numerical modelling of crack propagation automatic remeshing and comparison of different criteria modelling of a crack propagating through a finite element mesh under mixed mode conditions is of prime importance in fracture mechanics three different crack growth criteria and the respective crack paths prediction for several test cases are compared the maximal circumferential stress criterion the strain energy density fracture criterion and the criterion of the maximal strain energy release rate are implemented using advanced finite element techniques a fully automatic remesher enables to deal with multiple boundaries and multiple materials the propagation of the crack is calculated with both remeshing and nodal relaxation several examples are presented to check for the robustness of the numerical techniques and to study specific features of each criterion

a higher order scheme for two dimensional quasi static crack growth simulations an efficient scheme for the simulation of quasi static crack growth in two dimensional linearly elastic isotropic specimens is presented the crack growth is simulated in a stepwise manner where an extension to the already existing crack is added in each step in a local coordinate system each such extension is represented as a polynomial of some user specified degree n the coefficients of the polynomial describing an extension are found by requiring that the mode ii stress intensity factor is equal to zero at certain points of the extension if a crack grows from a pre existing crack so that a kink develops the leading term describing the crack shape close to the kink will in a local coordinate system be proportional to x 3 2 we therefore allow the crack extensions to contain such a term in addition to the monomial terms the discontinuity in the crack growth direction at a kink the kink angle is determined by requiring that the mode ii stress intensity factor should be equal to zero for an infinitesimal extension of the existing crack to implement the scheme accurate values of the stress intensity factors and t stress are needed in each step of the simulation these fracture parameters are computed using a previously developed integral equation of the second kind c 2007 elsevier b v all rights reserved less

variable node elements for non matching meshes by means of mls moving least square scheme a new class of finite elements is described for dealing with non matching meshes for which the existing finite elements are hardly efficient the approach is to employ the moving least square mls scheme to devise a class of elements with an arbitrary number of nodal points on the parental domain this approach generally leads to elements with the rational shape functions which significantly extends the function space of the conventional finite element method with a special choice of the nodal points and the base functions the method results in useful elements with the polynomial shape functions for which the c 1 continuity breaks down across the boundaries between the subdomains comprising one element the present scheme possesses an extremely high potential for applications which deal with various problems with discontinuities such as material inhomogeneity crack propagation phase transition and contact mechanics the effectiveness of the new elements for handling the discontinuities due to non matching interfaces is demonstrated using appropriate examples

interface element method iem for a partitioned system with non matching interfaces abstract a novel method for non matching interfaces on the boundaries of finite elements in partitioned domains is presented by introducing interface elements in this paper the interface element method iem satisfies the continuity conditions exactly through interface element domains without recourse to lagrange multiplier technique the interface elements take an interpolation scheme used in meshless methods to join partitioned domains the moving least square mls approximations in the present study are implemented to construct the shape functions of the interface elements the compatibility of displacements on the boundaries of the finite elements and the interface elements is always preserved in this method and the completeness of the shape functions of the interface elements transfers rigid body motions and strain fields correctly moreover alignment of the boundaries of sub domains in the mls approximations and integration domains provides a consistent numerical integration the numerical examples show that the iem is a useful tool for the analysis of a partitioned system and for a global local analysis

a new mesh generation scheme for arbitrary planar domains this paper describes a new algorithm to generate interior nodes within any arbitrary multi connected regions the boundary nodes and the interior nodes are then linked up to form the best possible triangular elements by a completely revised technique in an efficient and stable manner owing to the generality of the central generation program the global domain is allowed to be divided into as many irregular subdomains as desired in order to model closely the actual physical situation moreover the boundaries of the sub domains are updated from time to time when necessary to include the possibilities of progressive refinement around a sharp corner generating radiating mesh from a prescribed node generating mesh between two circular arcs etc despite its flexibility and capabilities data for triangulation have been kept to a minimum by a logical input module no connectivity information between subregions is needed and common boundaries are defined once only all these features have contributed to a powerful method to generate 3 node or 6 node triangular element meshes of great variety within the most irregular heterogeneous regions

multigrid on the interface for mortar mixed finite element methods for elliptic problems we consider mixed finite element approximations of second order elliptic equations on domains that can be described as a union of subdomains or blocks we assume that the subdomain grids are locally defined and need not match across the block boundaries specially chosen mortar finite element spaces are introduced on the interfaces for approximating the scalar variable pressure the mortars also serve as lagrange multipliers for imposing flux matching conditions the method is implemented by reducing the algebraic system to a positive definite interface problem in the mortar spaces this problem is then solved using a multigrid on the interface with conjugate gradient smoothing the algorithm is very efficient in a distributed parallel computing environment as only subdomain solves are required on each conjugate gradient iteration the standard variational assumptions for the multigrid are not satisfied since the interface bilinear forms vary from level to level we present theoretical results for the convergence of the v cycle and the w cycle computational results in two and three dimensions are given to illustrate and confirm the theory

a variational principle for the formulation of partitioned structural systems a continuum based variational principle is presented for the formulation of the discrete governing equations of partitioned structural systems this application includes coupled substructures as well as subdomains obtained by mesh decomposition the present variational principle is derived by a series of modifications of a hybrid functional originally proposed by atluri for finite element development the interface is treated by a displacement frame and a localized version of the method of lagrange multipliers interior displacements are decomposed into rigid body and deformational components to handle floating subdomains both static and dynamic versions are considered an important application of the present principle is the treatment of nonmatching meshes that arise from various sources such as separate discretization of substructures independent mesh refinement and global local analysis the present principle is compared with that of a globalized version of the multiplier method copyright 2000 john wiley sons ltd

multivectorial generalization of the cartan map a multivectorial generalization of the spinors to vectors cartan map is constructed with space time as a base space constructed from spinors dirac spinors and spinors pairs being particular cases onto a multivector space with two internal symmetries one of them is the fundamental space time clifford group c 1 3 and the other an isotopic space in multivectorial representation related with the more common gauge groups the algebraic properties of this map and of the operators representing observables are studied the inversion map is also presented the quaternion projection of the map is shown as are its properties and its mathematical and physical meaning the procedure presented here is compared with other spinor vector maps used in the literature

non matching mesh gluing by meshless interpolation an alternative to lagrange multipliers rewards of using non matching meshes are great in many aspects sub meshing a complex structure in a sub structure wise manner separately and or in parallel selective local refinement unlimited scalability guarantee for generating meshes in increasingly large scale finite element simulation etc however when meshes do not match a gluing algorithm is required to enforce inter domain continuity non matching terminologically originates from mesh discretization in nature and the non matching mesh issue is therefore avoidable or does not exist in a node based or meshless discretization in meshless methods motivated by this a gluing algorithm is developed based on meshless interpolation the gluing is accomplished by continuous trial and test functions across non matching meshes constructed using nodes only the developed gluing algorithm is tested in static and wave propagation problems in two and three dimensions it is demonstrated that the gluing algorithm does not deteriorate convergence and accuracy compared with the one piece conforming mesh compared with lagrange multiplier gluing one of the most common approaches the current algorithm has two significant benefits 1 easier implementation in any dimension and 2 positive definite banded system matrices not acting against equation solvers and hence better suited for large scale finite element analysis

vector level sets for description of propagating cracks in finite elements a new level set method is developed for describing surfaces that are frozen behind a moving front such as cracks in this formulation the level set is described in two dimensions by a three tuple the sign of the level set function and the components of the closest point projection to the surface the update of the level set is constructed by geometric formulas which are easily implemented results are given for growth of lines in two dimensions that show the method is very accurate the method combines very naturally with the extended finite element method xfem where the discontinuous enrichment for cracks is best described in terms of level set functions examples of crack growth simulations obtained by combining this level set method with the extended finite element method are given copyright 2003 john wiley sons ltd

mls based variable node elements compatible with quadratic interpolation part i formulation and application for non matching meshes two dimensional variable node elements compatible with quadratic interpolation are developed using the moving least square mls approximation the mapping from the parental domain to the physical element domain is implicitly obtained from mls approximation with the shape functions and their derivatives calculated and saved only at the numerical integration points it is shown that the present mls based variable node elements meet the patch test if a sufficiently large number of integration points are employed for numerical integration the cantilever problem with non matching meshes is chosen to check the feasibility of the present mls based variable node elements and the result is compared with that from the lower order case compatible with linear interpolation copyright 2005 john wiley sons ltd

on spinors and null vectors we investigate the relations between spinors and null vectors in clifford algebra of any dimension with particular emphasis on the conditions that a spinor must satisfy to be simple also pure in particular we prove i a new property for null vectors each of them bisects spinor space into two subspaces of equal size ii that simple spinors form one dimensional subspaces of spinor space iii a necessary and sufficient condition for a spinor to be simple that generalizes a theorem of cartan and chevalley which becomes a corollary of this result we also show how to write down easily the most general spinor with a given associated totally null plane

interface element method treatment of non matching nodes at the ends of interfaces between partitioned domains abstract a methodology for interface element method iem to combine partitioned domains with non matching nodes at the ends of interfaces is presented the iem is introduced to satisfy the continuity and the compatibility conditions on non matching interfaces between partitioned finite element domains interface elements are defined on the finite elements bordering on the interfaces and the moving least square mls approximations are employed to construct the shape functions of the interface elements by modifying the shape functions of the interface elements at the ends of non matching interfaces partitioned domains are glued such that all properties of the iem are satisfied the modifications are made to sub domains and weight functions in the mls approximations the numerical examples show that the present iem is very effective for the analysis of a partitioned system and for global local analysis

a six state minimal time solution to the firing squad synchronization problem abstract from balzer s work 1967 we know that the firing squad synchronization problem has a minimal time solution with eight states we show that such a solution exists with only six states our method is somewhat different from all previous ones the initial line is iteratively divided in two inequal parts so that each new right part can be treated as the homothetical image of a shorter initial line

a hybrid extended finite element level set method for modeling phase transformations a hybrid numerical method for modelling the evolution of sharp phase interfaces on fixed grids is presented we focus attention on two dimensional solidification problems where the temperature field evolves according to classical heat conduction in two subdomains separated by a moving freezing front the enrichment strategies of the extended finite element method x fem are employed to represent the jump in the temperature gradient that governs the velocity of the phase boundary a new approach with the x fem is suggested for this class of problems whereby the partition of unity is constructed with c1 polynomials and enriched with a c0 function this approach leads to jumps in temperature gradient occurring only at the phase boundary and is shown to significantly improve estimates for the front velocity temporal derivatives of the temperature field in the vicinity of the phase front are obtained with a projection that employs discontinuous enrichment in conjunction with a finer finite difference grid the level set method is used to represent the evolution of the phase interface an iterative procedure is adopted to satisfy the constraints on the temperature field on the phase boundary the robustness and utility of the method is demonstrated with several benchmark problems of phase transformation copyright 2002 john wiley sons ltd

a method of finite element tearing and interconnecting and its parallel solution algorithm a novel domain decomposition approach for the parallel finite element solution of equilibrium equations is presented the spatial domain is partitioned into a set of totally disconnected subdomains each assigned to an individual processor lagrange multipliers are introduced to enforce compatibility at the interface nodes in the static case each floating subdomain induces a local singularity that is resolved in two phases first the rigid body modes are eliminated in parallel from each local problem and a direct scheme is applied concurrently to all subdomains in order to recover each partial local solution next the contributions of these modes are related to the lagrange multipliers through an orthogonality condition a parallel conjugate projected gradient algorithm is developed for the solution of the coupled system of local rigid modes components and lagrange multipliers which completes the solution of the problem when implemented on local memory multiprocessors this proposed method of tearing and interconnecting requires less interprocessor communications than the classical method of substructuring it is also suitable for parallel vector computers with shared memory moreover unlike parallel direct solvers it exhibits a degree of parallelism that is not limited by the bandwidth of the finite element system of equations

on the numerical modelling of quasi static crack growth in linear elastic fracture mechanics in this paper we present a strategy for the simulation of a propagating crack under mixed mode linear elastic conditions using a discontinuous finite element method a key issue is to accurately compute the incremental change in the kink angle of the propagating crack during subsequent steps we have chosen to work with a domain formulation of the material force vector as a criteria for the propagation direction we describe the theoretical background together with the numerical implementation in detail and show some results for different loading conditions copyright 2005 john wiley sons ltd

a quasi static discontinuous galerkin configurational force crack propagation method for brittle materials summary this paper presents a framework for r adaptive quasi static configurational force cf brittle crack propagation cast within a discontinuous galerkin dg symmetric interior penalty sipg finite element scheme cracks are propagated in discrete steps with a staggered algorithm along element interfaces which align themselves with the predicted crack propagation direction the key novelty of the work is the exploitation of the dg face stiffness terms existing along element interfaces to propagate a crack in a mesh independent r adaptive quasi static fashion driven by the cf at the crack tip this adds no new degrees of freedom to the data structure additionally as dg methods have element specific degrees of freedom a geometry driven p adaptive algorithm is also easily included allowing for more accurate solutions of the cf on a moving crack front further for non determinant systems we introduce an average boundary condition that restrains rigid body motion leading to a determinant system to the authors knowledge this is first time such a boundary condition has been described the proposed formulation is validated against single and multiple crack problems with single and mixed mode cracks demonstrating the predictive capabilities of the method this article is protected by copyright all rights reserved

seven state solutions to the firing squad synchronization problem abstract we show that seven states are enough to implement minsky like solutions to the firing squad synchronization problem in a linear network of n finite state cellular automata with null transmission delay

development of three dimensional interface elements for coupling of non matching hexahedral meshes gluing of a non matching interface between dissimilar meshes is one of challenging tasks in computational mechanics the interface element method iem has been developed using an appropriate interpolation scheme between partitioned finite element meshes the continuity of displacements across the interface is satisfied exactly and the completeness of interface element shape functions provides a reasonable transfer of strain fields between dissimilar finite element meshes research related to the iem has been mainly accomplished in two dimensions because the construction of interface elements in three dimensions is not as simple as the case of two dimensions in this paper a new scheme is presented to construct the interface elements for connecting dissimilar hexahedral finite element meshes with an arbitrarily curved non matching interface element edges crossing any other edges in an interface region are modified into continuous intersection polygons to eliminate overlays and gaps between dissimilar meshes and these polygons are divided into triangles to create prism shaped interface elements numerical experiments on a linear elasticity problem with non matching meshes illustrate the effectiveness of the method

inverse extraction of cohesive zone laws by field projection method using numerical auxiliary fields summary the cohesive zone law relates the cohesive tractions with the cohesive separations within the fracture process zone of a material and is used to quantify the strength and toughness of the material determining the material s cohesive zone law however is a nontrivial inverse problem of finding unknown tractions and separations from measurement data previously a field projection method was established to extract the cohesive zone laws from far field data using interaction j integrals between the physical field of interest and auxiliary analytical probing fields here we extend the universality of the field projection method and its ease of numerical implementation by using numerical auxiliary fields these numerical fields are generated by systematically imposing uniform surface tractions element by element along the crack faces in finite element models then interaction j and m integrals between these auxiliary probing fields and the measurement field are used to reconstruct the traction and separation relationship along the crack faces the effectiveness of this method in extracting the cohesive zone law from measured displacements in the far field region is demonstrated through numerical experiments copyright 2012 john wiley sons ltd

clustered generalized finite element methods for mesh unrefinement non matching and invalid meshes in spite of significant advancements in automatic mesh generation during the past decade the construction of quality finite element discretizations on complex three dimensional domains is still a difficult and time demanding task in this paper the partition of unity framework used in the generalized finite element method gfem is exploited to create a very robust and flexible method capable of using meshes that are unacceptable for the finite element method while retaining its accuracy and computational efficiency this is accomplished not by changing the mesh but instead by clustering groups of nodes and elements the clusters define a modified finite element partition of unity that is constant over part of the clusters this so called clustered partition of unity is then enriched to the desired order using the framework of the gfem the proposed generalized finite element method can correctly and efficiently deal with i elements with negative jacobian ii excessively fine meshes created by automatic mesh generators iii meshes consisting of several sub domains with non matching interfaces under such relaxed requirements for an acceptable mesh and for correctly defined geometries today s automated tetrahedral mesh generators can practically guarantee successful volume meshing that can be entirely hidden from the user a detailed technical discussion of the proposed generalized finite element method with clustering along with numerical experiments and some implementation details are presented copyright 2006 john wiley sons ltd

mls based variable node elements compatible with quadratic interpolation part ii application for finite crack element two dimensional finite crack elements for simulation of propagating cracks are developed using the moving least square mls approximation the mapping from the parental domain to the physical element domain is implicitly obtained from mls approximation with the shape functions and their derivatives calculated and saved only at the numerical integration points the mls based variable node elements are extended to construct the crack elements which allow the discontinuity of crack faces and the crack tip singularity the accuracy of the crack elements is checked by calculating the stress intensity factor under mode i loading the crack elements turn out to be very efficient and accurate for simulating crack propagations only with the minimal amount of element adjustment and node addition as the crack tip moves numerical results and comparison to the results from other works demonstrate the effectiveness and accuracy of the present scheme for the crack elements copyright 2005 john wiley sons ltd

a new three dimensional variable node finite element and its application for fluid solid interaction problems abstract a new three dimensional variable node element is proposed to achieve an efficient connection of non matching interfaces between dissimilar finite element meshes the variable node elements at interfaces are compatible with conventional finite elements and satisfy the interface conditions of continuity and completeness across non matching meshes the present method thereby provides a seamless connection between dissimilar finite element meshes and a correct load transfer across non matching interfaces therefore it leads to an efficient approach for solving a class of problems involving the non matching interfaces such as fluid solid interaction problems numerical examples are presented to show the effectiveness of the present method for solving fluid solid interaction problems with non conforming interfaces and the usefulness and application of the present method are discussed

domain integral formulation for stress intensity factor computation along curved three dimensional interface cracks new domain integrals for extracting mixed mode stress intensity factors along curved three dimensional bimaterial interface cracks are derived in the derivation the asymptotic auxiliary fields for the plane problem of a bimaterial interface crack are imposed along a curved crack front the general crack tip interaction integral a contour integral surrounding a point on the crack front which is evaluated in the limit as the contour is shrunk onto the crack tip is then expressed in domain form which is more suitable for numerical computation a consequence of imposing the auxiliary fields along a curved crack front is that the auxiliary stress fields do not satisfy equilibrium and the auxiliary strain fields do not satisfy compatibility the terms which arise due to the lack of equilibrium and compatibility are not sufficiently singular to contribute to the crack tip interaction integral or to affect its path independence however these terms become important when domain integral representations are introduced because they involve fields which are not asymptotically close to the crack tip in order to compute the pointwise stress intensity factors along the crack front the domain integrals are evaluated as a post processing step in the finite element method in the numerical results it is demonstrated that it is crucial to incorporate the terms that arise due to lack of equilibrium and compatibility of the auxiliary fields especially in regions where the local crack front curvature is high in the paper we present two numerical examples as a benchmark we first consider the problem of a penny shaped interface crack embedded in a cylinder the results for the complex stress intensity factor and phase angle are found to be in excellent agreement with the analytical solution the problem of an elliptical crack embedded between two dissimilar isotropic materials is also considered and the results are discussed

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

fast and robust level set update for 3d non planar x fem crack propagation modelling abstract in the x fem framework the need to represent a discontinuity independently of the structural mesh relies on the level set technique hence crack propagation can be simulated by an update of two distinct level sets the evolution of which is described by differential equations the aim of this paper is to analyse the resolution of these equations in order to formulate a robust and fast numerical process allowing 3d crack propagation simulations even in presence of high kink angles occurring in mixed mode propagation the numerical integration is accomplished by means of a robust finite difference upwind scheme applied to an auxiliary regular grid an alternative level set update equation and a fast localisation of the integration domain specifically developed for crack propagation problems are formulated and proposed in the paper in order to gain in stability robustness and performance

boundary element analysis of three dimensional mixed mode thermoelastic crack problems using the interaction and energy domain integrals a three dimensional boundary element method bem implementation of the interaction integral methodology for the numerical analysis of mixed mode three dimensional thermoelastic crack problems is presented in this paper the interaction integral is evaluated from a domain representation naturally compatible with the bem since stresses strains temperatures and derivatives of displacements and temperatures at internal points can be evaluated using the appropriate boundary integral equations several examples are analysed and the results compared with those available in the literature to demonstrate the efficiency and accuracy of the implementation to solve straight and curved crack front problems copyright 2007 john wiley sons ltd

reductions of topologically massive gravity ii first order realizations of second order lagrangians second order degenerate clement and sarioglu tekin lagrangians are casted into forms of various first order lagrangians the structures of the iterated tangent bundle and acceleration bundle are presented as a suitable geometric framework hamiltonian analyses of these equivalent formalisms are performed by means of the dirac bergmann constraint algorithm all formulations are shown to possess only second class constraints

a multivectorial dirac equation the multivectorial generalization of the cartan map for c 1 3 space time clifford algebra and an arbitrary gauge group in an isotopic space is applied to the standard dirac equation to generate the multivectorial dirac equation using both geometrical and physical reasoning a particular case discussed by reifler and morris j math phys 26 2059 1985 is projected from the general multivectorial dirac equation to discuss the properties and limitations associated to their quaternion model the use of the general multivectorial dirac equation which can be defined on any space time manifold is also illustrated

geometrical properties of the algebraic spinors for r3 1 the different geometrical properties of majorana even dirac and chevalley spinors in the clifford algebra approach are investigated

non conforming mesh gluing in the finite elements method a methodology to connect two or more non conforming meshes generated from a geometric model is presented the problem leads to a variational problem subject to constraints the emphasis of the work is on constraints construction two methods namely discrete connection and continuous connection are developed the relation with hybrid formulations is considered and two application examples are presented

mode decomposition of three dimensional mixed mode cracks via two state integrals a numerical scheme is proposed to obtain the individual stress intensity factors in an axisymmetric crack and in a three dimensional mixed mode crack the procedures presented here are based on the path independence of j and m integrals and mutual or two state conservation integrals which involve two elastic fields a useful method to decompose the stress intensity factors along curved three dimensional cracks under mixed mode is derived by using appropriate auxiliary fields for the plane problems the choice of the auxiliary fields available is critical to success of the present scheme and in this study it is made of not only the asymptotic plane strain solution which requires some remedy in application of the two state integral due to the lack of equilibrium and compatibility but a numerical solution with a given stress intensity as well some numerical examples of penny shaped cracks are presented to investigate the applicability and effectiveness of the method for problems of axisymmetric and three dimensional cracks

a new computational approach to contact mechanics using variable node finite elements in this paper a new computational strategy for two dimensional contact problems is developed with the aid of variable node finite elements within the range of infinitesimal deformations the variable node elements which are among mls moving least square based finite elements enable us to transform node to surface contact problems into node to node contact problems this contact formulation with variable node elements leads to an accurate and effective solution procedure needless to mention that the contact patch test is passed without any additional treatment through several numerical examples we demonstrate its simplicity and the effectiveness of the proposed scheme

modeling holes and inclusions by level sets in the extended finite element method a methodology to model arbitrary holes and material interfaces inclusions without meshing the internal boundaries is proposed the numerical method couples the level set method s osher j a sethian j comput phys 79 1 1988 12 to the extended finite element method x fem n moes j dolbow t belytschko int j numer methods engrg 46 1 1999 131 in the x fem the finite element approximation is enriched by additional functions through the notion of partition of unity the level set method is used for representing the location of holes and material interfaces and in addition the level set function is used to develop the local enrichment for material interfaces numerical examples in two dimensional linear elastostatics are presented to demonstrate the accuracy and potential of the new technique

partitioned formulation of internal fluid structure interaction problems by localized lagrange multipliers abstract a partitioned formulation of compressible internal fluid structure interaction problems is presented by employing a displacement model for both the fluid and structure partitioning is effected by a localized version of the method of lagrange multipliers which assigns two independent sets of lagrange multipliers to the structural and fluid interfaces two major features of the present formulation include an interface compliance normalization that helps capture the predominant physics of interaction phenomena when the interfaces are characterized by two radically different rigidities and a novel transformation of the displacement model into a fluid pressure model that is suitable for both transient and vibration analyses the present formulation first solves for the interface lagrange multipliers which are subsequently used to solve for the structural displacements and the fluid displacement or pressure by employing two independent analysis modules

some problems of spinor and algebraic spinor structures a concrete realization of the milnor lichnerowicz spinor bundle by algebraic spinors is considered in the case when the holonomy group of the levi civita connection is equal to the crumeyrolle group some relationships between the existence of parallel spinor fields on a space time manifold m and its topological invariants are given

a unitary representation of sl 2 r a given unitary representation of the group sl 2 r belonging to the discrete series is shown to involve necessarily some special functions in particular laguerre and hardy pollaczek polynomials various realizations of this representation are investigated including the coherent states one more generally it is shown that the representations of the discrete series of the universal covering of sl 2 r involves generalized laguerre and pollaczek polynomials the riemann zeta function is shown to be concerned with these representations

on the algebra of dirac bispinor densities factorization and inversion theorems the algebraic system formed by dirac bispinor densities i i is discussed the inverse problem given a set of 16 real functions i which satisfy the bispinor algebra find the spinor to which they correspond is solved an expedient solution to this problem is obtained by introducing a general representation of dirac spinors it is shown that this form factorizes into the product of two noncommuting projection operators acting on an arbitrary constant spinor

an interaction integral method for 3d curved cracks in nonhomogeneous materials with complex interfaces this work derives an interaction integral for the computation of mixed mode stress intensity factors sifs in three dimensional 3d nonhomogeneous materials with continuous or discontinuous properties the present method is based on a two state integral by the superposition of actual and auxiliary fields in 3d domain formulation of the interaction integral derived here the integrand does not involve any derivatives of material properties furthermore the formulation can be proved to be still valid even when the integral domain contains material interfaces therefore it is not necessary to limit the material properties to be continuous for the present formulation on account of these advantages the application range of the interaction integral can be greatly enlarged this method in conjunction with the finite element method fem is employed to solve several representative fracture problems according to the comparison between the results and those from the published lectures good agreement demonstrates the validation of the interaction integral the results show that the present interaction integral is domain independent for nonhomogeneous materials with interfaces

a numerical procedure for interaction integrals developed for curved cracks of general shape in 3 d this study presents a numerical procedure for the evaluation of interaction energy integrals used to extract mixed mode stress intensity factors the interaction energy integral is expressed as a domain integral and the proposed numerical procedure delivers accurate results for three dimensional cracks with curved crack fronts and curved crack surfaces for a rather general set of integration domains it is clearly shown that when the curvature of the crack surface becomes sufficiently large special care must be taken in the evaluation of both the volume and the area integrals involved to improve the accuracy in the evaluation of the former a composite rule for the gaussian quadrature scheme is employed four benchmark geometries with available analytical solutions are considered firstly mesh design parameters for planar cracks with straight and curved crack fronts are established secondly non planar cracks with straight and curved crack fronts are employed to examine the accuracy of the numerical procedure

antisymmetrical 3 d stress field near the crack front of a thin elastic plate abstract based on detailed three dimensional finite clement analysis the near tip field of a thin elastic plate remotely subjected to mode ii antisymmctrical loading is investigated the computed results show the transition to a three dimensional state to occur near the radial distance from the crack tip of 1 5 times the plate thickness in the close vicinity of the crack front the asymptotic stress field is characterized by a combination of plane strain mode ii and anti plane mode iii singular 1 r fields the domain of such fields extends approximately 0 5 of the thickness in the radial direction the mixed mode stress intensity factors along the crack front are determined from 3 d conservation integrals and unlike the case of symmetrical loading their magnitudes are greater towards the free surface near the intersection of the crack front and free surface the stress field converges to the antisymmetrical corner singularity solution the asymptotic form of stress near the intersection under general loading conditions is presented along with the corner stress intensity factors

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

the mortar finite element method with lagrange multipliers the present paper deals with a variant of a non conforming domain decomposition technique the mortar finite element method in the opposition to the original method this variant is never conforming because of the relaxation of the matching constraints at the vertices and the edges in 3d of subdomains it is shown that written under primal hybrid formulation the approximation problem issued from a discretization of a second order elliptic equation in 2d is nonetheless well posed and provides a discrete solution that satisfies optimal error estimates with respect to natural norms finally the parallelization advantages consequence of this variant are also addressed

an adaptive h refinement using transition element for plate bending problems an adaptive h refinement procedure utilizing compatible 5 to 7 node quadrilateral transition elements together with 4 node elements is presented for reissner mindlin plate bending problems by introducing the transition elements which have physical midside nodes some difficulties associated with imposing displacement constraints on irregular nodes to enforce interelement compatibility in common adaptive h refinement on quadrilateral mesh are easily overcome numerical examples are presented to show the effectiveness of using the transition elements for the adaptive h refinement

a clifford algebra quantization of dirac s electron positron field the quantum field theory of free dirac particles four component massive spin 1 2 particles is derived by a segal quantization procedure first details are given on how the spinor space of dirac is actually a minimal left ideal of the clifford algebra associated with a lorentz inner product space and how the homogeneous group actions break the natural two component quaternion structure to give familiar four component complex spinors second wigner s procedure for constructing unitary representations of the poincare group is used to construct the appropriately induced infinite dimensional representation of the inhomogeneous group starting from the above four dimensional nonunitary representation third and finally segal s procedure for quantizing classical fermion fields is adapted to this infinite dimensional hilbert space to obtain the clifford algebra of annihilation creation operators for spin 1 2 particles the familiar fock space appears as a minimal left ideal in this second clifford algebra

an improved interface element with variable nodes for non matching finite element meshes extensive improvements of the interface element method iem are proposed for the efficient treatment of non matching finite element meshes our approach enables us to establish the master element via the moving least square mls approximation and so to remove the cumbersome process of constructing interface elements the values of shape functions and their derivatives are therefore mapped from the master element as in the conventional finite element method for the assurance of convergence and compatibility condition a patch test is demonstrated through several examples of 2d linear elasticity the convergence rate is compared between the present interface element and the previous version

locking free stabilized conforming nodal integration for meshfree mindlin reissner plate formulation abstract the cause of shear locking in mindlin reissner plate formulation is due to the inability of the numerical formulation in representing pure bending mode without producing parasitic shear deformation lack of kirchhoff mode to resolve shear locking in meshfree formulation of mindlin reissner plates the following two issues are addressed 1 construction of approximation functions capable of reproducing kirchhoff modes and 2 formulation of domain integration of galerkin weak form capable of producing exact solution under pure bending condition in this study we first identify the kirchhoff mode reproducing conditions kmrc and show that the employment of a second order monomial basis in the reproducing kernel or moving least square approximation of translational and rotational degrees of freedom is an effective means to meet kmrc next the integration constraints that fulfill bending exactness be in the galerkin meshfree discretization of mindlin reissner plate are derived a nodal integration with curvature smoothing stabilization that fulfills be is then formulated for mindlin reissner plate the curvature smoothing stabilization is introduced in the nodally integrated galerkin weak form the resulting meshfree formulation is stable and free of shear locking in the limit of thin plate both computational efficiency and accuracy are achieved in the proposed meshfree mindlin reissner plate formulation

pseudo euclidean hurwitz pairs in any signature the author considers the pseudo euclidean hurwitz problem as formulated in a recent study by lawrynowicz and rembielinsky 1987 however he adopts a more coordinate free approach and employs the spinorial formalism developed by crumeyrolle 1989 to solve this problem completely his results in part disagree with those of lawrynowicz and rembielinsky in particular he uncovers some extra possibilities he also gives a link between pseudo euclidean hurwitz pairs and z2 graded lie algebras and discusses the introduction of some fibre bundle with pseudo euclidean hurwitz pairs

relating the power of cellular arrays to their closure properties there are many fundamental open problems concerning cellular arrays ca s for example 1 is the class of real time ca languages closed under reversal concatenation 2 2 are linear time ca s more powerful than real time ca s 3 3 are nonlinear time ca s more powerful than linear time ca s 4 4 does one way communication reduce the computing power of a ca although some of these problems appear to be easier to resolve than the others e g problem 1 seems easier than 2 no solution to any of these problems is forthcoming in this paper we investigate the relationships among these problems as well as prove some positive results concerning ca s we show a a the class of real time ca languages is closed under reversal if and only if linear time ca s are equivalent to real time ca s b if ca s are more powerful than ca s restricted to one way data communication i e one way ca s then nonlinear time ca s are more powerful than linear time ca s c c if the class of real time ca languages is closed under reversal then it is also closed under concatenation in the case of unary ca languages we show that the class is closed under concatenation we also show that the languagel 0n1m m n 0 mdividesn is a real time ca language disproving a conjecture of bucher and culik

spinors and space times dirac spinors for vector space times rs t are considered as real spinors of appropriate extended vector spaces rs t this extension is determined by the condition rs t rcs t the catalog of reality chirality conditions allowed for dirac spinors by the analysis of corresponding clifford algebras and their left minimal ideals are completed

a disk shaped domain integral method for the computation of stress intensity factors using tetrahedral meshes a novel domain integral approach is introduced for the accurate computation of pointwise j integral and stress intensity factors sifs of 3d planar cracks using tetrahedral elements this method is efficient and easy to implement and does not require a structured mesh around the crack front the method relies on the construction of virtual disk shaped integral domains at points along the crack front and the computation of domain integrals using a series of virtual triangular and line elements the accuracy of the numerical results computed for through the thickness penny shaped and elliptical crack configurations has been validated by using the available analytical formulations the average error of computed sifs remains below 1 for fine meshes and 2 3 for coarse ones the results of an extensive parametric study suggest that there exists an optimum mesh dependent domain radius at which the computed sifs are the most accurate furthermore the results provide evidence that tetrahedral elements are efficient reliable and robust instruments for accurate linear elastic fracture mechanics calculations

polygon scaled boundary finite elements for crack propagation modelling summary an automatic crack propagation modelling technique using polygon elements is presented a simple algorithm to generate a polygon mesh from a delaunay triangulated mesh is implemented the polygon element formulation is constructed from the scaled boundary finite element method sbfem treating each polygon as a sbfem subdomain and is very efficient in modelling singular stress fields in the vicinity of cracks stress intensity factors are computed directly from their definitions without any nodal enrichment functions an automatic remeshing algorithm capable of handling any n sided polygon is developed to accommodate crack propagation the algorithm is simple yet flexible because remeshing involves minimal changes to the global mesh and is limited to only polygons on the crack paths the efficiency of the polygon sbfem in computing accurate stress intensity factors is first demonstrated for a problem with a stationary crack four crack propagation benchmarks are then modelled to validate the developed technique and demonstrate its salient features the predicted crack paths show good agreement with experimental observations and numerical simulations reported in the literature copyright 2012 john wiley sons ltd

complementarity problem arising from static growth of multiple cracks and mls based numerical manifold method abstract the full response of a brittle structure containing multiple cracks to loading under the servo control is of vital importance in the evaluation of properties of the structure during crack growth the fracture toughness condition at all the crack tips as well as the equilibrium condition should be obeyed leading to a nonlinear complementarity problem ncp the vector valued function in the ncp depends implicitly on the cracking increments which in turn determine the stress field the stress field can be obtained through solving a mixed variational problem since the degrees of freedom in the discrete variational problem vary with cracking not only in magnitude but also in number the jacobian matrix of the ncp is hard to compute and it cannot be expected to be solved by the newton methods that involve the calculation of jacobian matrices therefore a well scaled projection contraction algorithm is designed the proposed procedure is able to simulate growth of multiple cracks in a natural way allowing the crack tips to stop anywhere with no sensitivity to node configuration or cracking increments through the analysis of some examples that have been widely tested many interesting and profound phenomena are found which have never been revealed

mls moving least square based finite elements for three dimensional nonmatching meshes and adaptive mesh refinement abstract with the aid of moving least square mls approximation a new class of three dimensional finite elements are proposed for treating nonmatching meshes and adaptive mesh refinement for which the existing finite elements are hardly efficient with a special choice of the weight function supports and the base functions the method results in useful elements with the polynomial shape function for which the c 1 continuity breaks down on the boundaries between the neighboring subdomains comprising one element the effectiveness of the new elements in handling the discontinuities due to nonmatching interfaces and automatic mesh refinement is demonstrated via three dimensional examples

on the exceptional equivalence of complex dirac spinors and complex space time vectors it is well known that there exists an equivalence of r8 vectors and spinors which has its roots in the rotational symmetry of the dynkin diagram for d4 we endow r8 with a real action of so 4 4 and restrict to so 3 1 under this restriction the r8 spinor decomposes into the direct sum of two real dirac spinors while the r8 vector decomposes into a real space time vector plus four real scalars the equivalence is preserved under this restriction it is shown that it is realized in the exceptional equivalence of a complex dirac spinor and a complex space time vector

a simple method for crack growth in mixed mode with x fem abstract in this paper a new method for level set update is proposed in the context of crack propagation modeling with the extended finite element method x fem and level sets compared with the existing methods such as the resolution of the hamilton jacobi equations this new method is much simpler because it does not required complex manipulations of the level sets this method called the projection method uses both a classical discretization of the surface of the crack segments for 2d cracks and triangles for 3d cracks and a level set representation of the crack this discretization is updated with respect to the position of the new crack front then the level sets are re computed using the true distance to the new crack by an orthogonal projection of each node of the structure onto the new crack surface then numerical illustrations are given on 2d and 3d academic examples finally three illustrations are given on 3d industrial applications

singular functions for heterogeneous composites with cracks and notches the use of equilibrated singular basis functions abstract in this paper a novel method is presented to solve problems with weak singularities in two dimensional heterogeneous media using equilibrated singular basis functions this especially includes crack problems in composites of functionally graded material types the method is mainly presented in a boundary formulation although it may be found quite useful in other mesh based or mesh less approaches as the extended finite element method xfem the present paper considers harmonic and elasticity problems the most distinguished advantage of the present method is that the solution progress advances without absolutely any knowledge of the analytical singularity order of the problem to this end the partial differential equation of the problem is approximately satisfied in a weighted residual approach after developing the formulation in a mapped polar co ordination some primary basis functions generated from chebyshev polynomials and trigonometric functions along with corresponding weight functions are employed the numerical examples either selected from the well known literature or solved by well established techniques will demonstrate the capability of the method in problems related to composite materials

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

piecewise polynomial shape functions for hp finite element methods abstract high order piecewise polynomial shape functions for quadrilateral finite elements are proposed the shape functions are tensor products of one dimensional piecewise functions based on legendre polynomials this allows the construction of h 1 conforming approximations on meshes with arbitrary levels of hanging nodes without the necessity for constrained approximation techniques furthermore meshes can be refined simply by inserting nodes on element edges application examples including the l shape domain a plate problem and a tie rod connection plate illustrate the applicability of the method

on an h type mesh refinement strategy based on minimization of interpolation errors abstract an adaptive finite element method is proposed which involves an automatic mesh refinement in areas of the mesh where local errors are determined to exceed a pre assigned limit the estimation of local errors is based on interpolation error bounds and extraction formulas for highly accurate estimates of second derivatives applications to several two dimensional model problems are discussed the results indicate that the method can be very effective for both regular problems and problems with strong singularities

boson algebra as a symplectic clifford algebra it is well known that the n fermion algebra is a complex clifford algebra of dimension 22n with the orthogonal group o 2n c as group of automorphisms the n boson algebra viewed similarly as a complex symplectic clifford algebra is investigated it is of infinite dimension and has the symplectic group sp 2n c as a group of automorphisms special attention is given to the case n 1 and various bases in particular the matrix elements of the bases between harmonic oscillator states and their relation with special functions are investigated

constructible functions in cellular automata and their applications to hierarchy results we investigate time constructible functions in one dimensional cellular automata ca it is shown that i if a function t n is computable by an o t n n time turing machine then t n is time constructible by ca and ii if two functions are time constructible by ca then the sum product and exponential functions of them are time constructible by ca as an application it is shown that if t1 n and t2 n are time constructible functions such that limnt1 n t2 n 0 and t1 n n then there is a language which can be recognized by a ca in t2 n time but not by any ca in t1 n time

the extended finite element method xfem for solidification problems an enriched finite element method for the multi dimensional stefan problems is presented in this method the standard finite element basis is enriched with a discontinuity in the derivative of the temperature normal to the interface the approximation can then represent the phase interface and the associated discontinuity in the temperature gradient within an element the phase interface can be evolved without re meshing or the use of artificial heat capacity techniques the interface is described by a level set function that is updated by a stabilized finite element scheme several examples are solved by the proposed method to demonstrate the accuracy and robustness of the method copyright 2001 john wiley sons ltd

domain integrals for axisymmetric interface crack problems new domain integrals for axisymmetric interface crack problems are derived special attention is given to the specification and subsequent treatment of auxiliary fields for the extraction of mixed mode stress intensity factors using interaction energy integrals the effect of crack front curvature is shown to play an important role in the derivation of the integrals numerical examples include an interface penny shaped crack and a longitudinal interface crack fiber pull out problem and yield very accurate and consistent results when compared with analytical solutions from the literature the method is particularly suited for the analysis of fiber pull out experiments and the accurate determination of fracture parameters such as energy release rate g mixed mode stressintensity factors ki and kii and phase angle

a novel scheme to generate meshes with hexahedral elements and poly pyramid elements the carving technique abstract a novel scheme for three dimensional mesh generation termed the carving technique is proposed with the aid of poly pyramid elements soaking the geometry information of a given model into a regular reference mesh with brick elements the reference mesh is trimmed by the surface of the model using the marching cube algorithm the trimmed elements are reconstructed by the proposed elements which here are termed the poly pyramid elements therefore the finite element mesh is automatically generated from the surface information shape functions of the poly pyramid elements are constructed by moving least square mls approximation numerical results are presented to examine the performance of the poly pyramid elements and to demonstrate the effectiveness of the proposed scheme

a simple algorithm for localized construction of non matching structural interfaces a simple and effective algorithm for the modular construction of non matched interfaces is presented for the partitioned solution of large scale structural problems the formulation is based on a recently developed four field variational principle which introduces a connection frame between the interfaced partitions a key result of the present study is a frame nodal placement criterion that uniquely determines the frame discretization into piecewise linear elements so that the interface patch test condition is satisfied a priori the method is demonstrated with several 2d and 3d example problems

calculation of fracture mechanics parameters for an arbitrary three dimensional crack by the equivalent domain integral method summary in this paper an equivalent domain integral edi method and the attendant numerical algorithms arc presented for the computation of a near crack tip field parameter the vector je integral and its variation along the front of an arbitrary three dimensional crack in a structural component account is taken of possible non elastic strains present in the structure in this case the near tip je values may be significantly different from the far field values jf especially under non proportional loading