advantages of the mixed format in geometrically nonlinear analysis of beams and shells using solid finite elements summary the paper deals with two main advantages in the analysis of slender elastic structures both achieved through the mixed stress and displacement format with respect to the more commonly used displacement one i the smaller error in the extrapolations usually employed in the solution strategies of nonlinear problems and ii the lower polynomial dependence of the problem equations on the finite element degrees of freedom when solid finite elements are used the smaller extrapolation error produces a lower number of iterations and larger step length in path following analysis and a greater accuracy in koiter asymptotic method to focus on the origin of the phenomenon the two formats are derived for the same finite element interpolation the reduced polynomial dependence improves the koiter asymptotic strategy in terms of both computational efficiency accuracy and simplicity copyright 2016 john wiley sons ltd

the denjoy wolff theorem in cn abstract if d is a bounded and strictly convex domain in c n and f d d is holomorphic and fixed point free then there exists d such that the sequence f n of the iterates of f converges in the compact open topology to the constant mapping taking the value

an efficient isogeometric solid shell formulation for geometrically nonlinear analysis of elastic shells abstract in this work an isogeometric solid shell model for geometrically nonlinear analyses is proposed it is based on a linear interpolation through the thickness and a nurbs interpolation on the middle surface of the shell for both the geometry and the displacement field the green lagrange strains are linearized along the thickness direction and a modified generalized constitutive matrix is adopted to easily eliminate thickness locking without introducing any additional unknowns and to model multi layered composite shells reduced integration schemes which take into account the high continuity of the shape functions are investigated to avoid interpolation locking and to increase the computational efficiency the relaxation of the constitutive equations at each integration point is adopted in the iterative scheme in order to reconstruct the equilibrium path using large steps and a low number of iterations even for very slender structures this strategy makes it possible to minimize the number of stiffness matrix evaluations and decompositions and it turns out to be particularly convenient in isogeometric analyses

orthogonality preservers in c algebras jb algebras and jb triples abstract we study orthogonality preserving operators between c algebras jb algebras and jb triples let t a e be an orthogonality preserving bounded linear operator from a c algebra to a jb triple satisfying that t 1 d is a von neumann regular element then t a e 2 r d every element in t a and d operator commute in the jb algebra e 2 r d and there exists a triple homomorphism s a e 2 r d such that t l d r d s where r d denotes the range tripotent of d in e an analogous result for a being a jb algebra is also obtained when t a b is an operator between two c algebras we show that denoting h t 1 then t orthogonality preserving if and only if there exists a triple homomorphism s a b satisfying h s z s z h h s z s z h and t z l h r h s z 1 2 h r h s z s z r h h this allows us to prove that a bounded linear operator between two c algebras is orthogonality preserving if and only if it preserves zero triple products

linear invariance of locally biholomorphic mappings in the unit ball of a jb triple abstract we study the notion of linear invariance on the unit ball of a j b triple x and we obtain some connection between the norm order of a linear invariant family and the starlikeness of order 1 2 also we give some result concerning the radius of univalence of some linear invariant families finally if the dimension of x is finite and if the norm order of a linear invariant family is finite then we prove the normality of the linear invariant family and we also obtain upper bounds on the distortion and the growth of mappings in a linear invariant family with specified norm order in particular our results are valid for the classical cartan domains and the unit polydisc

on the cr structure of compact group orbits associated with bounded symmetric domains let e be a complex vector space of finite dimension and let k gl e be a compact connected subgroup then for fixed a e the orbit k k a is a real analytic submanifold of e that inherits various structures from e for instance choosing a k invariant positive definite inner product x y on e makes k a riemannian manifold on which k acts transitively by isometries on the other hand k inherits from e a cauchy riemann structure cr structure that is given by the distribution of the maximal complex subspaces hx k tx k itx k of the real tangent spaces tx k e x k together with the complex structure on every hx k multiplication by i the subspace hx k is called the holomorphic tangent space to k at x see 9 and 4 as general references for cr manifolds of interest for the geometry of the orbit k k a with respect to its cr structure is the study of the cr functions or more generally cr mappings on k i e of smooth functions f k c that satisfy the tangential cauchy riemann differential equations in the sense that the restriction of the differential df to every holomorphic tangent space is complex linear for instance all holomorphic functions defined in an open neighbourhood of k e give by restriction real analytic cr functions on k actually we deal with the more general continuous cr functions on k which satisfy by definition the tangential cr equations in the distribution sense or equivalently which are locally uniform limits of sequences of smooth cr functions due to the approximation theorem of baouenditreves 6 in this context it is of interest to determine the space of all

an analytical geometric calibration method for circular cone beam geometry this work is a continuation of our previous work on geometric calibration in the circular cone beam geometry it is well known that seven parameters completely describe such a geometry in either flat panel x ray computed tomography or single pinhole spect imaging previously we developed a graphical procedure to determine the detector in plane rotation angle independently of the other six parameters using the discovered geometrical relationships in this paper we determine the remaining six parameters using the cone beam projections of a minimum of three point objects our method is analytical it makes use of the parameters of the fitted ellipse from the calibration data the parameter estimation is accurate in the noise free case or when there is moderate projection data truncation or shorter calibration scan range 360 we perform numerical evaluations to study the robustness of the proposed method under different projection noise levels and using different data acquisition ranges using a full 360 scan range the estimation accuracy and precision of our method are comparable or superior to previous methods using a shorter acquisition range there may be bias in the ellipse parameters obtained by simple algebraic fitting methods this bias will propagate to the estimated geometric parameters such bias can be mostly eliminated by using a more sophisticated fitting algorithm at the same noise level the geometric parameter estimation accuracies are comparable but the estimation precision degrades as the acquisition range becomes shorter

the denjoy wolff theorem in the open unit ball of a strictly convex banach space letxbe a complex strictly convex banach space with an open unit ballb for each compact holomorphic and fixed point free mappingf b bthere exists bsuch that the sequence fn of iterates offconverges locally uniformly onbto the constant map taking the value

a reduced integration solid shell finite element based on the eas and the ans concept large deformation problems in this paper we address the extension of a recently proposed reduced integration eight node solid shell finite element to large deformations the element requires only one integration point within the shell plane and at least two integration points over the thickness the possibility to choose arbitrarily many gauss points over the shell thickness enables a realistic and efficient modeling of the non linear material behavior only one enhanced degree of freedom is needed to avoid volumetric and poisson thickness locking one key point of the formulation is the taylor expansion of the inverse jacobian matrix with respect to the element center leading to a very accurate modeling of arbitrary element shapes the transverse shear and curvature thickness locking are cured by means of the assumed natural strain concept further crucial points are the taylor expansion of the compatible cartesian strain with respect to the center of the element as well as the taylor expansion of the second piola kirchhoff stress tensor with respect to the normal through the center of the element copyright 2010 john wiley sons ltd

statistical optimization for geometric fitting theoretical accuracy bound and high order error analysis a rigorous accuracy analysis is given to various techniques for estimating parameters of geometric models from noisy data first it is pointed out that parameter estimation for vision applications is very different in nature from traditional statistical analysis and hence a different mathematical framework is necessary after a general framework is formulated typical numerical techniques are selected and their accuracy is evaluated up to high order terms as a byproduct our analysis leads to a hyperaccurate method that outperforms existing methods

tits kantor koecher lie algebras of jb triples abstract we characterise the tits kantor koecher lie algebra of a jb triple which can be infinite dimensional in particular we show that a complex lie algebra is the tits kantor koecher lie algebra of a jb triple if and only if it has a real form which is isomorphic to the reduced lie algebra of a bounded symmetric domain matrix representations of these lie algebras are also presented

a robust non linear solid shell element based on a mixed variational formulation the paper is concerned with a geometrically non linear solid shell finite element formulation which is based on the hu washizu variational principle for the approximation of the independent displacement stress and strain fields the strain field is additively decomposed into two parts due to the fact that one part of the strain field is interpolated in the same manner as proposed by the enhanced assumed strain eas method it is denoted as eas field the other strain field is approximated with the same interpolation functions as the stress field in contrast to the eas concept the approximation spaces of the stresses and the enhanced assumed strains are not orthogonal consequently the stress field is not eliminated from the finite element equations for the displacements tri linear shape functions are considered shear locking and curvature thickness locking are treated using assumed natural strain interpolations a static condensation leads to a simple low order hexahedral solid shell element numerical tests show that the present model is very robust and allows larger load steps than an eas solid shell element

extrapolation locking and its sanitization in koiter s asymptotic analysis abstract this paper shows that the fem implementation of koiter s asymptotic method w t koiter on the stability of elastic equilibrium 1970 ph d thesis delft 1945 english transl nasa tt f10 883 1967 affdl tr70 25 outlined by casciaro et al finite element asymptotic analysis of slender elastic structures a simple approach int j num meth eng 35 1992 1397 1426 provides accurate and reliable results in the critical and post critical analysis of non linear elastic structures care however does have to be taken in implementing apparently minor details to avoid locking effects which adversely affect accuracy and which can destroy the method reliability as the effects related to the finite element interpolation have been discussed before this paper focuses on the non linear locking due to the use implicit in the method of finite distance extrapolations within this scope it is shown that perturbation algorithms based on compatible formulations can imply a strong critical and post critical locking when analysing structures characterized by high stiffness ratios in the presence of moderate pre critical rotations on the contrary perturbation algorithms based on independent extrapolations of displacements and stresses furnish reliable results in excellent agreement with those provided by step by step analysis at a small fraction of its computational cost

finite element analysis of post buckling dynamics in plates part i an asymptotic approach abstract various static and dynamic aspects of post buckled thin plates including the transition of buckled patterns post buckling dynamics secondary bifurcation and dynamic snapping mode jumping phenomenon are investigated systematically using asymptotical and non stationary finite element methods in part i the secondary dynamic instability and the local post secondary buckling behavior of thin rectangular plates under generalized mechanical and thermal loading is investigated using an asymptotic numerical method which combines koiter s nonlinear instability theory with the finite element technique a dynamic multi mode reduction method similar to its static single mode counterpart liapunov schmidt reduction is developed in this perturbation approach post secondary buckling equilibrium branches are obtained by solving the reduced low dimensional parametric equations and their stability properties are determined directly by checking the eigenvalues of the resulting jacobian matrix typical post secondary buckling forms transcritical supercritical and subcritical bifurcations are observed according to different combinations of boundary conditions and load types geometric imperfection analysis shows that not only the secondary bifurcation load but also changes in the fundamental post secondary buckling behavior are affected the post buckling dynamics and the global analysis of mode jumping of the plates are addressed in part ii

a riemannian framework for tensor computing tensors are nowadays a common source of geometric information in this paper we propose to endow the tensor space with an affine invariant riemannian metric we demonstrate that it leads to strong theoretical properties the cone of positive definite symmetric matrices is replaced by a regular and complete manifold without boundaries null eigenvalues are at the infinity the geodesic between two tensors and the mean of a set of tensors are uniquely defined etc we have previously shown that the riemannian metric provides a powerful framework for generalizing statistics to manifolds in this paper we show that it is also possible to generalize to tensor fields many important geometric data processing algorithms such as interpolation filtering diffusion and restoration of missing data for instance most interpolation and gaussian filtering schemes can be tackled efficiently through a weighted mean computation linear and anisotropic diffusion schemes can be adapted to our riemannian framework through partial differential evolution equations provided that the metric of the tensor space is taken into account for that purpose we provide intrinsic numerical schemes to compute the gradient and laplace beltrami operators finally to enforce the fidelity to the data either sparsely distributed tensors or complete tensors fields we propose least squares criteria based on our invariant riemannian distance which are particularly simple and efficient to solve

how to put probabilities on homographies we present a family of normal distributions over a matrix group together with a simple method for estimating its parameters in particular the mean of a set of elements can be calculated the approach is applied to planar projective homographies showing that using priors defined in this way improves object recognition

harmonic functions on topological groups and symmetric spaces let g be a metric group not necessarily locally compact acting on a metric space x for instance a right coset space of g we introduce and develop a basic structure theory for harmonic functions on x which is applicable to infinite dimensional riemannian symmetric spaces

an efficient mixed variational reduced order model formulation for nonlinear analyses of elastic shells summary the koiter newton method had recently demonstrated a superior performance for non linear analyses of structures compared to traditional path following strategies the method follows a predictor corrector scheme to trace the entire equilibrium path during a predictor step a reduced order model is constructed based on koiter s asymptotic post buckling theory which is followed by a newton iteration in the corrector phase to regain the equilibrium of forces in this manuscript we introduce a robust mixed solid shell formulation to further enhance the efficiency of stability analyses in various aspects we show that a hellinger reissner variational formulation facilitates the reduced order model construction omitting an expensive evaluation of the inherent fourth order derivatives of the strain energy we demonstrate that extremely large step sizes with a reasonable out of balance residual can be obtained with substantial impact on the total number of steps needed to trace the complete equilibrium path more importantly the numerical effort of the corrector phase involving a newton iteration of the full order model is drastically reduced thus revealing the true strength of the proposed formulation we study a number of problems from engineering and compare the results to the conventional approach in order to highlight the gain in numerical efficiency for stability problems this article is protected by copyright all rights reserved

on the fitting of surfaces to data with covariances we consider the problem of estimating parameters of a model described by an equation of special form specific models arise in the analysis of a wide class of computer vision problems including conic fitting and estimation of the fundamental matrix we assume that noisy data are accompanied by known covariance matrices characterizing the uncertainty of the measurements a cost function is first obtained by considering a maximum likelihood formulation and applying certain necessary approximations that render the problem tractable a newton like iterative scheme is then generated for determining a minimizer of the cost function unlike alternative approaches such as sampson s method or the renormalization technique the new scheme has as its theoretical limit the minimizer of the cost function furthermore the scheme is simply expressed efficient and unsurpassed as a general technique in our testing an important feature of the method is that it can serve as a basis for conducting theoretical comparison of various estimation approaches

selective and reduced numerical integrations for nurbs based isogeometric analysis we propose a new approach to construct selective and reduced integration rules for isogeometric analysis based on nurbs elements the notion of an approximation space that approximates the target space is introduced we explore the use of various approximation spaces associated with optimal patch wise numerical quadratures that exactly integrate the polynomials in approximation spaces with the minimum number of quadrature points patch rules exploit the higher continuity of spline basis functions the tendency of smooth spline functions to exhibit numerical locking in nearly incompressible problems when using a full gauss legendre quadrature is alleviated with selective or reduced integration stability and accuracy of the schemes are examined analyzing the discrete spectrum in a generalized eigenvalue problem we propose a local algorithm which is robust and computationally efficient to compute element by element the quadrature points and weights in patch rules the performance of the methods is assessed on several numerical examples in two dimensional elasticity and reissner mindlin shell structures

on the manifold of tripotents in jb triples the manifold of tripotents in an arbitrary jb triple z is considered a natural affine connection is defined on it in terms of the peirce projections of z and a precise description of its geodesics is given regarding this manifold as a fiber space by neher s equivalence the base space is a symmetric kahler manifold when z is a classical cartan factor and necessary and sufficient conditions are established for connected components of the manifold to admit a riemann structure

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

jordan triples and riemannian symmetric spaces we introduce a class of real jordan triple systems called jh triples and show via the tits kantor koecher construction of lie algebras that they correspond to a class of riemannian symmetric spaces including the hermitian symmetric spaces and the symmetric r spaces

fixed points and invariant domains of holomorphic mappings of the hilbert ball this paper is an extension of the joint work of the present author t sekowski and a stachura 4 there some methods of the theory of nonexpansive mappings were used to prove fixed point theorems for holomorphic self mappings of the unit ball in complex hilbert space earlier results on the existence of fixed points of holomorphic self mappings of domains in banach spaces may be found in works of earle and hamilton 2 hayden and suffridge 6 7 111 and rudin 9 all the results depend strongly on the consequences of the schwartz pick lemma and properties of so called invariant hyperbolic metrics detailed discussion of invariant metrics is contained in the long article by harris 5 and in the recent book by franzoni and vesentini 3 hyperbolic geometry of the unit ball in c is clearly described in a very recent book by rudin lo in spite of the fact that we are dealing with the infinite dimensional case we very often follow the notation terminology and some methods from this book a very interesting discussion of the one dimensional case has been given recently by burckel l invariant ellipsoids which we discuss here have their origin in the old papers by julia s and wolff 2

iteration of self maps on a product of hilbert balls abstract let d d 1 d p be a product of hilbert balls with coordinate maps j d d j on the closure d for j 1 p let f be a fixed point free self map on d which is nonexpansive in the kobayashi distance and compact for p 2 we describe the horospheres invariant under f and show that there exist a boundary point 1 p of d and a nonempty set j 1 p such that each limit function h of the iterates f n satisfies j j h d for all j j and j h j whenever j h d meets the boundary of d j for a single hilbert ball d 1 either l i m i n f n f 2 n 0 1 or f n converges locally uniformly to a constant map taking value at the boundary of d 1

state spaces of jb triples an atomic decomposition is proved for banach spaces which satisfy some affine geometric axioms compatible with notions from the quantum mechanical measuring process this is then applied to yield under appropriate assumptions geometric characterizations up to isometry of the unit ball of the dual space of a jb triple and up to complete isometry of one sided ideals in c algebras

low rank compact operators and tingley s problem abstract let e and b be arbitrary weakly compact jb triples whose unit spheres are denoted by s e and s b respectively we prove that every surjective isometry f s e s b admits an extension to a surjective real linear isometry t e b this is a complete solution to tingley s problem in the setting of weakly compact jb triples among the consequences we show that if k h k denotes the space of compact operators between arbitrary complex hilbert spaces h and k then every surjective isometry f s k h k s k h k admits an extension to a surjective real linear isometry t k h k k h k

relatively weakly open sets in closed balls of banach spaces and real jb triples of finite rank we prove that given a real jb triple x there exists a nonempty relatively weakly open subset of the closed unit ball of x with diameter less than 2 if and only if the banach space of x is isomorphic to a hilbert space moreover we give the structure of real jb triples whose banach spaces are isomorphic to hilbert spaces such real jb triples are also characterized in two different purely algebraic ways

asymptotic post buckling fem analysis using corotational formulation finite element asymptotic post buckling analysis being based on fourth order expansions of the strain energy requires that nonlinear structural modeling be accurate to same order at least with respect to the rigid motions of the elements a corotational description is proposed here as a general tool to satisfy this requirement of objectivity by referring each element to a local frame which moves rotates with the element so filtering its rigid motion in this description nonlinearity of the problem derives essentially from the change of reference from the global fixed frame to the local one the strain energy being governed by their relative rotations in finite kinematics this noticeably complicates the algebra for obtaining exact expressions of its variations quite simple basic expressions for the first four corotational derivatives of the strain energy are provided allowing the set up of a fourth order accurate asymptotic analysis starting from standard finite elements based on linear or simplified nonlinear local modelings the formulation is implemented for the analysis of 3d beam assemblages and several numerical results are presented and discussed showing the effectiveness and robustness of the proposed approach in reproducing the nonlinear equilibrium path in both cases of monomodal and coupled multimodal buckling

the koiter newton approach using von karman kinematics for buckling analyses of imperfection sensitive structures the koiter newton approach is a reduced basis method for nonlinear structural analyses the method combines koiter s approach as a predictor step and the newton arc length technique as a corrector step to trace the entire load displacement equilibrium path of a structure in a step by step manner this computationally highly efficient and accurate solution method has recently demonstrated a superior performance in nonlinear analyses compared to standard techniques in this paper we propose an extension to buckling imperfection sensitivity analyses exploiting the method s stability and reliability we present two different modeling techniques for imperfection loads that both profit from the koiter newton approach reducing the initial computation steps to a small fraction thereof we introduce von karman kinematics which neglect some nonlinear terms of the green strain displacement relations to further increase the computational efficiency of the analysis by an essential reduction of the computation effort required to obtain higher order derivatives of the strain energy using various numerical examples and benchmark tests we demonstrate the overall high quality and performance of the proposed method

isogeometric analysis for nonlinear planar kirchhoff rods weighted residual formulation and collocation of the strong form abstract high order shape functions used in isogeometric analysis allow the direct solution not only to the weighted residual formulation of the strong form opening the door to new integration schemes e g reduced gauss lobatto quadrature integration at superconvergent sites but also to collocation approaches e g using greville or superconvergent collocation points the goal of the present work is to compare these different methods through the application to the planar kirchhoff rod a fourth order rotation free formulation used to model slender beams under large deformations robustness of the geometrically nonlinear solution is improved using the mixed integration point mip newton a method that combines the advantages of displacement and mixed formulations based on the observations of the convergence plots convergence order estimates are provided for each discretization method advantages and weaknesses in terms of robustness and computation cost are also discussed for a set of benchmarks

complex geodesics and iterates of holomorphic maps on convex domains in ⁿ we study complex geodesics f where is the unit disk in c and belongs to a class of bounded convex domains in c n with no boundary regularity assumption along with continuity up to the boundary existence of such complex geodesics with two prescribed values z w is established as a consequence we obtain some new results from iteration theory of holomorphic self maps of bounded convex domains in c n

finite element asymptotic analysis of slender elastic structures a simple approach an asymptotic method directly derived from koiter s theory and suitable for the solution of elastic buckling problems and its natural adaptation to a numerical solution by means of a finite element technique are presented here the order of the extrapolation of the equilibrium equations has been intentionally kept very low because attention has been entirely devoted to all those features theoretical definitions eigenproblem numerical techniques suitable fem implementation which make such an approach competitive with respect to the classic step by step methods for plane frames and 3d pin jointed trusses the performances of the algorithm numerical accuracy and computational cost are compared with those of riks are length method

a reduced integration solid shell finite element based on the eas and the ans concept geometrically linear problems in this paper a new reduced integration eight node solid shell finite element is presented the enhanced assumed strain eas concept based on the hu washizu variational principle requires only one eas degree of freedom to cure volumetric and poisson thickness locking one key point of the derivation is the taylor expansion of the inverse jacobian with respect to the element center which closely approximates the element shape and allows us to implement the assumed natural strain ans concept to eliminate the curvature thickness and the transverse shear locking the second crucial point is a combined taylor expansion of the compatible strain with respect to the center of the element and the normal through the element center leading to an efficient and locking free hourglass stabilization without rank deficiency hence the element requires only a single integration point in the shell plane and at least two integration points in thickness direction the formulation fulfills both the membrane and the bending patch test exactly which has to the authors knowledge not yet been achieved for reduced integration eight node solid shell elements in the literature owing to the three dimensional modeling of the structure fully three dimensional matenal models can be implemented without additional assumptions

the classification of locally finite split simple lie algebras one of the great early achievements in lie theory is the classification of the finite dimensional simple complex lie algebras by w killing and e cartan more than 50 years later new aspects were added to this classification by the theory of coxeter groups and the visualization of the classification in terms of dynkin diagrams furthermore serre s description of the simple lie algebras by generators and relations provided a direct way to construct the lie algebras from the cartan matrix corresponding to the choice of a root base i e a system of simple roots

how to improve efficiency and robustness of the newton method in geometrically non linear structural problem discretized via displacement based finite elements abstract in this paper we show how to significantly improve the robustness and the efficiency of the newton method in geometrically non linear structural problems discretized via displacement based finite elements the strategy is based on the relaxation of the constitutive equations at each integration point this leads to an improved iterative scheme which requires a very low number of iterations to converge and can withstand very large steps in step by step analyses the computational cost of each iteration is the same as the original newton method the impressive performances of the proposal are shown by many numerical tests in geometrically non linear analysis the proposed strategy called mip newton seems worthy to replace the standard newton method in any finite element code based on displacement formulations its implementation in existing codes is very easy

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

a wolff theorem for finite rank bounded symmetric domains abstract we present a wolff theorem for all infinite dimensional bounded symmetric domains of finite rank namely if b is the open unit ball of any finite rank j b triple and f b b is a compact holomorphic map with no fixed point in b we prove convex f invariant subdomains of b of all sizes and at all points exist in the form of simple operator balls c t b for c b and t an invertible linear map these are exact infinite dimensional analogues of the invariant discs in the invariant ellipsoids in the hilbert ball and invariant domains in finite dimensional triples results are new for rank 2 even for classical spaces such as c algebras and j b algebras

holomorphic functions on symmetric banach manifolds of compact type are constant 1 throughout we use c to denote the one point compactification c of c let z denote a banach space over the complex numbers c let l z and l z denote respectively the space of continuous linear and anti linear or conjugate linear mappings from z to z endowed with the operator norm we consider a continuous triple product z3 z which is symmetric and linear in the outer variables and conjugate linear in the middle variable in particular this implies

generalised f algebras as predual algebras of jbw triples and characterisations of the fourier algebras on locally compact groups abstract we introduce the notion of a generalised f algebra as a banach algebra a whose banach space dual is a j b w triple with a certain additional condition on a distinguished character of a this generalises the well known notion of f algebras which in turn includes as special cases many important classes of banach algebras on locally compact groups and semigroups our main use of this new notion is to give some axiomatic characterisations of the fourier algebras on locally compact groups strengthening our previous work 37 but we also quickly review some well known results in f algebras that can be extended to the context of generalised f algebras

finite tripotents and finite jbw triples abstract we study two natural preorders on the set of tripotents in a jb triple defined in terms of their peirce decomposition and weaker than the standard partial order we further introduce and investigate the notion of finiteness for tripotents in jbw triples which is a natural generalization of finiteness for projections in von neumann algebras we analyze the preorders in detail using the standard representation of jbw triples we also provide a refined version of this representation in particular a decomposition of any jbw triple into its finite and properly infinite parts since a jbw algebra is finite if and only if the extreme points of its unit ball are just unitaries our notion of finiteness differs from the concept of modularity widely used in jordan structures so far the exact relationship of these two notions is clarified in the last section

unscented transformation based estimation of parameters of nonlinear models using heteroscedastic data this paper addresses the issue of estimating the parameters of nonlinear models using heteroscedastic data a weighted least squares problem formulation where the sum of the mahalanobis distance for all measurements is minimized forms the framework of this paper determining the mahalanobis distance requires the gradient of the cost function with respect to the noisy measurements which can be computationally expensive and infeasible for model which are discontinuous a derivative free approach to determine the mahalanobis distance as an error metric is proposed using the unscented transformation the advantages of using the proposed approach include a black box approach to evaluate the gradient weighted objective function precluding the need for analytical gradients and an improved estimation of the covariance numerical results for various applications such as triangulation using radar measurements ellipse and super ellipse fitting demonstrate the benefits of the proposed approach heteroscedastic data resulting from real x ray images are also used to illustrate the potential of the proposed approach highlightsderivative free approach of solving gradient weighted least squares problems improved approximation of the geometric distance for curve fitting improved performance of proposed technique demonstrated on three benchmarks monte carlo used to benchmark the reduction in bias in estimated parameters relevant to model fitting problems with heteroscedastic data

another look at results of wolff and julia type forj algebras abstract domains of invariance for certain classes of holomorphic mappings on the open unit ball of a j algebra are given

on grassmannians associated with jb triples then is a complex lie group that has precisely n 1 orbits e0 en in e each er is the locally closed complex submanifold of all matrices of rank r clearly er 1 is in the closure of er for every 1 r n and en is the unique open orbit for every pair of integers p q 0 let gp q be the grassmannian of all p planes in cp q then gp q is a compact symmetric hermitian manifold of dimension pq holomorphically equivalent to gq p every er is in a canonical way a equivariant holomorphic fibre bundle

optimal quadrature for univariate and tensor product splines abstract numerical integration is a core subroutine in many engineering applications including the finite element method fem isogeometric analysis is a fem technology that uses smooth b spline and nurbs basis functions traditionally gaussian quadrature was used for numerical integration but this yields suboptimal performance this is attributed to the fact that gaussian quadrature rules do not take inter element smoothness of the spline basis into account resulting in over integration the equations for exact quadrature are well known but prove notoriously hard to solve due to their nonlinear nature these generalized gauss rules were first introduced in hughes et al 2010 in the context of isogeometric analysis where newton iteration was utilized to study and tabulate several cases later homotopy continuation barto and calo 2015 was used as an alternative strategy for finding these rules in this paper we describe an algorithm to generalize on both of these techniques it is optimal in the sense that it will integrate a space of dimension n using no more than n 1 2 quadrature points the algorithm works on arbitrary nonuniform knot vectors of any polynomial degree and continuity and is demonstrated on polynomial orders up to 15 it extends to 2d and 3d integrals by tensor product

a simplified kirchhoff love large deformation model for elastic shells and its effective isogeometric formulation abstract isogeometric kirchhoff love elements have received an increasing attention in geometrically nonlinear analysis of elastic shells nevertheless some difficulties still remain among the others the highly nonlinear expression of the strain measure which leads to a complicated and costly computation of the discrete operators and the existence of locking which prevents the use of coarse meshes for slender shells and low order nurbs are key issues that need to be addressed in this work exploiting the hypothesis of small membrane strains we propose a simplified strain measure with a third order polynomial dependence on the displacement variables which allows an efficient evaluation of the discrete quantities numerical results show practically no difference to the original model even for very large displacements and composite structures patch wise reduced integrations are then investigated to deal with membrane locking in large deformation problems an optimal integration scheme for third order c 2 nurbs in terms of accuracy and efficiency is identified finally the recently proposed newton method with mixed integration points is used for the solution of the discrete nonlinear equations with a great reduction of the iterative burden with respect to the standard newton scheme

manifolds of tripotents in jb triples we describe the affine connections geodesics and symmetries of various banach manifolds of tripotents in jb triples which include the c algebras and hilbert spaces where the nonzero tripotents are respectively the partial isometries and the extreme points of the closed unit ball

from fns to heiv a link between two vision parameter estimation methods problems requiring accurate determination of parameters from image based quantities arise often in computer vision two recent independently developed frameworks for estimating such parameters are the fns and heiv schemes here it is shown that fns and a core version of heiv are essentially equivalent solving a common underlying equation via different means the analysis is driven by the search for a nondegenerate form of a certain generalized eigenvalue problem and effectively leads to a new derivation of the relevant case of the heiv algorithm this work may be seen as an extension of previous efforts to rationalize and interrelate a spectrum of estimators including the renormalization method of kanatani and the normalized eight point method of hartley

mixed formulation in koiter analysis of thin walled beams abstract the paper extends the asymptotic mixed formulation proposed in g garcea g salerno sanitizing of locking in koiter perturbation analysis through mixed formulation fourth world congress on computational mechanics buenos aires argentina 1988 g garcea g salerno r casciaro comput methods appl mech engrg 180 1 2 1999 137 167 to structures composed of an assemblage of flat slender elastic panels the same type of structure has already been investigated in a d lanzo g garcea r casciaro int j numer methods engrg 38 1995 2325 2345 a d lanzo g garcea int j numer methods engrg 39 1996 3007 3031 with a compatible formulation and using the usual hypothesis of negligible precritical rotations in order to avoid the extrapolation locking see also g garcea g a trunfio r casciaro comput methods appl mech engrg 165 1 4 1998 137 167 produced by the high axial to flexural stiffness ratio of the panels the use of a mixed formulation provides a consistent way of eliminating the extrapolation locking without introducing ad hoc approximations it is thus both reliable and accurate when combined with a quadratic strain displacement relationship as presented here it gives zero fourth order energy variations further computational simplifications and a natural linearization of the eigenvalue problem required by the buckling analysis an extensive numerical testing shows the effectiveness and robustness of the proposed approach

horoballs and iteration of holomorphic maps on bounded symmetric domains abstract given a fixed point free compact holomorphic self map f on a bounded symmetric domain d which may be infinite dimensional we establish the existence of a family h 0 of convex f invariant domains at a point in the boundary d of d which generalises completely wolff s theorem for the open unit disc in c further we construct horoballs at and show that they are exactly the f invariant domains when d is of finite rank consequently we show in the latter case that the limit functions of the iterates f n with weakly closed range all accumulate in one single boundary component of d

asymptotic post buckling analysis of rectangular plates by hc finite elements the present paper extends the finite element perturbation approach already presented for pin jointed and framed structures15 to rectangular thin plates koiter s asymptotic strategy2 is coupled with a high continuity finite element discretization of the plate 22 the consistency of the discrete model is discussed from the kinematical and numerical points of view and several numerical tests are reported it appears that use of the hc elements makes the perturbation algorithm insensitive to the locking phenomenon occurring in the evaluation of the postbuckling behaviour it also allows the use of very fine discretization meshes at low computational cost

an isogeometric formulation of the koiter s theory for buckling and initial post buckling analysis of composite shells abstract numerical formulations of the koiter theory allow the efficient prediction through a reduced model of the behavior of shell structures when failure is dominated by buckling in this work we propose an isogeometric version of the method based on a solid shell model a nurbs interpolation is employed on the middle surface of the shell to accurately describe the geometry and the high continuity typical of the displacement field in buckling problems and to directly link the cad model to the structural one a linear interpolation is then adopted through the thickness together with a modified generalized constitutive matrix which allows us to easily eliminate thickness locking and model multi layered composites reduced integration schemes which take into account the continuity of the shape functions are used to avoid interpolation locking and make the integration faster a mixed integration point strategy makes it possible to transform the displacement model into a mixed stress displacement one required by the koiter method to obtain accurate predictions without introducing stress interpolation functions the result is an efficient numerical tool for buckling and initial post buckling analysis of composite shells characterized by a low number of dofs and integration points and by a simple and quick construction of the reduced model

asymptotic numerical method for buckling analysis of shell structures with large rotations in this paper the buckling and post buckling of elastic structures taking into account large rotations are investigated using an asymptotic numerical method the critical points are detected by two different ways first by a bifurcation indicator second by analysing the poles of a pade approximant the first step of the post buckling branch is computed starting from the bifurcation point and using an extended system the remaining bifurcating branch is followed by the same algorithm as for the fundamental path several examples are tested to show the effectiveness of the proposed method

heteroscedastic regression in computer vision problems with bilinear constraint we present an algorithm to estimate the parameters of a linear model in the presence of heteroscedastic noise i e each data point having a different covariance matrix the algorithm is motivated by the recovery of bilinear forms one of the fundamental problems in computer vision which appears whenever the epipolar constraint is imposed or a conic is fit to noisy data points we employ the errors in variables eiv model and show why already at moderate noise levels most available methods fail to provide a satisfactory solution the improved behavior of the new algorithm is due to two factors taking into account the heteroscedastic nature of the errors arising from the linearization of the bilinear form and the use of generalized singular value decomposition gsvd in the computations the performance of the algorithm is compared with several methods proposed in the literature for ellipse fitting and estimation of the fundamental matrix it is shown that the algorithm achieves the accuracy of nonlinear optimization techniques at much less computational cost

optimal solid shells for non linear analyses of multilayer composites ii dynamics abstract we are presenting a simple low order solid shell element formulation having only displacement degrees of freedom dofs i e without rotational dofs that has an optimal number of parameters to pass the patch tests and thus allows for efficient and accurate analyses of large deformable multilayer shell structures using elements at extremely high aspect ratio with the dynamics referred to a fixed inertial frame the elements can be used to analyze multilayer shell structures undergoing large overall motion the formulation of this element is based on the mixed hu washizu variational principle leading to a novel enhancing strain tensor enhanced assumed strain eas method that renders the computation particularly efficient with improved in plane and out of plane bending behavior poisson thickness locking especially in refined analyses of composite structures involving a large number of high aspect ratio layers the energy momentum conserving algorithm in the context of current solid shell element is presented we discuss the eas formulation based on the displacement gradient and its complexity compared to formulation on the green lagrange strain shear locking and curvature thickness locking are treated using the assumed natural strain ans method the element has an optimal combination of the ans method and the minimal number of eas parameters required to pass the plate bending patch test numerical examples involving dynamic analyses with conservation of energy and momentum of multilayer shell structures having a large range of element aspect ratios are presented several implicit direct integration methods with without numerical dissipation are used and compared in terms of the accuracy stability and cost in multilayer shell structure finally we note that the topic in this paper is a fitting dedication to professor ekkehard ramm who has made important pioneering contributions in this research direction

estimation of planar curves surfaces and nonplanar space curves defined by implicit equations with applications to edge and range image segmentation the author addresses the problem of parametric representation and estimation of complex planar curves in 2 d surfaces in 3 d and nonplanar space curves in 3 d curves and surfaces can be defined either parametrically or implicitly with the latter representation used here a planar curve is the set of zeros of a smooth function of two variables x y a surface is the set of zeros of a smooth function of three variables x y z and a space curve is the intersection of two surfaces which are the set of zeros of two linearly independent smooth functions of three variables x y z for example the surface of a complex object in 3 d can be represented as a subset of a single implicit surface with similar results for planar and space curves it is shown how this unified representation can be used for object recognition object position estimation and segmentation of objects into meaningful subobjects that is the detection of interest regions that are more complex than high curvature regions and hence more useful as features for object recognition

on the structure of c0 semigroups of holomorphic caratheodory isometries in hilbert space abstract we establish closed formulas for all strongly continuous one parameter semigroups of holomorphic caratheodory isometries of the unit ball of a hilbert space in terms of spectral resolutions of skew self adjoint dilations related to the reich shoikhet nonlinear infinitesimal generator

unitary highest weight representations in hilbert spaces of holomorphic functions on infinite dimensional domains abstract automorphism groups of symmetric domains in hilbert spaces form a natural class of infinite dimensional lie algebras and corresponding banach lie groups we give a classification of the algebraic category of unitary highest weight modules for such lie algebras and show that infinite dimensional versions of the lie algebras s o 2 n have no unitary highest weight representations and thus do not meet the physical requirement of having positive energy highest weight modules correspond to unitary representations of global banach lie groups realized in hilbert spaces of vector valued holomorphic functions on the relevant domains in hilbert spaces the construction of such holomorphic representations of certain banach lie groups followed by the application of the general framework of harish chandra type groups in an appropriate banach setting leads to the integration of the lie algebra representation to a group representation the extension of this theory to infinite dimensional settings is explored

on the zelmanovian classification of prime jb triples complex jb triples are complex banach spaces endowed with a triple product subjected to suitable conditions of algebraic and analytic nature see section 1 for the definition they were introduced by w kaup in order to provide an algebraic setting for the study of bounded symmetric domains in complex banach spaces the open unit ball of every complex jb triple is a bounded symmetric domain ka1 and every bounded symmetric domain in any complex banach space is bi holomorphically equivalent to the open unit ball of a suitable complex jb triple ka3 fundamental examples of complex jb triples are provided by complex c algebras with triple product defined by xyz x 1 2 xy z zy x 1

a large rotation finite element analysis of 3d beams by incremental rotation vector and exact strain measure with all the desirable features abstract different strategies based on rotation vector and exact strain measure have been proposed over the years for analyzing flexible bodies undergoing arbitrary large rotations to avoid the singularity of the vector like parametrization the interpolation of the incremental rotation vector is the most popular approach in this context even if this leads to path dependence and numerical instability i e error accumulation it is also non objective although both objectivity and path independence are recovered with h and p refinement corotational approaches do not have these drawbacks even though the geometrically exact model is achieved by mesh refinement in this work we develop a novel strategy which uses the incremental nodal rotation vectors to define corotational nodal rotations which are then interpolated for the evaluation of the nonlinear strains this choice makes the approach singularity free allows for additive updates within each increment and preserves all the features of the theoretical problem for any mesh and interpolation rotational variables objectivity exact strain measure path independence and symmetric stiffness matrix for conservative loads this last property is a consequence of the direct differentiation of the relation between local and global rotations whose compact form also makes a simple and general definition of the internal forces and the tangent stiffness for any order of interpolation possible in addition we show how the common approach of interpolating incremental vectors can be made stable by a simple updating procedure based on local rotations carried out at the end of each increment in order to avoid cumulative errors geometrically exact 3d beams are considered as a demonstrative example an iterative strategy based on mixed integration points is used to solve the nonlinear discrete equations efficiently

iteration of holomorphic maps on lie balls abstract we investigate iterations of fixed point free holomorphic self maps on a lie ball of any dimension where a lie ball is a bounded symmetric domain and the open unit ball of a spin factor which can be infinite dimensional we describe the invariant domains of a holomorphic self map f on a lie ball d when f is fixed point free and compact and show that each limit function of the iterates f n has values in a one dimensional disc on the boundary of d we show that the mobius transformation g a induced by a nonzero element a in d may fail the denjoy wolff type theorem even in finite dimension we determine those which satisfy the theorem