nicolson based splitting inconsistent streamline upwinding method su is employed to spatially discretize the constitutive equation of viscoelastic fluids equal low order finite elements which violate the lbb compatibility conditions are successfully used in the proposed scheme in addition the oldroyd b and the ptt models have been integrated into the proposed scheme to solve the 4 1 sudden contraction flow problem the numerical results demonstrate prominent stability and accuracy of both pressure and stress distributions over the flow domains provided by the proposed scheme within the weissenberg number range studied in the present work as compared with the reference solutions reported in the literatures

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

an ale based iterative cbs algorithm for non isothermal non newtonian flow with adaptive coupled finite element and meshfree method this paper presents a generalized scheme of the fractional step algorithm using characteristic based split cbs in ale framework for the numerical simulation of incompressible non isothermal non newtonian fluid flows and applies it combined with the adaptive coupled finite element and meshfree method for spatial discretizations to the polymer injection molding process based on the idea to discretize the material time derivative instead of the spatial time derivative the characteristic galerkin method is derived in a more general way and is used to discretize the non newtonian momentum and the energy conservation equations an iterative procedure which makes the conservation equations satisfied in an implicit sense is introduced into the scheme to enhance its stability in the time domain numerical experiments with the power law fluid model demonstrate and validate the performance and the capability of the proposed scheme

meshfree iterative stabilized taylor galerkin and characteristic based split cbs algorithms for incompressible n s equations abstract this paper presents two stabilized schemes of the fractional step algorithm using characteristic based split and taylor galerkin like based split respectively in the meshfree context an iterative procedure which makes the convective term satisfy the momentum conservation equation in an implicit sense is introduced into the two schemes to allow much larger time step sizes a modified version of finite increment calculus process for incompressibility stabilization is developed to avoid the calculation of high order spatial derivatives numerical experiments demonstrate the capability and stability of the proposed schemes of the meshfree based fractional step method in the simulation of incompressible flows

smoothing and accelerated computations in the element free galerkin method two topics in the formulation and implementation of meshless methods are considered the smoothing of the approximating functions at concave boundaries and the speedup of the calculation of the approximating functions and their derivatives these techniques are described in the context of the element free galerkin method but they are applicable to other meshless methods results are presented for some elastostatic problems which show a moderate improvement in the accuracy of the smoothed interpolant the speedup in calculating the shape functions is about a factor of two

implementation of boundary conditions for meshless methods abstract boundaries and boundary conditions are an aspect of the numerical solution of partial differential equations where meshless methods have had to surmount many initial difficulties due to the lack of a finite element like kronecker delta condition furthermore it is frequently desirable especially in fluid mechanics to impose general nonlinear boundary and interface constraints this paper describes a computationally efficient algorithm based on d alembert s principle that can be used for general constraints both in meshless methods and finite elements first a method of partitioning meshless shape functions suitable for imposing linear boundary conditions is developed subsequently an analogous method is developed for nonlinear constraints special attention is given to imposing general boundary and fluid structure interface conditions on the navier stokes equations in terms of conservative variables numerical results using d alembert s principle with the reproducing kernel particle method rkpm including viscous supersonic flow past a naca 7012 airfoil are shown

a stabilized finite element method for incompressible viscous flows using a finite increment calculus formulation abstract a stabilized finite element formulation for incompressible viscous flows is derived the starting point are the modified navier stokes equations incorporating naturally the necessary stabilization terms via a finite increment calculus fic procedure application of the standard finite element galerkin method to the modified differential equations leads to a stabilized discrete system of equations overcoming the numerical instabilities emanating from the advective terms and those due to the lack of compatibility between approximate velocity and pressure fields the fic method also provides a natural explanation for the stabilization terms appearing in all equations for both the navier stokes and the simpler stokes equations transient solution schemes with enhanced stabilization properties are also proposed finally a procedure for computing the stabilization parameters is presented

streamline upwind petrov galerkin formulations for convection dominated flows with particular emphasis on the incompressible navier stokes equations abstract a new finite element formulation for convection dominated flows is developed the basis of the formulation is the streamline upwind concept which provides an accurate multidimensional generalization of optimal one dimensional upwind schemes when implemented as a consistent petrov galerkin weighted residual method it is shown that the new formulation is not subject to the artificial diffusion criticisms associated with many classical upwind methods the accuracy of the streamline upwind petrov galerkin formulation for the linear advection diffusion equation is demonstrated on several numerical examples the formulation is extended to the incompressible navier stokes equations an efficient implicit pressure explicit velocity transient algorithm is developed which accomodates several treatments of the incompressibility constraint and allows for multiple iterations within a time step the effectiveness of the algorithm is demonstrated on the problem of vortex shedding from a circular cylinder at a reynolds number of 100