efficient modification scheme of stress strain tensor for wrinkled membranes a new modification scheme of the stress strain tensor for wrinkled membranes is presented on the basis of the tension field theory the scheme is applicable to finite element analysis of partly wrinkled membranes with arbitrary shapes derivation of the modification scheme rests on an introduction of the so called wrinkle strain and a simplification of the virtual work equation of wrinkled membranes because all of the modifications required to account for wrinkling are totally confined within the stress strain relations of membranes the scheme can be easily implemented with existing finite element codes furthermore the modified stress strain tensor automatically leads to the consistent tangent stiffness matrix where changes in both the wrinkling direction and the amount of wrinkliness are taken into account three numerical examples are treated to show the accuracy and effectiveness of the proposed modification scheme

simple diagonal locally finite lie algebras the ground field f is an algebraically closed field of zero characteristic and bbb n is the set of natural numbers let l be a locally finite dimensional or em locally finite for brevity lie algebra assume for simplicity that l has countable dimension then one can choose finite dimensional subalgebras l i i in bbb n of l in such a way that l i subset l i 1 for all i and l bigcup i in bbb n l i the set l i mid i in bbb n is called a em local system of l assume that l is simple then all l i can be chosen to be perfect that is l i l i l i we shall call such local systems em perfect let s i s i 1 oplus ldots oplus s i n i be a levi subalgebra of l i where s i 1 ldots s i n i are simple components of s i and let v i k be the standard s i k module since l i is perfect for every k there exists a unique irreducible l i module cal v i k such that the restriction cal v i k downarrow s i k is isomorphic to v i k an embedding l i to l i 1 is called em diagonal if for each l any non trivial composition factor of the restriction cal v i 1 l downarrow l i is isomorphic to cal v i k or its dual cal v i k for some k we prove that a simple locally finite lie algebra l can be embedded into a locally finite associative algebra if and only if there exists a perfect local system l i i in bbb n of l such that all embeddings l i to l i 1 are diagonal note that this result can be considered as a version of ado s theorem for simple locally finite lie algebras let v be a vector space an element x in frak gl v is called em finitary if dim xv infty the finitary transformations of v form an ideal frak fgl v of frak gl v and any subalgebra of frak fgl v is called a em finitary lie algebra we classify all finitary simple lie algebras of countable dimension it turns out that there are only three frak sl infty f frak so infty f and frak sp infty f the author has classified all finitary simple lie algebras and will describe this in a subsequent paper the analogous problem in group theory has been recently solved by j i hall he classified simple locally finite groups of finitary linear transformations 1991 mathematics subject classification 17b35 17b65

comparisons of nonnegative splittings of matrices abstract the comparison of the asymptotic rates of convergence of two iteration matrices induced by two splitting of the same matrix has arisen in the work of many authors in this article some new comparison theorems for two nonnegative splittings a splitting a m n is nonnegative if m 1 exist and m 1 n is nonnegative are derived they extend the known results in the literature in addition we also point out three incorrect conditions in a paper by beauwens furthermore we give some reasonable conditions ensuring the strict inequality between the asymptotic convergence rates this also answers the open question which additional and appropriate conditions should be imposed on miller neumann splittings to obtain strict inequality finally some applications to a class of generalized aor sor and jor iterative methods whose special cases imply block also point aor sor and jor iterative methods for solving linear systems are discussed

some comparison theorems for nonnegative splittings of matrices in a recent paper the author has proposed some theorems on the comparison of the asymptotic rates of convergence of two nonnegative splittings they extended the corresponding result of miller and neumann and implied the earlier theorems of varga beauwens csordas and varga an open question by miller and neumann which additional and appropriate conditions should be imposed to obtain strict inequality was also answered this article continues to investigate the comparison theorems for nonnegative splittings the new results extend and imply the known theorems by the author miller and neumann

inflating a flat toroidal membrane abstract a flat toroidal geometry composed of a stack of two flat annular membranes bonded together at the inner and outer boundaries equators is proposed the finite inflation mechanics of the composite membrane under uniform internal pressure is considered the membranes are assumed to be identical homogeneous and isotropic solids described by the gent hyperelastic model with a relaxed strain energy density function the variational inflation mechanics problem yields the governing equations and boundary conditions which are recast as a nonlinear two point boundary value problem in a suitable form for efficient computation the effects of the inflation pressure and material properties on the state of stretch and geometry of the inflated toroidal membrane are obtained which exhibit a number of desirable features the phenomenon of wrinkling instability is observed near the outer equator of the torus at low pressures in spite of a positive gaussian curvature which is exactly opposite to the behavior observed in a curved torus wrinkling at the inner equator at high pressure semi analytical expressions of the cauchy stress resultants are obtained which match well with the numerical computations further the limit point instability pressure of the toroidal membrane is shown to have a remarkable power law dependence on a geometric parameter of the uninflated flat torus and the material chain extensibility parameter involving two universal constants

branching laws for tensor modules over classical locally finite lie algebras abstract let g and g be isomorphic to any two of the lie algebras gl sl sp and so let m be a simple tensor g module we introduce the notion of an embedding g g of general tensor type and derive branching laws for triples g g m where g g is an embedding of general tensor type more precisely since m is in general not semisimple as a g module we determine the socle filtration of m over g due to the description of embeddings of classical locally finite lie algebras given by dimitrov and penkov in 2009 our results hold for all possible embeddings g g unless g gl

numerical study of the wrinkling of a stretched thin sheet a thin sheet clamped at opposite ends and stretched develops wrinkles parallel to the direction of the applied tensile strain due to the hindered poisson lateral contraction at the clamps to study this phenomenon a variational model recently proposed by puntel deseri and fried is adopted the relevant energy functional includes bending and membranal contributions and is minimized subject to a constraint on the area of the mid surface of the sheet a fourth order partial differential equation is henceforth obtained and numerically implemented using b splines predictions are obtained concerning the number of wrinkles critical applied stretches and scaling relationships for wrinkle amplitude and wavelength both a linearized version of the boundary value problem based on the small slope approximation and a fully nonlinear one are considered their results are found to be in good agreement for the whole range of applied stretches taken into account comparisons with previous analytical results by puntel deseri and fried who used different boundary conditions and an ansatz on the deflection function are also provided the numerical results substantially confirm the validity of the analytical predictions the present work provides then an alternative numerical method for the study of wrinkling in thin sheets and supports the use of analytical and semi analytical solutions as viable options for specific geometries though further investigation particularly experimental is still needed extensive comparisons of the results with other studies available in the literature provide confirmation for the scaling laws and signal that predicted values of the critical stretches may only be accurate for higher length to width aspect ratios

a hierarchy of plate models derived from nonlinear elasticity by gamma convergence we derive a hierarchy of plate models from three dimensional nonlinear elasticity by convergence what distinguishes the different limit models is the scaling of the elastic energy per unit volume h where h is the thickness of the plate this is in turn related to the strength of the applied force h membrane theory derived earlier by le dret and raoult corresponds to 0 nonlinear bending theory to 2 von karman theory to 3 4 and linearized vk theory to 3 intermediate values of lead to certain theories with constraints a key ingredient in the proof is a generalization to higher derivatives of our rigidity result 29 which states that for maps v 0 1 3 3 the l2 distance of v from a single rotation is bounded by a multiple of the l2 distance from the set so 3 of all rotations

analysis of pulled axisymmetric membranes with wrinkling the nonlinear behavior of an axisymmetric hyperelastic membrane subjected to pulling forces is analyzed the membrane is considered to be ideal in the sense that it cannot carry compressive stress resultants if the membrane has a positive initial gaussian curvature the pulling gives rise to wrinkles which form over parts of the surface the full nonlinear equations governing the membrane behavior in the doubly tense and in the wrinkled regions are formulated and then solved using a numerical integration procedure solutions for various examples are presented with hookean and neo hookean constitutive behavior these include a few examples of wrinkled membranes with positive initial gaussian curvatures and one example of a membrane with a negative initial gaussian curvature where no wrinkles are formed

new numerical method for two dimensional partially wrinkled membranes based on the introduction of a nonnegative adjustable parameter into poisson s ratio a new numerical method is proposed to solve numerically the partially wrinkled membrane problems with arbitrary complex shapes three fundamental issues in this new method are addressed first a nonnegative adjustable parameter is introduced into the constitutive law automatically representing unwrinkled taut and wrinkled states of a membrane second a parametric variational principle is developed for the new membrane model third by the variational principle the original membrane problem is converted to a nonlinear mathematical programming problem the variational principle and the mathematical programming formulation lay a foundation for efficient numerical analysis of wrinkled membrane structures using finite element discretization three typical examples are given to show the effectiveness of this method

instability investigation on fluid loaded pre stretched cylindrical membranes this paper discusses the evaluation of instabilities on the quasi static equilibrium path of fluid loaded pre stretched cylindrical membranes and the switching to a secondary branch at a bifurcation point the membrane is represented by only the in plane stress components for which an incompressible isotropic hyperelastic material model is assumed the free inflation problem yields governing equations and boundary conditions which are discretized by finite differences and solved by a newton raphson method an incremental arclength cubic extrapolation method is used to find generalized equilibrium paths with different parametrizations limit points and bifurcation points are observed on the equilibrium path when fluid level is seen as the controlling parameter an eigen mode injection method is employed to switch to a secondary equilibrium branch at the bifurcation point a limit point with respect to fluid level is observed for a partially filled membrane when the aspect ratio length radius is high whereas for smaller aspect ratios the limit point with respect to fluid level is observed at over filling pre stretch is observed to have a stiffening effect in the pre limit zone and a softening effect in the post limit zone

equilibrium shapes of inflated inextensible membranes this paper proposes an effective method for directly determining the final equilibrium shapes of closed inextensible membranes subjected to internal pressures with reference to new high performance textile materials we assume that the mechanical response of a fabric membrane can be accurately represented by regarding it as a two state material in the active state the membrane is subject to tensile stresses and is virtually inextensible vice versa in the passive state it is unable to sustain any compressive stress so it contracts freely equilibrium of the membrane in the final configuration is enforced by recourse to the minimum total potential energy principle the lagrange multipliers method is used to solve the minimum problem by accounting for the aforesaid nonlinear constitutive law the set of governing equations is solved for the unknown coordinates of the equilibrium surface points closed form solutions are obtained for fully wrinkled cylindrical and axisymmetric membranes under homogeneous boundary conditions while a simple iterative procedure is used to numerically solve cases of axisymmetric membranes under various inhomogeneous boundary conditions the soundness of the proposed method is verified by comparing the results with solutions available in the literature

remarks on a theory of elasticity for fluid films a theory of elastic fluid films that generalizes classical notions of capillarity is described for the purely mechanical problem restrictions on energy minimizing states are obtained these restrictions are in accord with the experimental findings of kwok et al 1994

the modeling and numerical analysis of wrinkled membranes in this paper three fundamental issues regarding modeling and analysis of wrinkled membranes are addressed first a new membrane model with viable young s modulus and poisson s ratio is proposed which physically characterizes stress relaxation phenomena in membrane wrinkling and expresses taut wrinkled and slack states of a membrane in a systematic manner second a parametric variational principle is developed for the new membrane model third by the variational principle the original membrane problem is converted to a non linear complementarity problem in mathematical programming a parametric finite element discretization and a smoothing newton method are then used for numerical solution the proposed membrane model and numerical method are capable of delivering convergent results for membranes with a mixture of wrinkled and slack regions without iteration of membrane stresses three numerical examples are provided

a koszul category of representations of finitary lie algebras abstract we find for each simple finitary lie algebra g a category t g of integrable modules in which the tensor product of copies of the natural and conatural modules is injective the objects in t g can be defined as the finite length absolute weight modules where by absolute weight module we mean a module which is a weight module for every splitting cartan subalgebra of g the category t g is koszul in the sense that it is antiequivalent to the category of locally unitary finite dimensional modules over a certain direct limit of finite dimensional koszul algebras we describe these finite dimensional algebras explicitly we also prove an equivalence of the categories t o and t sp corresponding respectively to the orthogonal and symplectic finitary lie algebras o sp

on cartan subalgebras abstract in this paper we study the concept of a cartan subalgebra in the context of locally finite and borcherds kac moody lie algebras

rational approximations for ill conditioned equation systems in this study we present iterative methods using rational approximations e g pade approximants which work very well for strongly ill conditioned systems in principle all methods of the family are convergent one type of those methods has the advantage that their convergence behavior is very fast without additional a priori information on the optimal relaxation parameter

cartan subalgebras of root reductive lie algebras abstract root reductive lie algebras are direct limits of finite dimensional reductive lie algebras under injections which preserve the root spaces it is known that a root reductive lie algebra is a split extension of an abelian lie algebra by a direct sum of copies of finite dimensional simple lie algebras as well as copies of the three simple infinite dimensional root reductive lie algebras sl so and sp as part of a structure theory program for root reductive lie algebras cartan subalgebras of the lie algebra gl were introduced and studied in k h neeb i penkov cartan subalgebras of gl canad math bull 46 2003 597 616 in the present paper we refine and extend the results of k h neeb i penkov cartan subalgebras of gl canad math bull 46 2003 597 616 to the case of a general root reductive lie algebra g we prove that the cartan subalgebras of g are the centralizers of maximal toral subalgebras and that they are nilpotent and self normalizing we also give an explicit description of all cartan subalgebras of the simple lie algebras sl so and sp we conclude the paper with a characterization of the set of conjugacy classes of cartan subalgebras of the lie algebras gl sl so and sp with respect to the group of automorphisms of the natural representation which preserve the lie algebra

comparison results between jacobi and other iterative methods some comparison results between jacobi iterative method with the modified preconditioned simultaneous displacement mpsd iteration and other iterations for solving nonsingular linear systems are presented it is showed that spectral radius of jacobi iteration matrix b is less than that of several iteration matrices introduced in liu j numer methods comput appl 1 1992 58 under some conditions

on the convergence of some generalized preconditioned iterative methods this paper generalizes the preconditioning techniques introduced by evans 2 for the numerical solution of the linear system au b and defines two extrapolated versions of the gauss siedel method as well as an extrapolated version of the successive overrelaxation method finally it establishes some convergence theorems for the considered iterative schemes when a has particular properties such as being consistently ordered positive definite having weak diagonal dominance etc

infinite kostant cascades and centrally generated primitive ideals of u n in types a c abstract we study the center of u n where n is the locally nilpotent radical of a splitting borel subalgebra of a simple complex lie algebra g sl c so c sp c there are infinitely many isomorphism classes of lie algebras n and we provide explicit generators of the center of u n in all cases we then fix n with largest possible center of u n and characterize the centrally generated primitive ideals of u n for g sl c sp c in terms of the above generators as a preliminary result we provide a characterization of the centrally generated primitive ideals in the enveloping algebra of the nilradical of a borel subalgebra of sl n c sp 2 n c

inflation of nonlinearly deformed annular elastic membranes abstract the inflation of an isotropic nonlinear elastic membrane by means of a volume independent hydrostatic pressure is studied in particular we consider annular membranes which on the inner boundary have been subjected to an axial twist and a displacement normal to the plane of the membrane with the outer boundary fixed a direct two dimensional approach is adopted and by introducing a relaxed strain energy function the occurrence of wrinkled solutions is considered the governing equations are found to reduce to a system of first order differential equations which are then solved numerically for a mooney rivlin material over a range of boundary value problems

some comparison theorems for weak nonnegative splittings of bounded operators abstract the comparison of the asymptotic rates of convergence of two iteration matrices induced by two splittings of the same matrix has arisen in the works of many authors in this paper we derive new comparison theorems for weak nonnegative splittings and weak splittings of bounded operators in a general banach space and rather general cones and in a hilbert space which extend some of the results obtained by wo nicki japan j indust appl math 11 1994 289 342 and marek and szyld numer math 44 1984 23 35 furthermore we present new theorems also for bounded operator which extend some results by csordas and varga numer math 44 1984 23 35 for weak nonnegative splittings of matrices

incremental stresses in loaded orthotropic circular membrane tubes i theory abstract starting from the equations of general elastic nonlinear membrane theory in intrinsic form the equations governing the incremental state of stress in an orthotropic circular membrane tube are derived and discussed the tube is initially subjected to uniform internal pressure and to longitudinal extension which lead to large homogeneous deformation then some changes in loading and or geometry are considered e g an additional load is applied the shape of the boundary is changed or a slit is formed in the membrane these changes are regarded as small perturbations on the initial homogeneous state of stress the general form as well as some simplified forms of the equations are presented leading finally to a set of two equations in terms of two scalar potential functions two different variational formulations for the problem are also presented each of which may serve as a basis for numerical treatment

a novel variational algorithmic formulation for wrinkling at finite strains based on energy minimization application to mesh adaption this paper is concerned with an efficient novel algorithmic formulation for wrinkling at finite strains in contrast to previously published numerical implementations the advocated method is fully variational more precisely the parameters describing wrinkles or slacks together with the unknown deformation mapping are computed jointly by minimizing the potential energy of the considered mechanical system furthermore the wrinkling criteria are naturally included within the presented variational framework the proposed method allows to employ three dimensional constitutive models without any additional modification i e a projection in plane stress space is not required analogously to the wrinkling parameters the non vanishing out of plane component of the strain tensor results conveniently from relaxing the respective helmholtz energy of the membrane the proposed framework is very general and does not rely on any assumption regarding the symmetry of the material i e arbitrary anisotropic hyperelastic models can be consistently taken into account the advantages associated with such a variational method are manifold for instance it opens up the possibility of applying standard optimization algorithms to the numerical implementation this is especially important for highly non linear or singular problems such as wrinkling on the other hand minimization principles provide a suitable basis for a posteriori error estimation and thus for adaptive finite element formulations as a prototype a variational error indicator leading to an efficient h adaption for wrinkling is briefly discussed the performance of the wrinkling approach is demonstrated by selected finite element analyses

anisotropic membrane wrinkling theory and analysis abstract a complete theory of wrinkling of anisotropic elastic membranes is presented based on the notion of relaxed energy function the theory is obtained as a particular case of a general theory of saturated elasticity it is shown that when any given hyperelastic constitutive law is supplemented with a saturation condition the right cauchy green strain tensor abides by an additive decomposition law governed by a normality rule for the case of wrinkling these results are implemented into a numerical procedure and examples are presented

a variational formulation for finite deformation wrinkling analysis of inelastic membranes this paper is concerned with a novel fully variational formulation for finite deformation analysis of inelastic membranes with wrinkling in contrast to conventional approaches every aspect of the physical problem derives from minimization of suitable energy functionals a variational formulation of finite strain plasticity theory which leads to a minimization problem for the constitutive updates serves as the starting point for the derivations in order to take into account the kinematics induced by wrinkles and slacks a relaxed version of the finite strain functional is postulated in effect the local incremental stress strain relations are established via differentiation of the relaxed energy functional with respect to the strains hence the presented formulation is fully analogous to that of hyperelasticity with the sole exception that the aforementioned functional depends on history variables and accordingly it is path dependent the advantages associated with the developed variational method are manifold from a practical point of view the possibility of applying standard optimization algorithms to solve the minimization problem describing inelastic membranes is remunerative from a mathematical point of view on the other hand the energy of the system induces some sort of natural metric representing an essential requirement for error estimation and thus for adaptive finite element methods the presented derivation of the model allows to consider possible material symmetries in the elastic as well as plastic response of the material as a prototype a von mises type model is implemented the efficiency and performance of the resulting algorithm are demonstrated by means of numerical examples

elastic surface substrate interactions a theory for three dimensional finite deformations of elastic solids with conforming elastic films attached to their bounding surfaces is described the gurtin murdoch theory incorporating elastic resistance of the film to strain is generalized to account for the effects of intrinsic flexural resistance this modification yields a model that can be used to describe equilibrium deformations in the presence of compressive surface stress fields an associated variational theory is given and material symmetry considerations are discussed the theory is illustrated by examples

finite element analysis of dynamic response of wrinkling membranes a new iterative scheme for finite element analysis of wrinkling membranes originally devised for static analysis is extended for analyzing dynamic response of wrinkling membranes the scheme is found to be successfully implemented with an explicit total lagrangian finite element code based upon the central difference method the finite element implementation of the scheme is straightforward and only minor modifications are needed for existing membrane finite element codes in light of application for contact impact discussed are a couple of existing contact algorithms which are well suited for treating contact impact of wrinkling membranes with rigid bodies the validity of the scheme is demonstrated via a numerical simulation of an inflating automotive airbag made of orthotropic membranes under impulse pressure loading

locally semisimple and maximal subalgebras of the finitary lie algebras gl sl so and sp abstract we describe all locally semisimple subalgebras and all maximal subalgebras of the finitary lie algebras gl sl so and sp for simple finite dimensional lie algebras these classes of subalgebras have been described in the classical works of a malcev and e dynkin

differential equation for the amplitude of wrinkles introduction t he renewed interest in the phenomenonof wrinkling of membranes fueled by applications to the aerospace industry has spurred considerable activity on both the theoretical and computational aspectsof the subject althoughthe wrinklingphenomenonis known to be a case of shell buckling it seems unwise to utilize this knowledge in actual computations because treating the membrane as a shell with a vanishinglysmall thickness leads to the frustrating effects of numerical instability there exist on the other hand techniques based on themembrane theory alone that permit us to obtain with relative ease and numerical robustness not only the extent of thewrinkledzones but also the eldof directionsof thewrinkles 1i4 all that is needed therefore is a means for calculating the amplitude and wavelength of the wrinkles in an already known wrinkled domain in this note we derive an ordinary differential equation whose solution delivers such information for clarity of the presentation the equation is obtained under a number of simplifying assumptions mostly involving the smallness of the deformations however the method is straightforwardlyextendable to the general case our guiding principle has been to keep only those aspects of the model that are clearly determinant of the result while leaving all other aspects for future re nement we believe that this philosophy will serve to highlight the essential features rather than the technicalities of the proposedequation note that even under a geometrically andmaterially linear regime the resultingdifferentialequation is highly nonlinear the physical reason for this nonlinearityis to be foundin that becausewrinklingentailsno stress in thedirectionperpendicular to the wrinkles there exists a severe constraint between the wavelength and amplitude of the wrinkles this can be phrased intuitively as follows for a given amount of wrinkling strain the larger the number of wrinkles the smaller their amplitude to the best of our knowledge the only attempt in a direction similar to the one proposed herein is due to wong and pellegrino in their work these authors present a model basedmainly on the particular case of shearing of a rectangular panel their results are very valuable and will be used here as a benchmark for validation purposes

comparison theorems for weak splittings of bounded operators comparison theorems for weak splittings of bounded operators are presented these theorems extend the classical comparison theorem for regular splittings of matrices by varga the less known result by wo nicki and the recent results for regular and weak regular splittings of matrices by neumann and plemmons elsner and lanzkron rose and szyld the hypotheses of the theorems presented here are weaker and the theorems hold for general banach spaces and rather general cones hypotheses are given which provide strict inequalities for the comparisons it is also shown that the comparison theorem by alefeld and volkmann applies exclusively to monotone sequences of iterates and is not equivalent to the comparison of the spectral radius of the iteration operators

three dimensional analysis of wrinkled membranes using modification scheme of stress strain tensor three dimensional finite element analysis using conventional membrane elements tends to be numerically unstable because of their lack of bending stiffness additionally membrane structures are highly susceptible to localized buckling posing further numerical difficulties in this paper a modified stress strain tensor recently proposed by the authors to account for membrane wrinkling is applied to three dimensional finite element analysis of membrane structures with the aim to overcome the preceding numerical difficulties it is found through numerical investigations that the use of the modified stress strain tensor renders the iterative solution process remarkably stable and enables one to obtain the converged solution for those problems that are difficult to solve using conventional membrane elements

tension field theory a general theory of the tension field is developed for application to the analysis of wrinkling in isotropic elastic membranes undergoing finite deformations the principal contribution is a partial differential equation describing a geometrical property of tension trajectories this is one of a system of two equations which describes the state of stress independently of the deformation this system is strongly elliptic at any stable solution whereas the deformation is described by a system of parabolic type controllable solutions i e those states that can be maintained in any isotropic elastic material by application of edge tractions and lateral pressure alone are obtained the general axisymmetric problem is solved implicitly and the theory is applied to the solution of two representative examples existing small strain theories are shown to correspond to a singular limit of the general theory at which the underlying system changes from elliptic to parabolic type

a new computational framework for materials with different mechanical responses in tension and compression and its applications abstract materials possessing tension compression asymmetric behavior can be simulated by a bi modulus constitutive relation which assumes the materials have different moduli in tension and compression traditional iteration methods struggle for the convergence difficulty for such kind of constitutive model in this paper a new computational framework is established solution procedures under both small and finite deformations which have asymptotically quadratic rate of convergence have also been proposed and implemented in abaqus with umat numerical examples show that the proposed computational framework can be applied successfully to simulate the wrinkling analysis of thin plane membranes and explain some unusual cell mechanosensing phenomena