material state remapping in computational solid mechanics a computational procedure for remapping material state information from one finite element mesh to another is described the procedure is useful in connection with evolving meshes for inelastic problems as for example occur in the context of fracture simulation and adaptive mesh refinement the proposed method is based on weak enforcement of equality between corresponding fields on the two meshes where piecewise constant fields on both meshes are generalized from the quadrature point values the essential algorithmic problem is that of calculating the volume partition of an arbitrary convex region with respect to a covering set of disjoint convex regions instead of geometrically resolving the associated intersections the problem is herein approximated by a constrained optimization problem which may be readily and efficiently solved computationally this formulation is a main contribution of the paper computational examples are given that illustrate the effectiveness of the proposed procedure copyright 2002 john wiley sons ltd

central limit theorems for nonlinear functionals of stationary gaussian processes let x x t t be a stationary gaussian process on p leth x be the hilbert space of variables inl2 p which are measurable with respect tox and let u s s be the associated family of time shift operators we sayy h x withe y 0 satisfies the functional central limit theorem or fclt respectively the central limit theorem of clt if in respectively where y t t equiv int limits 0 tt u s circ yds mathord left vphantom int limits 0 tt u s circ yds left var left int limits 0 t u s circ yds right right 1 mathord left vphantom 1 2 right kern nulldelimiterspace 2 right kern nulldelimiterspace left var left int limits 0 t u s circ yds right right 1 mathord left vphantom 1 2 right kern nulldelimiterspace 2 andw is a standard wiener process on 0 1 this paper provides some general sufficient conditions onx andy ensuring thaty satisfies the clt or fclt examples ofy are given which satisfy the clt but not the fclt this work extends clt s of maruyama 1976 and breuer and major 1983

convergence analysis of a finite element method based on different moduli in tension and compression abstract when analyzing materials that exhibit different mechanical behaviors in tension and compression an iterative approach is required due to material nonlinearities because of this iterative strategy numerical instabilities may occur in the computational procedure in this paper we analyze the reason why iterative computation sometimes does not converge we also present a method to accelerate convergence this method is the introduction of a new pattern of shear modulus that was strictly derived according to the constitutive model based on the bimodular elasticity theory presented by ambartsumyan we test this procedure with a numerical example concerning a plane stress problem results obtained from this example show that the proposed method reduces the cost of computation and accelerates the convergence of the solution

noncentral convergence of multiple integrals fix 0 denote by g v 2 a gamma random variable with parameter v 2 and let n 2 be a fixed even integer consider a sequence f k of square integrable random variables belonging to the nth wiener chaos of a given gaussian process and with variance converging to 2v as k goes to infinity we prove that f k converges in distribution to 2g v 2 v if and only if e f k 4 12 e f k 3 tends to 12v 2 48v

reliable and efficient equilibrated a posteriori finite element error control in elastoplasticity and elastoviscoplasticity with hardening this paper establishes the reliability and efficiency of equilibrated a posteriori estimates for l 2 stress error control of conforming displacement finite element approximations of incremental plasticity and viscoplasticity with hardening explicit expressions for upper bounds of the reliability constant that enters the guaranteed upper error bound illustrate its crucial dependence on the hardening material constants numerical experiments show that adaptive finite element solutions with marking strategy based on the max refinement rule and local equilibrated error estimators lead to optimal empirical convergence rates 2005 elsevier b v all rights reserved

nonlinear static and dynamic analysis of shell structures with finite rotation a simple effective finite element incremental formulation and procedure for geometrically nonlinear static and dynamic analysis of a shell structure with finite rotations are presented based on both the total lagrangian and updated lagrangian description of motion the co rotation formulation is used for finite rotation the element employed here to implement the present method is a faceted shell element with loof nodes dkl lst an incremental iterative method based on the constant arc length method in conjunction with newton raphson method is implemented in the present study for static and newmark s integration scheme for dynamic analysis to demonstrate the accuracy and efficiency of the formulations and to compare the difference between the total and updated lagrangian formulation numerical studies are presented 0 1998 elsevier science s a all rights reserved

implantation of a nonlinear capability on a linear software system the present paper proposes a simple procedure which extends with minor additions an existing linear elastic program system aska to geometrically nonlinear applications involving large displacements but small strains such an attempt is of course not new numerous other techniques related to this subject are documented in a large list of publications which have appeared over the last twenty five years or so for the present purpose it suffices to quote in place of an extensive review a few pertinent papers l 8 at the same time we propose to discuss in what follows certain general principles of a geometrically nonlinear finite element analysis and their relation to the present work clearly an extension of a linear computational capability to nonlinear applications demands in the first instance a suitable incrementation procedure pertinent equations determining the so called incremental equilibrium are well known inherent to the concept of an incremental transition from a given equilibrium state to another is the notion of a tangential stiffness matrix of the structure in this context the elastic material stiffness matrix already established for a linear analysis must be supplemented by the geometrical stiffness matrix which expresses the influence of the existing stress state on the incremental condition of equilibrium of the structure simple incrementation of the nonlinear response leads to a desired linearisation of the computational process but also to inevitable accumulating deviations from the true equilibrium solution in a first attempt to remove the error imposed by the linearisation higher order incremental approximations may be employed in the limit this approach leads to a fully nonlinear formulation of the problem for large deflections and entails as a rule software concepts larstran different from those valid in a linear analysis also important in this context is the development and implementation of numerical methods for the solution of the nonlinear governing equations the literature on the subject is still growing and partial overlapping of the methods is unavoidable the treatment of geometrically nonlinear problems is based on the equilibrium condition between internal stresses and applied loads for the unknown deflected configuration of the structure elastic structures do not require a priori an incremental application of the loading which proves however advantageous in the numerical process on the other hand incremen

accurate rigid body modes representation for a nonlinear curved thin shell element for certain highly curved shells such as bellows the formulation of a curved shell finite element with curvilinear displacement components may fail to properly model some rigid body modes even with either the explicit inclusion of rigid body terms or the use of high order displacement functions it is suggested in this paper that the rigid body modes can be properly included if the cartesian displacement components are used a 48 degree of freedom dof curved thin shell element is formulated and both the curvilinear and the cartesian forms are used for this investigation examples of the nonlinear analyses of a bellows shell and a spherical cap are given to demonstrate the advantage of using the cartesian formulation curved elements may also suffer from membrane locking which is caused by the inability of an element to bend without stretching numerical data are presented to show that the present element does not membrane lock some nonlinear examples are also presented to further demonstrate the versatility of this element

a new a posteriori error estimation for nonlinear time dependent finite element analysis abstract in this paper an error on the constitutive law labeled the dissipation error is used to measure the quality of finite element computations of plastic and viscoplastic structures whose behavior is described by internal variables this measure takes into account all the classical sources of error involved in the computation the space discretization the mesh the time discretization and the iterative technique used to solve the nonlinear discrete problem more specifically to quantify the quality of the space and time discretizations two quantities called indicators are introduced the efficiency of both the error and the indicators is shown for several examples

stein s method and exact berry esseen asymptotics for functionals of gaussian fields we show how to detect optimal berry esseen bounds in the normal approximation of functionals of gaussian fields our techniques are based on a combination of malliavin calculus stein s method and the method of moments and cumulants and provide de facto local one term edgeworth expansions the findings of the present paper represent a further refinement of the main results proven in nourdin and peccati probab theory related fields 145 2009 75 118 among several examples we discuss three crucial applications i to toeplitz quadratic functionals of continuous time stationary processes extending results by ginovyan probab theory related fields 100 1994 395 406 and ginovyan and sahakyan probab theory related fields 138 2007 551 579 ii to exploding quadratic functionals of a brownian sheet and iii to a continuous time version of the breuer major clt for functionals of a fractional brownian motion

numerical analysis of time depending primal elastoplasticity with hardening the quasi static elastoplastic evolution problem with combined isotropic and kinematic hardening is considered with emphasis on optimal convergence of the lowest order scheme in each time step of a generalized midpoint scheme such as the implicit euler or the crank nicolson scheme the spatial discretization consists of minimizing a convex but nonsmooth function on a subspace of continuous piecewise linear resp piecewise constant trial functions an a priori error estimate is established for the fully discrete method which for smooth data and a smooth exact solution proves linear convergence as the mesh size tends to zero strong convergence of the time derivatives is established under mild conditions on the mesh and time step sizes numerical experiments confirm our theoretical predictions on the improved spatial convergence and indicate that the crank nicolson scheme is not always superior over the implicit euler scheme in practice

a mixed finite element for shell model with free edge boundary conditions part 3 numerical aspects abstract the mixed formulation for shells which is presented here is based on koiter s model for thin elastic shells the kirchhoff love s kinematical relations being ensured through the use of lagrange multipliers after a brief recall of the mixed variational formulation we give an appropriate choice for finite elements approximation then we develop some aspects related to geometry approximation and numerical implementation in particular in order to overcome membrane locking improvements are suggested and we check the good behaviour of this formulation on some classical examples of published papers

limit theorems for nonlinear functionals of a stationary gaussian sequence of vectors limit theorems for functions of stationary mean zero gaussian sequences of vectors satisfying long range dependence conditions are considered depending on the rate of decay of the coefficients the limit law can be either gaussian or the law of a multiple ito wiener integral we prove the bootstrap of these limit theorems in the case when the limit is normal a sufficient bracketing condition for these limit theorems to happen uniformly over a class of functions is presented

analysis of transfer procedures in elastoplasticity based on the error in the constitutive equations theory and numerical illustration the aim of this work is to illustrate a methodology for the assessment of adaptive strategies for the solution of associative rate independent plasticity problems solved by employing the incremental displacement conforming finite element method this is the first step towards a more rational definition of transfer operators in terms of the ensuing error the motivating idea is the observation that change of data and or finite element mesh from one time interval to the other can be both related to a discontinuity jump of the approximate solution across the time instant t n thus reliable a posteriori estimates will have to depend not only on the time step and finite element mesh size but also on the value of the jump a new error estimate based on the error in the constitutive equations is developed which allows characterization of the discontinuity jump

large deflection analysis of shell structure by using corotational total lagrangian formulation abstract a corotational total lagrangian cr tl formulation using the von karman assumption is presented for the analysis of nonlinear shell problems this formulation is applicable for the nonlinear analysis of shell structures with large rotations but moderate deformations the numerical algorithm used here is an incremental iterative method based on the newton raphson method combined with constant arc length of incremental displacement vector in order to improve the convergence properties of the equilibrium iterations special care is taken in the calculation of the geometric stiffness matrix numerical examples are presented and compared with the results reported in the literature to demonstrate the accuracy and efficiency of the proposed method

information transfer between incompatible finite element meshes application to coupled thermo viscoelasticity this article is concerned with information transfer between non matching finite element meshes such a feature is not new in the literature but we focus herein on a geometric approach to transfer solution fields in order to be as application independent as possible moreover the dedicated case concerns the transfer of finite element fields defined at integration points of the meshes and allows iterative exchange of fields in both directions to do so we propose an extension to the mortar technique that fulfills these goals and that does not suffer from a high computational cost the application is the simulation of a strongly coupled thermo viscoelastic problem with phase transition solved with a partitioning technique

a curved quadrilateral element for static analysis of shells with geometric and material nonlinearities a 48 degrees of freedom quadrilateral element including the effect of both material and geometric nonlinearities is formulated and appropriate numerical procedures are adopted for the development of a systematic and efficient approach for the static nonlinear analysis of general shell structures the element surface is described by a variable order polynomial in curvilinear co ordinates the displacement functions are described by bicubic hermitian polynomials in curvilinear co ordinates without being confined to the assumption of axisymmetry this formulation allows for the treatment of shells with a more general shape and with a complex spread of plastic zones in the formulation for geometric nonlinearity the total lagrangian approach is adopted only small strains and small rotations are allowed in the formulation for plastic deformation the concept of a layered element model is used in the inelastic range the material is assumed to obey the von mises yield criterion and the prandtl reuss flow rule a tangential stiffness formulation is combined with the modified newton raphson iteration method for the solution of nonlinear problems a systematic choice of examples ranging from fiat plates to cylindrical panels and to spherical caps is solved and compared with available solutions to evaluate the recommended formulations and procedures in terms of their accuracy and efficiency

limit theorems for non linear functionals of gaussian sequences we prove limit theorems for sums of non linear functionals of gaussian sequences in certain cases we obtain a non gaussian limit with a norming factor n 0 1 2 the class of functionals we are investigating is a natural enlargement of the class investigated by m rosenblatt in 7 we prove our results by refining the method of the paper 3

a geometrically non linear tensorial formulation of a skewed quadrilateral thin shell finite element a 48 degree of freedom d o f skewed quadrilateral thin shell finite element including the effect of geometrical non linearity is formulated and appropriate numerical procedures are adopted for the development of an efficient approach for the static and dynamic analysis of general thin shell structures the element surface is described by a variable order polynomial in curvilinear co ordinates the displacement functions are described by bicubic hermitian polynomials in curvilinear co ordinates the directions of the curvilinear co ordinates at each nodal point are uniquely defined to coincide with the directions of the boundaries of the element in the present case of a skewed quadrilateral with non orthogonal curvilinear coordinates the coupling terms of the metric tensor and curvature tensor of the surface no longer vanish such as in the case of orthogonal co ordinates the tensor form is used in the setup of the shape functions geometric derivatives stiffness matrix and computer code this allows for the treatment of shells with irregular shapes and variable curvatures to evaluate the efficiency and accuracy of this formulation a systematic list of examples is chosen i linear and non linear static analysis of square and rhombic plates cylindrical and spherical shells ii linear vibrations of trapezoidal flat and curved plates iii large amplitude vibrations of a rhombic plate for the square plate and cylindrical and spherical shell shewed element meshes with various distortion angles are used to study the effect of the distortion angles on the accuracy of the results and to demonstrate the versatility of the present element all results are compared with alternative available solutions including those obtained using regular rectangular meshes pinched thin cylindrical and spherical shells are studied using different skewed meshes and various gauss integration meshes and no membrane locking phenomenon is observed

remarks on limit theorems for nonlinear functionals of gaussian sequences limit theorems for sums of nonlinear functionals of gaussian sequences typically obtain as limit distribution that of a single term in an expansion given by dobrushin 1 for a process subordinate to a gaussian process here we show how one can obtain limit theorems of this type where the limit distribution is that of a full expansion of dobrushin s type

a simple error estimator and adaptive procedure for practical engineerng analysis a new error estimator is presented which is not only reasonably accurate but whose evaluation is computationally so simple that it can be readily implemented in existing finite element codes the estimator allows the global energy norm error to be well estmated and alos gives a good evaluation of local errors it can thus be combined with a full adaptive process of refinement or more simply provide guidance for mesh redesign which allows the user to obtain a desired accuracy with one or two trials when combined with an automatic mesh generator a very efficient guidance process to analysis is avaiable estimates other than the energy norm have successfully been applied giving for instance a predetermined accuracy of stresses

asymptotic behavior of weighted quadratic and cubic variations of fractional brownian motion this note is devoted to a fine study of the convergence of some weighted quadratic and cubic variations of a fractional brownian motion b with hurst index h in 0 1 2 with the help of malliavin calculus we show that correctly renormalized the weighted quadratic variation of b that we consider converges in l 2 to an explicit limit when h 1 4 in the same spirit we also show that correctly renormalized the weighted cubic variation of b converges in l 2 to an explicit limit when h 1 6

mixed models and reduced selective integration displacement models for nonlinear shell analysis simple mixed models are developed for the geometrically nonlinear analysis of shells a total lagrangian description of the shell deformation is used and the analytical formulation is based on a form of the nonlinear shallow shell theory with the effects of transverse shear deformation and bending extensional coupling included the fundamental unknowns consist of eight stress resultants and five generalized displacements of the shell and the element characteristic arrays are obtained by using the hellinger reissner mixed variational principle the polynomial interpolation or shape functions used in approximating the stress resultants are in general of different degree than those used for approximating the generalized displacements the stress resultants are discontinuous at the element boundaries and are eliminated on the element level the equivalence and near equivalence between the mixed models developed herein and displacement models based on reduced selective integration of both transverse shear and extensional energy terms is discussed the use of reduction methods in conjunction with the mixed models is outlined and the advantages of mixed models over displacement models are delineated analytic expressions are derived for the rigid body and spurious or zero energy models for the various mixed models and their equivalent displacement models also the advantages of mixed models over equivalent displacement models are outlined numerical results are presented to demonstrate the high accuracy and effectiveness of the mixed models developed and to compare their performance with other mixed models reported in the literature

a posteriori error estimation and adaptivity for elastoplasticity using the reciprocal theorem we present a posteriori error estimators and adaptive methods for the finite element approximation of nonlinear problems and especially elastoplasticity the main characteristic of the proposed method is the introduction of duality techniques or in other notions the reciprocal theorem for error estimation at an equilibrium point the nonlinear boundary value problem and an additional linearized dual problem are considered the loading of the dual problem is specifically designed for capturing the influence of the errors of the entire domain to the considered variable our approach leads to easy computable refinement indicators for locally or integrally defined variables for instationary problems as elastoplasticity in a first step we neglect the errors due to time discretization and evaluate the error indicators within each time step for a stationary problem the versatility of the presented framework is demonstrated with numerical examples

the geometric stiffness of thick shell triangular finite elements for large rotations this paper is concerned with the development of the geometric stiffness matrix of thick shell finite elements for geometrically nonlinear analysis of the newton type a linear shell element that is comprised of the constant stress triangular membrane element and the triangular discrete kirchhoff mindlin theory dkmt plate element is upgraded to become a geometrically nonlinear thick shell finite element perturbation methods are used to derive the geometric stiffness matrix from the gradient in global coordinates of the nodal force vector when stresses are kept fixed the present approach follows earlier works associated with trusses space frames and thin shells it has the advantage of explicitness and clear physical insight a special procedure tailored to triangular elements is used to isolate pure rotations to enable stress recovery via linear elastic constitutive relations several examples are solved the results compare well with those available in the literature copyright 2005 john wiley sons ltd

adaptive finite element procedures for linear and non linear dynamics this paper discusses implementation and adaptivity of the discontinuous galerkin dg finite element method as applied to linear and non linear structural dynamic problems by the dg method both displacements and velocities are approximated as piecewise bilinear functions in space and time and may be discontinuous at the discrete time levels both implicit and explicit iterative algorithms for solving the resulted system of coupled equations are derived they are third order accurate and while the implicit procedure is unconditionally stable the explicit one is conditionally stable an h adaptive procedure based on the zienkiewicz zhu error estimate using the spr technique is applied numerical examples are presented to show the suitability of the dg method for both linear and non linear structural dynamic analysis copyright 1999 john wiley sons ltd

two finite element approximations of naghdi s shell model in cartesian coordinates we present a penalized version of naghdi s model and a mixed formulation of the same model in cartesian coordinates for linearly elastic shells with little regularity and finite element approximations thereof numerical tests are given that validate and illustrate our approach

two aggregate function based algorithms for analysis of 3d frictional contact by linear complementarity problem formulation three dimensional frictional contact is formulated as linear complementarity problem lcp by using the parametric variational principle and quadratic programming method two aggregate function based algorithms called respectively as self adjusting interior point algorithm and aggregate function smoothing algorithm are proposed for the solution of the lcp derived from the contact problems a nonlinear finite element code is developed for numerical analysis of 3d multi body contact problems four numerical examples are computed to demonstrate the applicability and computational efficiency of the methods proposed

adaptive finite element methods for parabolic problems i a linear model problem this paper is the first part in a series of papers on adaptive finite element methods for parabolic problems in this paper an adaptive algorithm is presented and analyzed for choosing the space a

a gradient based algorithm to solve inverse plane bimodular problems of identification abstract this paper presents a gradient based algorithm to solve inverse plane bimodular problems of identifying constitutive parameters including tensile compressive moduli and tensile compressive poisson s ratios for the forward bimodular problem a fe tangent stiffness matrix is derived facilitating the implementation of gradient based algorithms for the inverse bimodular problem of identification a two level sensitivity analysis based strategy is proposed numerical verification in term of accuracy and efficiency is provided and the impacts of initial guess number of measurement points regional inhomogeneity and noisy data on the identification are taken into accounts

adaptive fem analysis of selected elastic visco plastic problems abstract elastic visco plastic deformations modeled by the bodner partom constitutive equations s r bodner y partom constitutive equations elastic viscoplastic strain hardening materials j appl mech 42 1975 385 389 have been evaluated by the adaptive finite element method j m bass j t oden adaptive finite element methods for a class of evolution problems in viscoplasticity int j engrg sci 25 623 653 1987 l demkowicz j t oden w rachowicz o hardy toward a universal hp adaptive finite element strategy part 1 constrained approximation and data structure comput methods appl mech engrg 77 1989 79 112 we use the explicit residual error estimate i babuska w c rheinboldt error estimates for adaptive finite element computations int j numer methods engrg 12 1978 1597 1615 supplemented with a special term accounting for the fact that the right hand side of the equations we use is only approximated since it depends on the inelastic strains which are computed only at the gauss integration points we also address the problems of adaptation strategy and the method of solution transfer to a new mesh results of recent tests confirm efficiency and robustness of the approach

analysis of 2 d bimodular materials and wrinkled membranes based on the parametric variational principle and co rotational approach summary in the numerical analysis of 2 d bimodular materials strain discontinuity is problematic and the traditional iterative algorithm is frequently unstable this paper develops a stable algorithm for the large displacement and small strain analyses of 2 d bimodular materials and structures geometrically nonlinear formulations are based on the co rotational approach using the parametric variational principle pvp a unified constitutive equation is created to resolve the problem induced by strain discontinuity in the local coordinate system because the traditional stress iteration is not required the local linear stiffness matrix does not need to be updated when computing the global stiffness matrix and the nodal internal force vector the nonlinear problem is ultimately transformed into a complementarity problem that is simply solved by combing the newton raphson scheme and the mature quadratic programming algorithm numerical examples demonstrate that the pvp algorithm presents better convergence behavior than the traditional iterative algorithm by incorporating the concept of material modification the new algorithm is also be successfully extended to the wrinkling analysis of thin membranes copyright 2014 john wiley sons ltd

central limit theorems for sequences of multiple stochastic integrals we characterize the convergence in distribution to a standard normal law for a sequence of multiple stochastic integrals of a fixed order with variance converging to 1 some applications are given in particular to study the limiting behavior of quadratic functionals of gaussian processes

a posteriori error estimation and mesh adaptation for finite element models in elasto plasticity a new approach to a posteriori error estimation and adaptive mesh design based on techniques from optimal control is presented for primal mixed finite element models in elasto plasticity this method uses global duality arguments for deriving weighted a posteriori error bounds for arbitrary functionals of the error representing physical quantities of interest in these estimates local residuals of the computed solution are multiplied by certain weights which are obtained by solving a linearized global dual problem numerically the resulting local error indicators are used in a feed back process for generating economical meshes this approach is developed here for the hencky and prandtl reuss models in linear elastic perfect plasticity its performance is demonstrated for a plane strain benchmark problem

spectral discretization of a naghdi shell model we consider the naghdi equations which model a thin three dimensional shell we propose a spectral discretization of this problem in the case where the midsurface of the shell is weakly regular we perform the numerical analysis of the discrete problem and prove optimal error estimates

mesh refinement strategies without mapping of nonlinear solutions for the generalized and standard fem analysis of 3 d cohesive fractures summary a robust and efficient strategy is proposed to simulate mechanical problems involving cohesive fractures this class of problems is characterized by a global structural behavior that is strongly affected by localized nonlinearities at relatively small sized critical regions the proposed approach is based on the division of a simulation into a suitable number of sub simulations where adaptive mesh refinement is performed only once based on refinement window s around crack front process zone s the initialization of newton raphson nonlinear iterations at the start of each sub simulation is accomplished by solving a linear problem based on a secant stiffness rather than a volume mapping of nonlinear solutions between meshes the secant stiffness is evaluated using material state information stored read on crack surface facets which are employed to explicitly represent the geometry of the discontinuity surface independently of the volume mesh within the generalized finite element method framework moreover a simplified version of the algorithm is proposed for its straightforward implementation into existing commercial software data transfer between sub simulations is not required in the simplified strategy the computational efficiency accuracy and robustness of the proposed strategies are demonstrated by an application to cohesive fracture simulations in 3 d copyright 2016 john wiley sons ltd

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

a new 48 d o f quadrilateral shell element with variable order polynomial and rational b spline geometries with rigid body modes a 48 degrees of freedom d o f quadrilateral thin elastic shell finite element using variable order polynomial functions b spline functions and rational b spline functions to model the shell surface is developed this development may allow the stiffness formulation of the shell element to be linked to the geometry data bases created by computer aided design systems the displacement functions are that of bicubic hermitian polynomials the displacement functions and d o f are expressed and investigated in both the curvilinear and cartesian forms the cuivilinear form is simpler and can provide the proper solution for a certain class of shell problems for certain highly curved shells such as bellows however the curvilinear form fails to properly model some rigid body modes even with either the explicit inclusion of rigid body terms or the high order displacement functions it is suggested in this study that such difficulty can be circumvented and the rigid body modes can be properly included if a cartesian form is used for displacement functions the strain displacement equations are expressed in curvilinear co ordinates thus the cartesian displacement functions require a transformation to curvilinear displacement at each numerical integration point examples include a pinched cylinder a translational shell under central load a uniformly loaded hypar shell a pressurized ovel shell a semi toroidal bellows and a u shaped bellows for the first four examples geometric modellings consist of polynomials of second order subparametric third order isoparametric and fourth and fifth order both superparametric as well as b spline functions of fourth and fifth order the geometries of the pinched cylinder the semi toroidal bellows and the u shaped bellows were modelled exactly using rational b spline functions all the results obtained are in good agreement with alternative existing solutions

generalized szego theorems and asymptotics of cumulants by graphical methods we obtain some general asymptotics results about a class of deterministic sums called sums with dependent indices which generalize a classical theorem fo szego the above type of sums is encountered when establishing covergence to the gaussian distribution of sums of wick products by the method of cumulants our asymptotic results reduce in this situation the proof of the central limit thoerem to the study of the connectivity of a family of associated graphs

local linear regression estimation under long range dependence strong consistency and rates we consider the nonparametric estimation of multivariate regression functions and their derivatives for a regression model with long range dependent errors we adopt a local linear fitting approach and establish strong consistency and rates for the estimators of the regression function and its derivatives the rates of convergence depend on the amount of smoothing relative to the strength of the long range dependence lrd resulting in distinct rates for small and large bandwidths moreover the conditions determining this dichotomy are different for the estimates of the regression function than for the estimates of its derivatives

error estimation and adaptive meshing in strongly nonlinear dynamic problems we present work aimed at developing a general framework for mesh adaption in strongly nonlinear possibly dynamic problems we begin by showing that the solutions of the incremental boundary value problem for a wide class of materials including nonlinear elastic materials compressible newtonian fluids and viscoplastic solids obey a minimum principle provided that the constitutive updates are formulated appropriately this minimum principle can be taken as a basis for asymptotic error estimation in particular we chose to monitor the error of a lower order projection of the finite element solution the optimal mesh size distribution then follows from a posteriori error indicators which are purely local i e can be computed element by element we demonstrate the robustness and versatility of the computational framework with the aid of convergence studies and selected examples of application

properties of nonlinear transformations of fractionally integrated processes this paper shows that the properties of nonlinear transformations of a fractionally integrated process depend strongly on whether the initial series is stationary or not transforming a stationary gaussian i d process with d 0 leads to a long memory process with the same or a smaller long memory parameter depending on the hermite rank of the transformation any nonlinear transformation of an antipersistent gaussian i d process is i 0 for non stationary i d processes every integer power transformation is non stationary and exhibits a deterministic trend in mean and in variance in particular the square of a non stationary gaussian i d process still has long memory with parameter d whereas the square of a stationary gaussian i d process shows less dependence than the initial process simulation results for other transformations are also discussed

large displacements of shells including material nonlinearities abstract the paper presents a finite element formulation of shells with large deflections including elastoplastic material behaviour the elements utilized are the so called degenerated shell elements with special emphasis on the simple 4 node quadrilateral both the total lagrangian and the updated lagrangian formulation are considered for the treatment of plastic behaviour the concept of a layered element model is proposed and investigated for both the tangential modulus method and the initial load method in the final section sample problems are presented and compared with reference solutions it is shown that the 4 node element is very well suited to the class of problems under consideration it is characterized by an easy applicability high accuracy and low rates of computer time in appendix a an analytical solution of a cantilever beam subjected to an end load including geometrical and material nonlinearities is presented

joint convergence along different subsequences of the signed cubic variation of fractional brownian motion the purpose of this paper is to study the convergence in distribution of two subsequences of the signed cubic variation of the fractional brownian motion with hurst parameter h 1 6 we prove that under some conditions on both subsequences the limit is a two dimensional brownian motion whose components may be correlated and we find explicit formulae for its covariance function

error estimates for space time discretizations of a rate independent variational inequality this paper deals with error estimates for space time discretizations in the context of evolutionary variational inequalities of rate independent type after introducing a general abstract evolution problem we address a fully discrete approximation and provide a priori error estimates the application of the abstract theory to a semilinear case is detailed in particular we provide explicit space time convergence rates for classical strain gradient plasticity and the isothermal souza auricchio model for shape memory alloys

constitutive relation error estimators for visco plastic finite element analysis with softening a posteriori error estimators based on constitutive relation residuals have been developed for 20 years in particular at cachan this approach has a strong physical meaning and is quite general here we introduce an extended constitutive relation error estimators family able to measure the quality of finite element computations of structures which exhibit plastic viscoplastic behavior with softening these measures take into account over the studied time interval all the classical error sources involved in the computation the space discretization the mesh the time discretization and the iterative technique used to solve the nonlinear discrete problem

the empirical process of a short range dependent stationary sequence under gaussian subordination consider the stationary sequencex 1 g z 1 x 2 g z 2 whereg is an arbitrary borel function andz 1 z 2 is a mean zero stationary gaussian sequence with covariance functionr k e z 1 z k 1 satisfyingr 0 1 and 1 r k m where withi denoting the indicator function andf the continuous marginal distribution function of the sequence x n the integerm is the hermite rank of the family i g x f x x r letf n be the empirical distribution function ofx 1 x n we prove that asn the empirical processn 1 2 f n f converges in distribution to a gaussian process in the spaced

degenerated isoparametric finite elements using explicit integration the kinematics of degenerated finite elements using explicit integration are investigated in particular for geometric nonlinear applications two representations of the nodal rotational degrees of freedom are investigated the first adopts the infinitesimal representation of rotations while the second uses a valid large rotation representation a method of explicit integration is presented which satisfies rigid body rotations under arbitrary large rotations the accuracy and convergence of these formulations are investigated

asymptotic behavior of weighted quadratic variations of fractional brownian motion the critical case h 1 4 we derive the asymptotic behavior of weighted quadratic variations of fractional brow nian motion b with hurst index h 1 4 this completes the only missing case in a very recent work by i nourdin d nualart and c a tudor moreover as an application we solve a recent conjecture of k burdzy and j swanson on the asymptotic behavior of the riemann sums with alternating signs associated to b

a faceted shell element with loof nodes a flat shell element which utilizes the linear strain triangle lst for membrane representation and a plate bending element labelled dkl for discrete kirchhoff element with loof nodes previously derived by the authors in reference 1 is presented this element is free from the deficiencies of displacement incompatibility singularity with coplanar elements inability to model intersections and low order membrane strain representation which are associated with existing faceted shell elements the results of the numerical examples indicate that the convergence characteristics of this element are good

on error estimates and adaptivity in elastoplastic solids applications to the numerical simulation of strain localization in classical and cosserat continua the a posteriori error estimates based on the post processing approach are introduced for elastoplastic solids the standard energy norm error estimate established for linear elliptic problems is generalized here to account for the presence of internal variables through the norm associated with the complementary free energy this is known to represent a natural metric for the class of elastoplastic problems of evolution in addition the intrinsic dissipation functional is utilized as a basis for a complementary a posteriori error estimates a posteriori error estimates and adaptive refinement techniques are applied to the finite element analysis of a strain localization problem as a model problem the constitutive equations describing a generalization of standard j2 elastoplasticity within the cosserat continuum are used to overcome serious limitations exhibited by classical continuum models in the post instability region the proposed a posteriori error estimates are appropriately modified to account for the cosserat continuum model and linked with adaptive techniques in order to simulate strain localization problems superior behaviour of the cosserat continuum model in comparison to the classical continuum model is demonstrated through the finite element simulation of the localization in a plane strain tensile test for an elastopiastic softening material resulting in convergent solutions with an h refinement and almost uniform error distribution in all considered error norms

geometrically nonlinear formulation for the axisymmetric shell elements a geometrically nonlinear formulation using total lagrangian approach is presented for the axisymmetric shell elements the basic element is formulated using the co ordinates of the mid surface nodes and the mid surface nodal point normals an important aspect of the formulation presented here is that the restriction on the magnitude of the nodal rotations is eliminated this is accomplished by retaining true nonlinear nodal rotation terms in the definition of the displacement field and the consistent derivation of the element properties based on this displacement field the element properties are derived and presented in detail numerical examples are also presented to demonstrate the element behaviour and the accuracy

adaptive finite element methods in computational mechanics we present a general approach to adaptivity for finite element methods and give applications to linear elasticity non linear elasto plasticity and nonlinear conservation laws including numerical results

cumulants on the wiener space abstract we combine infinite dimensional integration by parts procedures with a recursive relation on moments reminiscent of a formula by barbour 1986 and deduce explicit expressions for cumulants of functionals of a general gaussian field these findings yield a compact formula for cumulants on a fixed wiener chaos virtually replacing the usual graph diagram computations adopted in most of the probabilistic literature

large displacement analysis of thin plates and shells using a flat facet finite element formulation the large displacement analysis of flat faceted shell element previously developed by meek and tan 15 is further developed this element has been already tested in the nonlinear range via the use of the total lagrangian formulation and a somewhat cumbersome procedure for the calculation of the joint orientation matrices at each step of the calculations 25 however this approach is quite complex and by taking advantage of the positions of the rotational degrees of freedom being located at the loof nodes along the edges and normal to the edges a simple and elegant formulation is obtained the theory is developed in incremental form and the updated lagrangian approach with the co rotational formulation is employed numerical examples are presented and compared with other published results to verify the proposed formulation

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

central limit theorems for quadratic forms with time domain conditions we establish the central limit theorem for quadratic forms t s 1 n b t s p m n x t x s of the bivariate appell polynomials p m n x t x s under time domain conditions these conditions relate the weights b t and the covariances of the sequences p m n x t x s and x t the time domain approach together with the spectral domain approach developed earlier yields a general set of conditions for central limit theorems

corotational nonlinear dynamic analysis of thin shell structures with finite rotations a new formulation for corotational nonlinear dynamic analysis of thin shell structures involving large displacements and finite rotations has been presented in this paper by introducing the kinematic description of the geometrically exact quasi static shell model to describe the motion of an arbitrary material point in a triangular shell element the new expressions for the inertial force vector and tangent inertia matrix were derived systematically the elastic deformation was handled by using the consistent symmetrizable equilibrated corotational formulation which is independent with respect to the local finite element modeling an energy momentum conserving algorithm and an energy decaying momentum conserving algorithm were developed for nonlinear dynamic analysis by applying the generalized energy momentum method in the corotational formulation three classic numerical examples including the dynamic response free motion and dynamic buckling of thin shell structures were computed to verify the ac

limit theorems for fourier transforms of functionals of gaussian sequences limit theorems with a non gaussian in fact nonstable limiting distribution have been obtained under suitable conditions for partial sums of instantaneous nonlinear functions of stationary gaussian sequences with long range dependence analogous limit theorems are here obtained for finite fourier transforms of instantaneous nonlinear functions of stationary gaussian sequences with long range dependence

an algorithm for finite element analysis of partly wrinkled membranes a generalization and numerical implementation is presented of the stein hedgepeth 1961 continuum theory for the analysis of partly wrinkled membranes such as the tensioned membrane surfaces which are found in spacecraft structural components the approach has its basis in experimental observations showing that when wrinkles develop in a membrane parallel to the x direction the associated overall contraction in the y direction exceeds that predicted by the poisson s ratio effect

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

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

a posteriori analysis of penalized and mixed formulations of koiter s shell model we are interested in finite element approximations of a koiter model for linearly elastic shells with little regularity to perform conforming method we present a penalized and a mixed formulations of the model allowing to approximate and to enforce weakly mechanical constraints respectively we establish existence and uniqueness of the solution to the both formulations moreover a posteriori analysis is led yielding an upper bound and a lower bound of the error finally numerical results are presented to illustrate the efficiency of the a posteriori estimators we therefore propose a mesh adaptivity strategy relying on these indicators

vibration analysis of bimodulus laminated cylindrical panels this paper deals with the flexural vibration behavior of bimodular laminated composite cylindrical panels with various boundary conditions the formulation is based on first order shear deformation theory and bert s constitutive model the governing equations are derived using finite element method and lagrange s equation of motion an iterative eigenvalue approach is employed to obtain the positive and negative half cycle free vibration frequencies and corresponding mode shapes a detailed parametric study is carried out to study the influences of thickness ratio aspect ratio lamination scheme edge conditions and bimodularity ratio on the free vibration characteristics of bimodulus angle and cross ply composite laminated cylindrical panels it is interesting to observe that there is a significant difference between the frequencies of positive and negative half cycles depending on the panel parameters through the thickness distribution of modal stresses for positive half cycle is significantly different from that for negative half cycle unlike unimodular case wherein the stresses at a particular location in negative half cycle would be of same magnitude but of opposite sign of those corresponding to positive half cycle finally the effect of bimodularity on the steady state response versus forcing frequency relation is studied for a typical case

a unified formulation of small strain corotational finite elements i theory this paper presents a unified theoretical framework for the corotational cr formulation of finite elements in geometrically nonlinear structural analysis the key assumptions behind cr are i strains from a corotated configuration are small while ii the magnitude of rotations from a base configuration is not restricted following a historical outline the basic steps of the element independent cr formulation are presented the element internal force and consistent tangent stiffness matrix are derived by taking variations of the internal energy with respect to nodal freedoms it is shown that this framework permits the derivation of a set of cr variants through selective simplifications this set includes some previously used by other investigators the different variants are compared with respect to a set of desirable qualities including self equilibrium in the deformed configuration tangent stiffness consistency invariance symmetrizability and element independence we discuss the main benefits of the cr formulation as well as its modeling limitations

error estimate procedure in the finite element method and applications statically and kinematically admissible fields are explicitly derived from the finite element solution of the primal form of linear models the error on constitutive law for these fields yields an expression of the finite element error moreover the contribution of each element to this error allows to implement an automatic mesh refinement procedure leading to a uniform distribution of a given accuracy

adaptive mesh refinement in strain localization problems an adaptive meshing method tailored to problems of strain localization is given the adaption strategy consists of equi distributing the variation of the velocity field over the elements of the mesh a heuristic justification for the use of variations as indicators is advanced and possible connections with interpolation error bounds are discussed meshes are constructed by delaunay triangulation it is shown how the hu washizu principle determines a consistent transfer operator for the state variables examples of application are given which demonstrate the versatility of the method

conforming finite element approximation for shells with little regularity this work concerns the construction of a computer code for a new model of linear thin shells whose midsurfaces can have charts with discontinuous second derivatives we use a conforming approximation by finite elements of class c1 argyris element

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

clt and other limit theorems for functionals of gaussian processes conditions for the clt for non linear functionals of stationary gaussian sequences are discussed with special references to the borderline between the clt and the non clt examples of the non clt for such functionals with the norming factor sqrt n are given

transfer operators for evolving meshes in small strain elasto placticity abstract together with error evaluation and mesh refinement transfer operators represent the essential component of the adaptive procedure applied to history dependent materials aspects of the transfer operation discussed in this work relate to equilibrium conditions consistency with the constitutive equation geometric issues and diffusion of state variables between successive meshes in this paper attention is restricted to small strain rate independent elasto plasticity numerical examples are presented to illustrate some practical features of the computational procedure

stein s method on wiener chaos we combine malliavin calculus with stein s method in order to derive explicit bounds in the gaussian and gamma approximations of random variables in a fixed wiener chaos of a general gaussian process our approach generalizes refines and unifies the central and non central limit theorems for multiple wiener ito integrals recently proved in several papers from 2005 to 2007 by nourdin nualart ortiz latorre peccati and tudor we apply our techniques to prove berry esseen bounds in the breuer major clt for subordinated functionals of fractional brownian motion by using the well known mehler s formula for ornstein uhlenbeck semigroups we also recover a technical result recently proved by chatterjee concerning the gaussian approximation of functionals of finite dimensional gaussian vectors

quadratic programming method in numerical simulation of metal forming process abstract in this paper a quadratic programming qp model based on a parametric variational principle is proposed for elastic plastic ep finite element analysis of metal forming processes the contact problem with friction between blank and tools is treated in the same way as in plastic analysis the penalty factors which are normally introduced into the algorithm for contact analysis have a direct influence on accuracy of solution there is no available rule for choosing a reasonable value of these factors for simulation of metal forming and they are therefore cancelled through a special technique so that the numerical results can be of high accuracy the algorithms for contact analysis and plastic analysis are established in one frame and consistent with each other compared with the conventional ep fem the newly developed method requires no tedious iterative procedures and has no convergence problems to apply this method easily to simulation of metal forming detailed forms of some key matrices or vectors for 2d fem and 3d fem are presented and a parametric loading algorithm for the qp model is developed which is suitable for qp problem with free variables and can decrease memory cost by avoiding the introduction of additional slack variables and improve the solution efficiency to some extent finally the proposed qp model is validated by two examples analysis of v notched tension test and analysis of the drawing of a square box one of the benchmarks proposed at numisheet93 it can be seen that the accuracy of solution of the new ep fem based on qp is better than that of the conventional ep fem based on iteration to make the new ep fem more applicable to metal forming industries it is necessary to develop a more efficient qp algorithm that is suitable for large scale problems

on weak convergence in dynamical systems to self similar processes with spectral representation let x u t be an aperiodic dynamical system set smf f f o tm 1 where f is a measurable function on x let y t be one of a class of self similar process with a nice spectral representation for instance either a fractional brownian motion a hermite process or a harmonizable fractional stable motion we show that there is an f on x and constants am so that am s mt t 4 y t the convergence being understood in the sense of weak convergence of all finite dimensional distributions in t

asymptotic distributions of the sample mean autocovariances and autocorrelations of long memory time series we derive the asymptotic distributions of the sample mean autocovariances and autocorrelations for a time series whose autocovariance function has the powerlaw decay 0 o 1 as the results differ in important respects from the corresponding results for short memory processes whose autocovariance functions are absolutely summable for long memory processes the variances of the sample mean and of the sample autocovariances and autocorrelations for 0 12 are not of asymptotic order n 1 when 0 12 the asymptotic distributions of the sample autocovariances and autocorrelations are not normal

a posteriori error estimation for elasto plastic problems based on duality theory abstract in this paper we introduce a new approach to a posteriori error estimation for elasto plastic problems based on the duality theory of the calculus of variations we show that in spite of the prevailing view duality methods provide a viable way for obtaining computable a posteriori error estimates for nonlinear boundary value problems without directly solving the dual problem rigorous mathematical analysis leads to what we call duality error estimators consisting of two parts the error in the constitutive law and the error in the equilibrium equations this representation is both physically meaningful and computationally important the duality error estimators hold for any conforming approximation of the exact solution regardless of whether or not they satisfy the galerkin orthogonality condition in particular they encompass the familiar smoothening or gradient averaging techniques commonly used in practice we prove that the duality error estimators are equivalent to the error when the approximate solution is the exact solution of the discretised problem moreover in the case of linear elasticity the known residual type error estimators can be obtained from the duality error estimators numerical results for a model elasto plastic problem show the accuracy of the duality error estimators

a mixed finite element for shell model with free edge boundary conditions part 1 the mixed variational formulation abstract after a very brief recall on general shell theory we construct a mixed variational formulation based on the introduction of a new unknown the rotation of the normal to the medium surface in koiter shell theory for instance this rotation can be expressed with respect to the three components of the displacement field of the medium surface and their derivatives the lagrange multiplier corresponding to this relation known as the kirchhoff love kinematical assumption is also introduced as an independent unknown there are two main difficulties one is due to the differential geometry of surfaces and is rather technical the other is to define correctly the dual space for the kirchhoff love relation the difficulty is similar to the one met in the characterization of the dual space of the sobolev space h 1 being the medium surface of the shell for which a boundary component appears except for clamped shells which is a very restrictive situation