isogeometric analysis using t splines we explore t splines a generalization of nurbs enabling local refinement as a basis for isogeometric analysis we review t splines as a surface design methodology and then develop it for engineering analysis applications we test t splines on some elementary two dimensional and three dimensional fluid and structural analysis problems and attain good results in all cases we summarize the current status of t splines their limitations and future possibilities

use of higher order shape functions in the scaled boundary finite element method the scaled boundary finite element method is a novel semi analytical technique whose versatility accuracy and efficiency are not only equal to but potentially better than the finite element method and the boundary element method for certain problems this paper investigates the possibility of using higher order polynomial functions for the shape functions two techniques for generating the higher order shape functions are investigated in the first the spectral element approach is used with lagrange interpolation functions in the second hierarchical polynomial shape functions are employed to add new degrees of freedom into the domain without changing the existing ones as in the p version of the finite element method to check the accuracy of the proposed procedures a plane strain problem for which an exact solution is available is employed a more complex example involving three scaled boundary subdomains is also addressed the rates of convergence of these examples under p refinement are compared with the corresponding rates of convergence achieved when uniform h refinement is used allowing direct comparison of the computational cost of the two approaches the results show that it is advantageous to use higher order elements and that higher rates of convergence can be obtained using p refinement instead of h refinement copyright 2005 john wiley sons ltd

rotation free isogeometric thin shell analysis using pht splines this paper presents a novel approach for isogeometric analysis of thin shells using polynomial splines over hierarchical t meshes pht splines the method exploits the flexibility of t meshes for local refinement the main advantage of the pht splines in the context of thin shell theory is that it achieves c1 continuity so the kirchhoff love theory can be used in pristine form no rotational degrees of freedom are needed numerical results show the excellent performance of the present method

voronoi cell finite element model based on micropolar theory of thermoelasticity for heterogeneous materials in this paper a new voronoi cell finite element model is developed for solving steady state heat conduction and micropolar thermoelastic stress analysis problems in arbitrary heterogeneous materials the method is based on the natural discretization of a multiple phase domain into basic structural elements by dirichlet tessellation tessellation process results in a network of polygons called voronoi polygons in this paper formulations are developed for treating these polygons as elements in a finite element mesh furthermore a composite voronoi cell finite element model is developed to account for the presence of a second phase inclusion within a polygonal element various numerical examples are executed for validating the effectiveness of this model in the analysis of the temperature and stress fields for micropolar elastic materials effective material properties are derived for microstructures containing different distributions of second phase

quadratic maximum entropy serendipity shape functions for arbitrary planar polygons in this paper we present the development of quadratic serendipity shape functions on planar convex and nonconvex polygons drawing on the work of bompadre et al 2012 1 and hormann and sukumar 2008 2 we adopt a relative entropy measure for signed positive or negative shape functions with nodal prior weight functions that have the appropriate zero set on the boundary of the polygon we maximize the objective functional subject to the constraints for quadratic completeness proposed by rand et al 2013 3 along an edge of a polygon the approximation is identical to univariate bernstein polynomials the choice of the nodal prior weight function ensures that the shape functions satisfy a weak kronecker delta property on each edge the shape functions are well defined for arbitrary planar polygons without self intersections on using a modified numerical integration scheme we show that the quadratic patch test is passed on polygonal meshes with convex and nonconvex elements numerical tests for the poisson equation on self similar trapezoidal meshes and quasiuniform polygonal meshes are presented which reveal the sound accuracy of the method and optimal rates of convergence in the l2l2 norm and the h1h1 seminorm are established

the p version of the finite element method compared to an adaptive h version for the deformation theory of plasticity a p version of the finite element method is applied to the deformation theory of plasticity and the results are compared to a state of the art adaptive h version it is demonstrated that even for nonlinear elliptic problems the p version is a very efficient discretization strategy

polytope finite elements in this paper finite elements based on arbitrary convex and non convex polytopes are introduced polytopes in combination with natural element coordinates necs permit a uniform element formulation of interpolation functions that are independent of the dimension of space localization and the number of vertices necs based on the natural neighbor interpolation are restricted to the polytope and can be understood as an extension of the barycentric coordinates on simplexes the differentiation and integration of these interpolation functions on the basis of necs is essential for finite element approximations the accuracy of the finite element interpolation or approximation can be controlled by either applying the h version or by utilizing the p version of the finite element method fem advantages in the handling of hanging nodes are discussed furthermore we present construction methods for lagrangian as well as for hierarchical interpolation functions based on necs numerical experiments on different convex and non convex decompositions will show the usability accuracy and convergence of the developed polytope fem copyright 2007 john wiley sons ltd

extended voronoi cell finite element model for multiple cohesive crack propagation in brittle materials this paper introduces an extended voronoi cell finite element model x vcfem for modelling cohesive crack propagation in brittle materials with multiple cracks the cracks are modelled by a cohesive zone model and their incremental directions and growth lengths are determined in terms of the cohesive energy near the crack tip extension to vcfem is achieved through enhancements in stress functions in the assumed stress hybrid formulation in addition to polynomial terms the stress functions include branch functions in conjunction with level set methods and multi resolution wavelet functions in the vicinity of crack tips the wavelet basis functions are adaptively enriched to accurately capture crack tip stress concentrations conditions and methods of stability are enforced in x vcfem for improved convergence with propagating cracks two classes of problems are solved and compared with existing solutions in the literature for validation of the x vcfem algorithms the first set corresponds to results for static cracks while in the latter set the propagation of cohesive cracks are considered comparison of x vcfem simulation results with results in literature for several fracture mechanics problems validates the effectiveness of x vcfem copyright 2005 john wiley sons ltd

a unified 3d based technique for plate bending analysis using scaled boundary finite element method summary this paper presents a unified technique for solving the plate bending problems by extending the scaled boundary finite element method the formulation is based on the three dimensional governing equation without enforcing the kinematics of plate theory only the in plane dimensions are discretised into finite elements any two dimensional displacement based elements can be employed the solution along the thickness is expressed analytically by using a matrix function the proposed technique is consistent with the three dimensional theory and applicable to both thick and thin plates without exhibiting the numerical locking phenomenon moreover the use of higher order spectral elements allows the proposed technique to better represent curved boundaries and to achieve high accuracy and fast convergence numerical examples of various plate structures with different thickness to length ratios demonstrate the applicability and accuracy of the proposed technique copyright 2012 john wiley sons ltd

generalized gaussian quadrature rules on arbitrary polygons in this paper we present a numerical algorithm based on group theory and numerical optimization to compute efficient quadrature rules for integration of bivariate polynomials over arbitrary polygons these quadratures have desirable properties such as positivity of weights and interiority of nodes and can readily be used as software libraries where numerical integration within planar polygons is required we have used this algorithm for the construction of symmetric and non symmetric quadrature rules over convex and concave polygons while in the case of symmetric quadratures our results are comparable to available rules the proposed algorithm has the advantage of being flexible enough so that it can be applied to arbitrary planar regions for the integration of generalized classes of functions to demonstrate the efficiency of the new quadrature rules we have tested them for the integration of rational polygonal shape functions over a regular hexagon for a relative error of 10 8 in the computation of stiffness matrix entries one needs at least 198 evaluation points when the region is partitioned whereas 85 points suffice with our quadrature rule copyright 2009 john wiley sons ltd

embedded interfaces by polytope fem in this paper the polytope finite element method is employed to model an embedded interface through the body independent of the background fem mesh the elements that are crossed by the embedded interface are decomposed into new polytope elements which have some nodes on the interface line the interface introduces discontinuity into the primary variable strong or into its derivatives weak both strong and weak discontinuities are studied by the proposed method through different numerical examples including fracture problems with traction free and cohesive cracks and heat conduction problems with dirichlet and dirichlet neumann types of boundary conditions on the embedded interface for traction free cracks which have tip singularity the nodes near the crack tip are enriched with the singular functions through the extended finite element method the concept of natural element coordinates necs is invoked to drive shape functions for the produced polytopes a simple treatment is proposed for concave polytopes produced by a kinked interface and also for locating crack tip inside an element prior to using the singularity enrichment the proposed method pursues some implementational details of extended generalized finite element methods for interfaces but here the additional dofs are constructed on the interface lines in contrast to x g fem which attach enriched dofs to the previously existed nodes copyright 2011 john wiley sons ltd

conforming polygonal finite elements summary in this paper conforming finite elements on polygon meshes are developed polygonal finite elements provide greater flexibility in mesh generation and are better suited for applications in solid mechanics which involve a significant change in the topology of the material domain in this study recent advances in meshfree approximations computational geometry and computer graphics are used to construct different trial and test approximations on polygonal elements a particular and notable contribution is the use of meshfree natural neighbour nn basis functions on a canonical element combined with an affine map to construct conforming approximations on convex polygons this numerical formulation enables the construction of conforming approximation on n gons n 3 and hence extends the potential applications of finite elements to convex polygons of arbitrary order numerical experiments on second order elliptic boundary value problems are presented to demonstrate the accuracy and convergence of the proposed method copyright 2004 john wiley sons ltd

construction of polygonal interpolants a maximum entropy approach in this paper we establish a link between maximizing information theoretic entropy and the construction of polygonal interpolants the determination of shape functions on n gons n 3 leads to a non unique under determined system of linear equations the barycentric co ordinates i which form a partition of unity are associated with discrete probability measures and the linear reproducing conditions are the counterpart of the expectations of a linear function the i are computed by maximizing the uncertainty h 1 2 n i log i subject to the above constraints the description is expository in nature and the numerical results via the maximum entropy maxent formulation are compared to those obtained from a few distinct polygonal interpolants the maximum entropy formulation leads to a feasible solution for i in any convex or non convex polygon this study is an instance of the application of the maximum entropy principle wherein least biased inference is made on the basis of incomplete information copyright 2004 john wiley sons ltd

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

an enriched meshless method for non linear fracture mechanics this paper presents an enriched meshless method for fracture analysis of cracks in homogeneous isotropic non linear elastic two dimensional solids subject to mode i loading conditions the method involves an element free galerkin formulation and two new enriched basis functions types i and ii to capture the hutchinson rice rosengren singularity field in non linear fracture mechanics the type i enriched basis function can be viewed as a generalized enriched basis function which degenerates to the linear elastic basis function when the material hardening exponent is unity the type ii enriched basis function entails further improvements of the type i basis function by adding trigonometric functions four numerical examples are presented to illustrate the proposed method the boundary layer analysis indicates that the crack tip field predicted by using the proposed basis functions matches with the theoretical solution very well in the whole region considered whether for the near tip asymptotic field or for the far tip elastic field numerical analyses of standard fracture specimens by the proposed meshless method also yield accurate estimates of the j integral for the applied load intensities and material properties considered also the crack mouth opening displacement evaluated by the proposed meshless method is in good agreement with finite element results furthermore the meshless results show excellent agreement with the experimental measurements indicating that the new basis functions are also capable of capturing elastic plastic deformations at a stress concentration effectively copyright 2003 john wiley sons ltd

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

an algorithm for the mean and variance of the noncentral hypergeometric distribution the mean and variance of the noncentral hypergeometric distribution are essential for obtaining maximum likelihood estimates for conditional logistic models for 2 x 2 tables the numerical difficulty in directly computing them using the definition is discussed in detail by satten and kupper 1990 they also give an algorithm based on a continued fraction representation for the mean we present here another algorithm based on two equations in harkness 1965

near capacity three stage turbo detection of irregular convolutional coded joint sphere packing modulation and space time coding conventional two stage turbo detected schemes typically suffer from a bit error rate ber floor preventing them from achieving infinitesimally low ber values especially when the inner coding stage is of non recursive nature we circumvent this deficiency by proposing a three stage turbo detected sphere packing sp aided space time block coding stbc stbc sp scheme where a rate 1 recursive inner precoder is employed to avoid having a ber floor the convergence behaviour of this serially concatenated scheme is investigated with the aid of 3d extrinsic information transfer exit charts furthermore the capacity of the stbc sp scheme is determined and an algorithm is proposed for calculating a tighter upper bound on the maximum achievable bandwidth efficiency based on the exit charts of the stbc sp demapper the proposed three stage turbo detected scheme operates within about 1 0 db of the capacity and within 0 5 db of the maximum achievable bandwidth efficiency limit

a scaled boundary polygon formulation for elasto plastic analyses this study presents a novel scaled boundary polygon formulation to model elasto plastic material responses in structures the polygons have flexible mesh generation capabilities and are more accurate than standard finite elements especially for problems with cracks and notches shape functions of arbitrary n sided polygons are constructed using the scaled boundary finite element method these shape functions are conforming and linearly complete when modeling a crack strain singularities are analytically modeled without enrichment standard finite element procedures are used to formulate the stiffness matrix and residual load vector the nonlinear material constitutive matrix and the internal stresses are approximated locally in each polygon by a polynomial function the stiffness matrix and the residual load vector are matrix power integrals that can be evaluated analytically even when a strain singularity is present standard nonlinear equation solvers e g the modified newton raphson algorithm are used to obtain the nonlinear response of the structure the proposed formulation is validated using several numerical benchmarks

the scaled boundary finite element method alias consistent infinitesimal finite element cell method for diffusion note 264 reference lch article 1999 008doi 10 1002 sici 1097 0207 19990810 45 10 3 0 co 2 eview record in web of science record created on 2007 04 24 modified on 2016 08 08

a matrix function solution for the scaled boundary finite element equation in statics the scaled boundary finite element method is a fundamental solution less boundary element method based on finite elements it leads to semi analytical solutions for displacement and stress fields which permits problems with singularities or in infinite domains to be handled conveniently and accurately however the present eigenvalue method for solving the scaled boundary finite element equation requires additional treatments for multiple eigenvalues with parallel eigenvectors which results from logarithmic terms in the solutions a matrix function solution for the scaled boundary finite element equation in statics is presented in this paper it is numerically stable for multiple or near multiple eigenvalues as it is based on real schur decomposition power functions logarithmic functions and their transitions as occurring in fracture mechanics composites and two dimensional unbounded domains are represented semi analytically no a priori knowledge on the types and orders of singularity are required when simulating stress singularities

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

the scaled boundary finite element method alias consistent infinitesimal finite element cell method for elastodynamics the scaled boundary finite element method alias the consistent infinitesimal finite element cell method is developed starting from the governing equations of linear elastodynamics only the boundary of the medium is discretized with surface finite elements yielding a reduction of the spatial dimension by one no fundamental solution is necessary and thus no singular integrals must be evaluated general anisotropic material is analysed without any increase in computational effort boundary conditions on free and fixed surfaces and on interfaces between different materials are enforced exactly without any discretization this method is exact in the radial direction and converges to the exact solution in the finite element sense in the circumferential directions for a bounded medium symmetric static stiffness and mass matrices with respect to the degrees of freedom on the boundary result without any additional assumption a stress singularity is represented very accurately as the condition on the boundary in the vicinity of the point of singularity is satisfied without spatial discretization

a p version finite element approach for two and three dimensional problems of the j2 flow theory with non linear isotropic hardening in this paper an implementation of a two and three dimensional p version approach to the j 2 flow theory with non linear isotropic hardening for small displacements and small strains is presented based on higher order quadrilateral and hexahedral element formulations a newton raphson iteration scheme combined with a radial return algorithm is applied to find approximate solutions for the underlying physically non linear model problem curved boundaries are taken care of with the blending function method allowing an accurate representation of geometry with only a few p elements numerical examples demonstrate that the p version supplies efficient and accurate approximations to this class of physically non linear problems