subdivision surfaces a new paradigm for thin shell finite element analysis we develop a new paradigm for thin shell finite element analysis based on the use of subdivision surfaces for i describing the geometry of the shell in its undeformed configuration and ii generating smooth interpolated displacement fields possessing bounded energy within the strict framework of the kirchhoff love theory of thin shells the particular subdivision strategy adopted here is loop s scheme with extensions such as required to account for creases and displacement boundary conditions the displacement fields obtained by subdivision are h2 and consequently have a finite kirchhoff love energy the resulting finite elements contain three nodes and element integrals are computed by a one point quadrature the displacement field of the shell is interpolated from nodal displacements only in particular no nodal rotations are used in the interpolation the interpolation scheme induced by subdivision is non local i e the displacement field over one element depend on the nodal displacements of the element nodes and all nodes of immediately neighbouring elements however the use of subdivision surfaces ensures that all the local displacement fields thus constructed combine conformingly to define one single limit surface numerical tests including the belytschko et al 10 obstacle course of benchmark problems demonstrate the high accuracy and optimal convergence of the method

groupe de chow de codimension deux des varietes definies sur un corps de nombres un theoreme de finitude pour la torsion letx be a smooth projective variety defined over a number field and let ch2 x denote the chow group of codimension two cycles modulo rational equivalence we show that if the cohomology grouph2 x ox vanishes then the torsion subgroup of ch2 x is a finite group this result covers all previous results in this direction the hypothesish2 x ox 0 is used to lift line bundles

isogeometric kirchhoff love shell formulations for general hyperelastic materials abstract we present formulations for compressible and incompressible hyperelastic thin shells which can use general 3d constitutive models the necessary plane stress condition is enforced analytically for incompressible materials and iteratively for compressible materials the thickness stretch is statically condensed and the shell kinematics are completely described by the first and second fundamental forms of the midsurface we use c 1 continuous isogeometric discretizations to build the numerical models numerical tests including structural dynamics simulations of a bioprosthetic heart valve show the good performance and applicability of the presented methods

an isogeometric continuum shell element for non linear analysis an isogeometric continuum shell formulation is proposed in which nurbs basis functions are used to construct the reference surface of the shell through the thickness behavior is interpolated using a higher order b spline which is in contrast to the standard continuum shell solid like shell formulation where a linear lagrange shape function is typically used in the thickness direction the present formulation yields a complete isogeometric representation of the continuum shell the shell element is implemented in a standard finite element code using bezier extraction which facilitates numerical integration on the reference surface of the shell through the thickness integration is done using a connectivity array which determines the support of a b spline basis function over an element the formulation has been verified using different linear and geometrically non linear examples the ability of the formulation in modelling buckling of static delaminations in composite materials is also demonstrated

the arithmetic of zero cycles on surfaces with geometric genus and irregularity zero let x be a smooth projective geometrically irreducible surface over a perfect field f throughout this paper it will be assumed that the geometric genus pg and the irregularity q of x both vanish denote the separable closure of f by f let x x be the surface obtained from x by base extension it will also be assumed that the group ao x of rational equivalence classes of zero cycles of degree zero on x vanishes this is a technical hypothesis which could presumably be eliminated at the expense of working with ker ao x ao x for want of a better name and for ease in stating various results any surface which satisfies these three hypotheses will be called a pseudo rational surface bloch 2 has conjectured that the vanishing of ao x should follow from the assumption that po q 0 this was proven by bloch kas and lieberman 5 for all such surfaces which are not of general type i e which have kodaira dimension less than 2 it has also been proven for particular surfaces of general type by inose and mizukami 23 barlow 1 and keum 25 consequently the class of pseudo rational surfaces includes rational surfaces enriques surfaces elliptic surfaces with q 0 the classical godeaux surface burniat inoue surfaces campedelti surfaces and the surfaces of barlow and of keum this paper will study ao x for pseudo rational surfaces defined over fields of number theoretic interest bloch 4 introduced k theoretic techniques into the study of zero cycles on rational surfaces his work was extended 7 12 15 27 28 32 36 to achieve a thorough understanding of such cycles colliot th616ne and raskind 10 developed this machinery further to study codimension two cycles on any variety the author 14 applied these techniques to enriques surfaces raskind 30 used them to study zero cycles on pseudo rational surfaces one of the main results of this paper is a new proof of the following theorem of raskind 31

reduced basis isogeometric methods rb iga for the real time simulation of potential flows about parametrized naca airfoils abstract we present a reduced basis rb method based on isogeometric analysis iga for the rapid and reliable evaluation of pde systems characterized by complex geometrical features at the current state of the art this is the first case of coupling between rb and iga methods the construction of the rb method relies on an isogeometric boundary element method iga bem as the high fidelity technique allowing a direct interface with computer aided design cad tools a suitable empirical interpolation method eim ensures an efficient offline online decomposition between the construction and the evaluation of the rb method we consider the real time simulation of potential flows past airfoils parametrized with respect to the angle of attack and the naca number identifying their shape and we provide a validation of our methodology with respect to experimental data and reference numerical codes showing in both cases a very good agreement

a hierarchic family of isogeometric shell finite elements a hierarchic family of isogeometric shell finite elements based on nurbs shape functions is presented in contrast to classical shell finite element formulations inter element continuity of at least c1 enables a unique and continuous representation of the surface normal within one nurbs patch this does not only facilitate formulation of kirchhoff love type shell models for which the standard galerkin weak form has a variational index of 2 but it also offers significant advantages for shear deformable reissner mindlin type shells and higher order shell models for a 5 parameter shell formulation with reissner mindlin kinematics a hierarchic difference vector which accounts for shear deformations is superimposed onto the rotated kirchhoff love type director of the deformed configuration this split into bending and shear deformations in the shell kinematics results in an element formulation which is free from transverse shear locking without the need to apply further remedies like reduced integration assumed natural strains or mixed finite element formulations the third member of the hierarchy is a 7 parameter model including thickness change and allowing for application of unmodified three dimensional constitutive laws the phenomenon of curvature thickness locking coming along with this kinematic extension again is automatically avoided by the hierarchic difference vector concept without any further treatment membrane locking and in plane shear locking are removed by two different approaches firstly elimination via the discrete strain gap dsg method and secondly removal of parasitic membrane strains using a hybrid mixed method based on the hellinger reissner variational principle the hierarchic kinematic structure of the three different shell formulations allows a straightforward combination of these elements within one mesh and is thus the ideal basis for a model adaptive approach

extended isogeometric boundary element method xibem for three dimensional medium wave acoustic scattering problems a boundary element method bem based on non uniform rational b splines nurbs is used to find solutions to three dimensional wave scattering problems governed by the helmholtz equation the method is extended in a partition of unity sense multiplying the nurbs functions by families of plane waves this method is called the extended isogeometric boundary element method xibem in this paper the collocation xibem formulation is described and numerical results are given the numerical results are compared against closed form or converged solutions comparisons are made against the conventional boundary element method and the non enriched isogeometric bem igabem when compared to non enriched boundary element simulations using xibem significantly reduces the number of degrees of freedom required to obtain a solution of a given error thus with a fixed computational resource problems of a shorter wavelength can be solved

treatment of reissner mindlin shells with kinks without the need for drilling rotation stabilization in an isogeometric framework this work presents a framework for the computation of complex geometries containing intersections of multiple patches with reissner mindlin shell elements the main objective is to provide an isogeometric finite element implementation which neither requires drilling rotation stabilization nor user interaction to quantify the number of rotational degrees of freedom for every node for this purpose the following set of methods is presented control points with corresponding physical location are assigned to one common node for the finite element solution a nodal basis system in every control point is defined which ensures an exact interpolation of the director vector throughout the whole domain a distinction criterion for the automatic quantification of rotational degrees of freedom for every node is presented an isogeometric reissner mindlin shell formulation is enhanced to handle geometries with kinks and allowing for arbitrary intersections of patches the parametrization of adjacent patches along the interface has to be conforming the shell formulation is derived from the continuum theory and uses a rotational update scheme for the current director vector the nonlinear kinematic allows the computation of large deformations and large rotations two concepts for the description of rotations are presented the first one uses an interpolation which is commonly used in standard lagrange based shell element formulations the second scheme uses a more elaborate concept proposed by the authors in prior work which increases the accuracy for arbitrary curved geometries numerical examples show the high accuracy and robustness of both concepts the applicability of the proposed framework is demonstrated

variational implementation of immersed finite element methods dirac distributions are often crucial components of the solid fluid coupling operators in immersed solution methods for fluid structure interaction fsi problems this is certainly so for methods like the immersed boundary method ibm or the immersed finite element method ifem where dirac distributions are approximated via smooth functions by contrast a truly variational formulation of immersed methods does not require the use of dirac distributions either formally or practically this has been shown in the finite element immersed boundary method feibm where the variational structure of the problem is exploited to avoid dirac distributions at both the continuous and the discrete level in this paper we generalize the feibm to the case where an incompressible newtonian fluid interacts with a general hyperelastic solid specifically we allow i the mass density to be different in the solid and the fluid ii the solid to be either viscoelastic of differential type or purely elastic and iii the solid to be either compressible or incompressible at the continuous level our variational formulation combines the natural stability estimates of the fluid and elasticity problems in immersed methods such stability estimates do not transfer to the discrete level automatically due to the non matching nature of the finite dimensional spaces involved in the discretization after presenting our general mathematical framework for the solution of fsi problems we focus in detail on the construction of natural interpolation operators between the fluid and the solid discrete spaces which guarantee semi discrete stability estimates and strong consistency of our spatial discretization

a nurbs based immersed methodology for fluid structure interaction abstract we introduce an isogeometric immersed and fully implicit formulation for fluid structure interaction fsi the method focuses on viscous incompressible flows and nonlinear hyperelastic incompressible solids which are a common case in various fields such as for example biomechanics in our fsi method we utilize an eulerian mesh on the whole domain and a lagrangian mesh on the solid domain the lagrangian mesh is arbitrarily located on top of the eulerian mesh in a non conforming fashion due to the formulation of our problem based on the immersed finite element method ifem we do not need mesh update or remeshing algorithms the fluid structure interface is the boundary of the lagrangian mesh but cuts arbitrarily the eulerian mesh the generalized method is used for time discretization and nurbs based isogeometric analysis is employed for the spatial discretization on both fluid and solid domains the information transfer between the two meshes is carried out using the nurbs functions which avoids the use of the so called discretized delta functions the higher order and especially the higher continuity of nurbs functions allow us to deal with severe mesh distortion in the lagrangian mesh in comparison with classical c 0 linear piecewise functions as we prove numerically our numerical solutions attain good agreement with theoretical data for free falling objects in two and three dimensions which confirms the feasibility of our methodology

nitsche s method combined with space time finite elements for ale fluid structure interaction problems we propose a weak method for handling the fluid structure interface in finite element fluid structure interaction based on nitsche s method abh math univ hamburg 36 1971 9 we assume transient incompressible newtonian flow and for the structure undamped linear elasticity for the time discretization we use the time continuous energy conserving galerkin method for the structure and for the fluid we employ the time discontinuous galerkin method this means that the velocity becomes piecewise constant on each timestep for the fluid matching the time derivative of the displacements in the solid which is also piecewise constant over a time step we formulate the method and report some numerical examples using space time oriented elements for the fluid in order to mimic lagrangian or ale type simulations

a natural framework for isogeometric fluid structure interaction based on bem shell coupling abstract the interaction between thin structures and incompressible newtonian fluids is ubiquitous both in nature and in industrial applications in this paper we present an isogeometric formulation of such problems which exploits a boundary integral formulation of stokes equations to model the surrounding flow and a non linear kirchhoff love shell theory to model the elastic behavior of the structure we propose three different coupling strategies a monolithic fully implicit coupling a staggered elasticity driven coupling and a novel semi implicit coupling where the effect of the surrounding flow is incorporated in the non linear terms of the solid solver through its damping characteristics the novel semi implicit approach is then used to demonstrate the power and robustness of our method which fits ideally in the isogeometric paradigm by exploiting only the boundary representation b rep of the thin structure middle surface

immersed finite element method abstract in this paper the immersed finite element method ifem is proposed for the solution of complex fluid and deformable structure interaction problems encountered in many physical models in ifem a lagrangian solid mesh moves on top of a background eulerian fluid mesh which spans over the entire computational domain hence the mesh generation is greatly simplified moreover both fluid and solid domains are modeled with the finite element methods and the continuity between the fluid and solid sub domains are enforced via the interpolation of the velocities and the distribution of the forces with the reproducing kernel particle method rkpm delta function in comparison with the immersed boundary ib method the higher ordered rkpm delta function enables the fluid domain to have nonuniform spatial meshes with arbitrary geometries and boundary conditions the use of such kernel functions may eventually open doors to multi scale and multi resolution modelings of complex fluid structure interaction problems rigid and deformable spheres dropping in channels are simulated to demonstrate the unique capabilities of the proposed method the results compare well with the experimental data to the authors knowledge these are the first solutions that deal with particulate flows with very flexible solids

a nitsche type formulation and comparison of the most common domain decomposition methods in isogeometric analysis this paper provides a detailed elaboration and assessment of the most common domain decomposition methods for their application in isogeometric analysis the methods comprise a penalty approach lagrange multiplier methods and a nitsche type method for the nitsche method a new stabilized formulation is developed in the context of isogeometric analysis to guarantee coercivity all these methods are investigated on problems of linear elasticity and eigenfrequency analysis in 2d in particular focus is put on non uniform rational b spline patches which join nonconformingly along their common interface thus the application of isogeometric analysis is extended to multi patches which can have an arbitrary parametrization on the adjacent edges moreover it has been shown that the unique properties provided by isogeometric analysis that is high order functions and smoothness across the element boundaries carry over for the analysis of multiple domains copyright 2013 john wiley sons ltd

fuzzy relational compositions abstract this paper investigates the fuzzy relational compositions defined by bandler and kohout it is indicated that these compositions have to be modified in order to capture the desired interpretation several alternative definitions are suggested and discussed the paper concludes with an overview of the properties of these improved fuzzy relational compositions

multi patch nonsingular isogeometric boundary element analysis in 3d abstract a multi patch nonsingular isogeometric boundary element method igabem for 3d problems is presented that provides accurate solutions for multi patch igabem in order to conveniently implement this method based on the greville abscissae a new collocation method moves the first and the last collocation points of each parametric direction inside of their patches and a simple method for merging equations handles the extra equations the numerical results verify the accuracy and efficiency of the present method by comparing it to the conventional igabem

on the hyper elastic formulation of the immersed boundary method abstract the immersed boundary ib method is both a mathematical formulation and a numerical method for fluid structure interaction problems in which immersed incompressible visco elastic bodies or boundaries interact with an incompressible fluid previous formulations of the ib method were not able to treat appropriately immersed materials of finite nonzero thickness modeled by general hyper elastic constitutive laws because of the lack of appropriate transmission conditions between the immersed body and the surrounding fluid in the case of a nonzero jump in normal stress at the solid fluid interface such a jump does not arise when the solid is comprised of fibers that run parallel to the interface but typically does arise in other cases e g when the solid contains elastic fibers that terminate at the solid fluid interface we present a derivation of the ib method that takes into account in an appropriate way the missing term the derivation presented in this paper starts from a separation of the stress that appears in the principle of virtual work the stress is divided into its fluid like and solid like components and each of these two terms is treated in its natural framework i e the eulerian framework for the fluid like stress and the lagrangian framework for the solid like stress we describe how the ib method can be used in conjunction with standard formulations of continuum mechanics models for immersed incompressible elastic materials and present some illustrative numerical experiments

an extended isogeometric thin shell analysis based on kirchhoff love theory abstract an extended isogeometric element formulation xiga for analysis of through the thickness cracks in thin shell structures is developed the discretization is based on non uniform rational b splines nurbs the proposed xiga formulation can reproduce the singular field near the crack tip and the discontinuities across the crack it is based on the kirchhoff love theory where c 1 continuity of the displacement field is required this condition is satisfied by the nurbs basis functions hence the formulation eliminates the need of rotational degrees of freedom or the discretization of the director field facilitating the enrichment strategy the performance and validity of the formulation is tested by several benchmark examples

on chow and brauer groups of a product of mumford curves let c1 cd be mumford curves defined over a finite extension of open image in new window and let x c1 cd we shall show the following 1 the cycle map ch0 x n h2d x n d is injective for any non zero integer n 2 the kernel of the canonical map ch0 x hom br x open image in new window defined by the brauer manin pairing coincides with the maximal divisible subgroup in ch0 x

a finite element boundary element method for three dimensional large displacement fluid structure interaction abstract this paper presents a hybrid finite element boundary element method for fluid structure interaction simulations of inflatable structures the flow model consists of the steady stokes equation which admits a boundary integral formulation the structure is represented by a kirchhoff love shell the boundary element approximation of the stokes equation reduces the flow problem to an integral equation on the actual structure configuration thus obviating the need for volumetric meshing of the strongly deforming fluid domain the stokes model moreover exhibits a lubrication effect that acts as an intrinsic mechanism to treat the ubiquitous self contact that occurs in inflation problems the aggregated fluid structure interaction problem composed of the boundary integral equation and the kirchhoff love shell connected by dynamic and kinematic interface conditions is approximated by means of isogeometric discretizations to accommodate the smoothness requirements on the approximation spaces imposed by the flexural rigidity in the kirchhoff love shell and to provide an accurate and smooth representation of the boundary for the boundary element method auxiliary results presented in this paper are 1 a parametrization free kirchhoff love formulation 2 establishment of a cubic relationship between distance and tractions due to the lubrication effect and 3 the interpretation of the lagrange multiplier pertaining to fluid incompressibility as the total excess pressure

efficient isogeometric nurbs based solid shell elements mixed formulation and b method abstract in this work solid shell nurbs elements are developed in order to address static problems of slender structures under small perturbations a single layer of elements is considered through the thickness of the shell and the degree of approximation in that direction is chosen to be equal to two a full 3d constitutive relation is assumed the objective is to obtain highly accurate low degree elements to be used in coarse meshes in order to do that we propose a mixed method from which we derive a b projection to deal with locking the main idea is to modify the interpolation of the average stresses and strains through the thickness more precisely we develop two finite elements the first element which is based on the mixed method or equivalently on the b projection is extremely accurate but leads to a fully populated global stiffness matrix to improve the efficiency the second element uses a local least squares type procedure to define a new b projection leading to a sparse global stiffness matrix the quality and efficiency of the methods are assessed through several usual test cases and by comparison with other published techniques