co rotational beam elements with warping effects in instability problems the present paper investigates the formulation of 3d co rotational beam elements for the buckling and post buckling analysis of frame structures following pacoste and eriksson comput methods app

global smoothing of calabi yau threefolds yoshinori namikawa i j h m steenbrink 2 i department of mathematics sophia university kioi cho tokyo 102 japan 2 mathematical institute university of nijmegen toernooiveld 6525 ed nijmegen the netherlands oblatum 10 x 1994 13 vi 1995 introduction friedman fr has studied the relationship between local and global deforma tions of a threefold z with isolated hypersurface singularities which admits small resolutions one of his main results is as follows let z be a moishezon threefold with only ordinary double points pl p assume that the canon ical line bundle

structural instability analyses based on generalised path following this paper describes how quasi static conservative instability problems can be completely described using generalised path following procedures for augmented equilibrium formulations in particul

element formulation and numerical techniques for stability problems in shells in the context of instability problems in shells or shell like structures the objective of the present paper is twofold primarily the paper describes how quasi static conservative instability problems can be considered in a multi parametric context where generalized path following procedures for augmented equilibrium problems are used as computational tools these allow systematic treatment of the higher dimensional solution sets generated under the variations of certain parameters deemed relevant for the given problem the efficient implementation of the above mentioned procedures requires however as an essential ingredient a non linear finite element which is not only accurate but also inexpensive to this end a systematic view on a corotational total lagrangian formulation is described the tric element of argyris and coworkers is slightly modified and introduced as core element formulation special emphasis is given to the alternative methods for treatment of finite three dimensional rotations with reference to both the element definition and solution algorithms numerical examples verify the element capabilities and the possibility to completely describe instability phenomena of large discretized models

polarized endomorphisms of complex normal varieties it is shown that a complex normal projective variety has non positive kodaira dimension if it admits a non isomorphic quasi polarized endomorphism the geometric structure of the variety is described by methods of equivariant lifting and fibrations

numerical analysis of complex instability behaviour using incremental iterative strategies the paper describes how quasi static conservative instability problems can be analysed in a multi parametric space using generalised path following procedures for augmented equilibrium problems

building blocks of amplified endomorphisms of normal projective varieties let x be a normal projective variety a surjective endomorphism f x rightarrow x is int amplified if f l l h for some ample cartier divisors l and h this is a generalization of the so called polarized endomorphism which requires that f h sim qh for some ample cartier divisor h and q 1 we show that this generalization keeps all nice properties of the polarized case in terms of the singularity canonical divisor and equivariant minimal model program

groupes commutatifs d automorphismes d une variete kahlerienne compacte let v be a compact kahler manifold let gbe a commutative subgroup of aut v and u the set of elements of zero entropy of g then u is a group and gis isomorphic to the direct product g u g where g is a subgroup of gsuch that all elements of g id are of positive entropy moreover g is a free commutative group with rank g dim v 1 the estimate is sharp when rank g dim v 1 u is finite rank g satisfies other inequalities involving the dimensions of dolbeault cohomology groups of v

a consistent co rotational formulation for non linear three dimensional beam elements abstract this paper describes a co rotational formulation for three dimensional beams in which both the internal force vector and tangent stiffness matrix are consistently derived from the adopted strain measures the latter relate to standard beam theory but are embedded in a continuously rotating frame a set of numerical examples show that the element provides an excellent numerical performance

a geometrical nonlinear eccentric 3d beam element with arbitrary cross sections abstract in this paper a finite element formulation of eccentric space curved beams with arbitrary cross sections is derived based on a timoshenko beam kinematic the strain measures are derived by exploitation of the green lagrangean strain tensor thus the formulation is conformed with existing nonlinear shell theories finite rotations are described by orthogonal transformations of the basis systems from the initial to the current configuration since for arbitrary cross sections the centroid and shear center do not coincide torsion bending coupling occurs in the linear as well as in the finite deformation case the linearization of the boundary value formulation leads to a symmetric bilinear form for conservative loads the resulting finite element model is characterized by 6 degrees of freedom at the nodes and therefore is fully compatible with existing shell elements since the reference curve lies arbitrarily to the line of centroids the element can be used to model eccentric stiffener of shells with arbitrary cross sections

beam elements in instability problems this paper deals with the formulation of beam elements for the numerical analysis of instability phenomena in frame type structures total versus co rotational approaches are discussed comparatively for both two dimensional and three dimensional problems and the similarities between the two types are outlined in the context of 3d beam elements special attention is given to the parameterisation of the orthogonal transformation used to define the rotational field of the beam the technique advocated in the paper is based on the so called rotational vector this leads to symmetric stiffness matrices and avoids the need for special updating procedures for the rotational variables a set of test problems for which the critical behaviour is governed by fold cusp and butterfly catastrophes is used to assess the performances of the considered element types it is shown that analytically verified identities in element formulation also hold in numerical application the examples also show how complex instability behaviour can be reproduced by all elements where sufficient accuracy is introduced into the kinematic expressions the analytical derivation of element expressions with symbolic manipulations from stated basic assumptions is consistently used in the paper

automorphism groups of positive entropy on minimal projective varieties abstract we determine the geometric structure of a minimal projective threefold having two independent and commutative automorphisms of positive topological entropy and generalize this result to higher dimensional smooth minimal pairs x g as a consequence we give an effective lower bound for the first dynamical degree of these automorphisms of x fitting the boundary case

a numerical criterion for uniruledness an n dimensional variety x over an algebraically closed field k is said to be uniruled if there exist an n 1 dimensional k variety w and a dominant rational map f p x w x x is called separably uniruled if f is a separable map i e k p x w is a finite separable extension of k x via f if x is uniniled then there exists a rational curve passing through a general k valued point of x and the converse is true by the countability of the components of the hilbert scheme provided that the ground field k is uncountable uniruled varieties are of importance in the classification of varieties it is conjectured that in characteristic 0 uniruledness is equivalent to k xc this article gives a numerical criterion for a projective variety to be uniruled

salem numbers in dynamics on kahler threefolds and complex tori let x be a compact kahler manifold of dimension k le 4 and f x rightarrow x a pseudo automorphism if the first dynamical degree lambda 1 f is a salem number we show that either lambda 1 f lambda k 1 f or lambda 1 f 2 lambda k 2 f in particular if dim x 3 then lambda 1 f lambda 2 f we use this to show that if x is a complex 3 torus and f is an automorphism of x with lambda 1 f 1 then f has a non trivial equivariant holomorphic fibration if and only if lambda 1 f is a salem number if x is a complex 3 torus having an automorphism f with lambda 1 f lambda 2 f 1 but is not a salem number then the picard number of x must be 0 3 or 9 and all these cases can be realized

on isolated singularities with a noninvertible finite endomorphism abstract we prove that if x 0 x 0 is a finite endomorphism of an isolated singularity such that deg 2 and is etale in codimension 1 then x is q gorenstein and log canonical

ergodic properties of rational mappings with large topological degree let x be a projective manifold and f x x a rational mapping with large topological degree dt ek 1 f the k 1 th dynamical degree of f we give an elementary construction of a probability measure ef such that d n t fn ef for every smooth probability measure on x we show that every quasiplurisubharmonic function is ef integrable in particular ef does not charge either points of indeterminacy or pluripolar sets hence ef is f invariant with constant jacobian f ef dt ef we then establish the main ergodic properties of ef it is mixing with positive lyapunov exponents preimages of hmost h points as well as repelling periodic points are equidistributed with respect to ef moreover when dimc x 3 or when x is complex homogeneous ef is the unique measure of maximal entropy

equilibrium subsets for multi parametric structural analysis the paper discusses multi parametric formulations for structural equilibrium problems by seeking subsets of equilibrium states which also fulfil extra conditions more detailed information on structural behaviour can be obtained these conditions can be related to analyses of e g critical behaviour imperfections or optimisation the paper shows a general problem setting and some interesting augmentations a solution method for the special case of one dimensional equilibrium subsets is described the algorithm is a generalisation of a path following algorithm where new methods are developed for the evaluation of the path tangent and for the isolation of special solution points examples are used to show the properties and the possibilities of the ideas

positions of convex bodies associated to extremal problems and isotropic measures abstract we show that there are close relations between extremal problems in dual brunn minkowski theory and isotropic type properties for some borel measures on the sphere the methods we use allow us to obtain similar results in the context of firey brunn minkowski theory we also study reverse inequalities for dual mixed volumes which are related with classical positions such as l position or isotropic position

canonical desingularization in characteristic zero by blowing up the maximum strata of a local invariant this article contains an elementary constructive proof of resolution of singularities in characteristic zero our proof applies in particular to schemes of finite type and to analytic spaces so we recover the great theorems of hironaka we introduce a discrete local invariant rm inv x a whose maximum locus determines a smooth centre of blowing up leading to desingularization to define rm inv x we need only to work with a category of local ringed spaces x x cal o x satisfying certain natural conditions if a in x then rm inv x a depends only on widehat cal o x a more generally rm inv x is defined inductively after any sequence of blowings up whose centres have only normal crossings with respect to the exceptional divisors and lie in the constant loci of rm inv x cdot the paper is self contained and includes detailed examples one of our goals is that the reader understand the desingularization theorem rather than simply know it is true

finite element analysis of two and three dimensional elasto plastic frames the natural approach abstract the paper presents a finite element analysis of large deformations in elasto plastic frames attention is focused on the step by step analysis of the nonlinear behaviour of such structures advantage is taken of the so called natural formulation in terms of the generalised cross sectional forces limit state functions applying to different loading conditions and frame geometries are implemented into a computer program a number of test examples illustrate practical applications

a geometrically exact rod model incorporating shear and torsion warping deformation abstract a fully nonlinear three dimensional rod model is developed that incorporates transverse shear and torsion warping deformation the geometric setting is that of a constrained body model with configuration space modeled on r3 so 3 r a differentiable manifold the proposed model incorporates the classical notion of bi moment and bi shear in a fully nonlinear geometrically exact context explicit properly invariant constitutive equations that generalize those of the linearized theory are developed the underlying variational formulation of the model is discussed and computational procedures employing a galerkin projection are addressed numerical examples are presented that illustrate the performance of the formulation

a theorem of tits type for compact kahler manifolds we prove a theorem of tits type about automorphism groups for compact kahler manifolds which has been conjectured in the paper 9

families of rationally connected varieties recall that a proper variety x is said to be rationally connected if two general points p q x are contained in the image of a map g p x this is clearly a birationally invariant property when x is smooth this turns out to be equivalent to the a priori weaker condition that two general points can be joined by a chain of rational curves and also to the a priori stronger condition that for any finite subset x there is a map g p x whose image contains and such that gtx is an ample bundle

theory and numerics of three dimensional beams with elastoplastic material behaviour a theory of space curved beams with arbitrary cross sections and an associated finite element formulation is presented within the present beam theory the reference point the centroid the centre of shear and the loading point are arbitrary points of the cross section the beam strains are based on a kinematic assumption where torsion warping deformation is included each node of the derived finite element possesses seven degrees of freedom the update of the rotational parameters at the finite element nodes is achieved in an additive way applying the isoparametric concept the kinematic quantities are approximated using lagrangian interpolation functions since the reference curve lies arbitrarily with respect to the centroid the developed element can be used to discretize eccentric stiffener of shells due to the implemented constitutive equations for elastoplastic material behaviour the element can be used to evaluate the load carrying capacity of beam structures copyright 2000 john wiley sons ltd

simple hironaka resolution in characteristic zero building upon work of villamayor and bierstone milman we give a proof of the canonical hironaka principalization and desingularization the idea of homogenized ideals introduced in the paper gives a priori the canonicity of algorithm and radically simplifies the proof

building blocks of etale endomorphisms of complex projective manifolds etale endomorphisms of complex projective manifolds are constructed from two building blocks up to isomorphism if the good minimal model conjecture is true they are the endomorphisms of abelian varieties and the nearly etale rational endomorphisms of weak calabi yau varieties

rationality of rationally connected threefolds admitting non isomorphic endomorphisms we prove a structure theorem for non isomorphic endomorphisms of weak q fano threefolds cf theorem 1 3 or more generally for threefolds with big anti canonical divisor also provided is a criterion for a fibred rationally connected threefold to be rational as a consequence we show without using the classification that every smooth fano threefold having a non isomorphic surjective endomorphism is rational

potential density of rational points on the variety of lines of a cubic fourfold we prove the potential density of rational points on the variety of lines of a sufficiently general cubic fourfold defined over a number field where sufficiently general means that a condition of terasoma type is satisfied these varieties have trivial canonical bundle and have geometric picard number equal to one

algebraic varieties with automorphism groups of maximal rank we confirm to some extent the belief that a projective variety x has the largest number relative to the dimension of x of independent commuting automorphisms of positive entropy only when x is birational to a complex torus or a quotient of a torus we also include an addendum to an early paper zhang in adv math 225 2332 2340 2010 though it is not used in the present paper

finite rotation analysis and consistent linearization using projectors abstract a systematic procedure is presented that may be used to extend the capabilities of an existing linear finite element to accomodate finite rotation analysis this procedure is a generalization of the work presented in computers and structures volume 30 pp 257 267 the basis of our approach is the element independent co rotational algorithm where the element rigid body motion translations and rotations is separated from the deformational part of its total motion the variation of this co rotational relation results in a projector matrix with the property that a consistent internal force vector is invariant under its action the consistent tangent stiffness matrix is shown to depend on this invariance condition through the derivative of the projector this results in an unsymmetric tangent matrix whose anti symmetric part depends on the out of balance force vector in this paper we prove that using the symmetric part of the tangent matrix the newton iteration retains its quadratic rate of convergence this approach has been used to solve a number of large rotation test example problems the results demonstrate that it is possible to analyze structures undergoing large rotations within a general co rotational framework using simple and economical finite elements the resulting improvements in the performance of these simple elements are brought about through the use of convenient software utilities as pre and post processors to the element routines

element behavior in post critical plane frame analysis depending on the type of uni modal cuspoid catastrophe which governs the local behavior of a structure at a simple critical point correct prediction of the post critical path requires an accurat

co rotational flat facet triangular elements for shell instability analyses abstract this paper investigates the formulation of co rotational flat facet triangular elements for the numerical analysis of instability phenomena in shell structures the elements have three nodes with six degrees of freedom at each node the term co rotational relates here to the provision of a local system that continuously rotates and translates with the element following mainly nour omid and rankin b nour omid and c c rankin finite rotation analysis and consistent linearization using projectors comput methods appl mech engrg 93 1991 353 384 the definition of an element resorts to a change of variables from the local frame to the global one this is done through the use of a projector matrix which relates the variations of the local displacements to the variations of the global ones by extracting the rigid body modes from the latter the main difference from the original formulation lies in the parameterization of 3d finite rotations in contrast to the paper by nour omid and rankin a parameterization based on the rotational vector is here adopted and thus an additional change of variables has to be performed as a result the rotational variables become additive and the necessity of a special updating procedure is avoided the main feature of the adopted formulation is its independence of the local assumptions used to derive the internal forces and tangent stiffness in local coordinates for a certain class of elements i e elements with the same number of nodes and degrees of freedom the main co rotational framework is the same using this property three types of local formulations are considered a set of carefully chosen test problems is used in order to assess the performances of the three element types