on improved predictions for structural equilibrium path evaluations the paper describes how several procedures for higher order predictions have been introduced in order to improve the convergence speed in a general finite element program for non linear structural

a multilevel computational strategy for handling microscopic and macroscopic instabilities this paper presents a numerical technique to deal with instability phenomena in the context of heterogeneous materials where buckling may occur at both macroscopic and or microscopic scales we limit ourselves to elastic materials but geometrical nonlinearity is taken into account at both scales the proposed approach combines the multilevel finite element analysis fe2 and the asymptotic method anm in that framework the unknown nonlinear constitutive relationship at the macroscale is found by solving a local finite element problem at the microscale in contrast with fe2 the use of the asymptotic development allows to transform the nonlinear microscopic problems into a sequence of linear problems thus a direct analogy with classical linear homogenization can be made to construct a localisation tensor at each step of the asymptotic development and an explicit macroscopic constitutive relationship can be constructed at each step furthermore the salient features of the anm allow treating instabilities and limit points in a very simple way at both scales the method is tested and illustrated through numerical examples involving local instabilities which have ignificant influence on the macroscopic behavior

bayesian reliability analysis of series systems of binomial subsystems and components a bayesian procedure is presented for estimating the reliability of a series system of independent binomial subsystems and components the method considers either test or prior data perhaps both or neither at the system subsystem and component level beta prior distributions are assumed throughout inconsistent prior judgments are averaged within the simple to use procedure the method is motivated by the following practical problem it is required to estimate the overall reliability of a certain air to air heat seeking missile system containing five major subsystems with up to nine components per subsystem the posterior distribution of the overall missile system reliability from which the required estimates are obtained is computed

a predictor corrector method for structural nonlinear analysis abstract a predictor corrector method is presented for the efficient and reliable analysis of structural nonlinear behaviors the key idea lies on modifying the starting point of iterations of the newton iterative method the conventional newton method starts iterations at the previously converged solution point however in the present predictor corrector method a point close to the converged solution of the current step is predicted first and then the newton method starts iterative procedure at the predicted point the predictor the neural network in the present study recognizes the pattern of the previously converged solutions to predict the starting point of the current step then the corrector the standard newton method in the present study is used to obtain the converged solution by iterative computation starting at the predicted point numerical tests are conducted to demonstrate the effectiveness and reliability of the present predictor corrector method the performance of the present method is compared with the conventional newton method and riks continuation method the present predictor corrector method saves computational cost significantly and yields stable results without diverging for the nonlinear analysis with monotonous deformation path as well as complicated deformation path including buckling and post buckling behaviors

models algorithms and error estimation for computational viscoelasticity this article reviews numerical algorithms for problems in solid polymer viscoelasticity in both small and large deformation for the linear small strain case we review both the quasistatic and the dynamic problem and give recent results on a posteriori error estimation for the large strain case we focus on the formulation and computational modelling of constrained membrane inflation the application of which is to the thermoforming process

bifurcation points and bifurcated branches by an asymptotic numerical method and pade approximants the aim of this work is to develop a reliable and fast algorithm to compute bifurcation points and bifurcated branches it is based upon the asymptotic numerical method anm and pade approximants the bifurcation point is detected by analysing the poles of pade approximants or by evaluating along the computed solution branch a bifurcation indicator well adapted to anm several examples are presented to assess the effectiveness of the proposed method that emanate from buckling problems of thin elastic shells especially problems involving large rotations are discussed copyright 2004 john wiley sons ltd

dynamic stability of spinning viscoelastic cylinders at finite deformation the study of spinning axisymmetric cylinders undergoing finite deformation is a classic problem in several industrial settings the tire industry in particular we present a stability analysis of spinning elastic and viscoelastic cylinders using arpack to compute eigenvalues and eigenfunctions of finite element discretizations of the linearized evolution operator we show that the eigenmodes correspond to n peak standing or traveling waves for the linearized problem with an additional index describing the number of oscillations in the radial direction we find a second hierarchy of bifurcations to standing waves where these eigenvalues cross zero and confirm numerically the existence of finite amplitude standing waves for the nonlinear problem on one of the new branches in the viscoelastic case this analysis permits us to study the validity of two popular models of finite viscoelasticity we show that a commonly used finite deformation linear convolution model results in non physical energy growth and finite time blow up when the system is perturbed in a linearly unstable direction and followed nonlinearly in time on the other hand sidoroff style viscoelastic models are seen to be linearly and nonlinearly stable as is physically required 2014 elsevier ltd all rights reserved

computation of critical boundaries on equilibrium manifolds the study of various equilibrium phenomena leads to nonlinear equations 1 f y u 0 where y in r n is a vector of behavior or state variables u in r p a vector of p geqq 2 parameters or controls and f d subset r n times r p to r n a sufficiently differentiable map the solution set of 1 in r n times r p is often called the equilibrium surface of the problem and in many applications it is of interest to determine the critical boundary that is the set of solutions of 1 where the derivative d y f x is singular for example in structural problems these points may represent buckling points after characterizing the various properties of the problem we present three different numerical methods which allow for a computational trace of paths in the critical boundary these methods represent extensions of the earlier developed locally parametrized continuation method for tracing regular paths on the equilibrium surface they permit for instance a direct computational deter

the post critical analysis of axisymmetric hyper elastic membranes by the finite element method abstract an axisymmetric finite element that can model rubber like hyper elastic material has been employed to study post critical response in the inflation of axisymmetric membranes an extensive parametric study has been performed to investigate the non linear response of a tube under internal pressure the issue of combined proportional and non proportional loading in the context of incremental iterative solution is discussed further a robust bracketing procedure useful to compute clustered bifurcation points is proposed finally the eigen mode injection method is used to branch into the post critical paths contrary to previous findings the newton raphson method worked satisfactorily in all the cases tested

some computational aspects of the stability analysis of nonlinear structures abstract the perturbation method and the continuation method are the two most popular techniques for the solution of finite element equations that describe instability phenomena this paper presents a summary of the principles involved and describes some trends in the development of these techniques

mixed formulation and locking in path following nonlinear analysis abstract the arc length riks strategy has rapidly become a standard tool for path following analysis of nonlinear structures due to its theoretical ability to surpass limit points the aim of this paper is to show that the failures in convergence that are occasionally experienced are not related to proper defects of the algorithm but come from a subtle locking effect intrinsic to the nonlinear nature of the problem as a consequence its sanitization has to be pursued within a reformulation of the structural model the use of a mixed stress displacement variant of the algorithm in particular appears very promising in this respect the topic is discussed with reference to the analysis of nonlinear frames using a mixed version of the nonlinear beam model discussed in 39 it is shown that with no extra computational cost and only a minor modification in coding with respect to a purely compatible formulation it is possible to achieve a noticeable improvement in convergence and a real gain in both computational time and overall robustness of the algorithm

graph cut based discrete valued image reconstruction efficient graph cut methods have been used with great success for labeling and denoising problems occurring in computer vision unfortunately the presence of linear image mappings has prevented the use of these techniques in most discrete amplitude image reconstruction problems in this paper we develop a graph cut based framework for the direct solution of discrete amplitude linear image reconstruction problems cast as regularized energy function minimizations we first analyze the structure of discrete linear inverse problem cost functions to show that the obstacle to the application of graph cut methods to their solution is the variable mixing caused by the presence of the linear sensing operator we then propose to use a surrogate energy functional that overcomes the challenges imposed by the sensing operator yet can be utilized efficiently in existing graph cut frameworks we use this surrogate energy functional to devise a monotonic iterative algorithm for the solution of discrete valued inverse problems we first provide experiments using local convolutional operators and show the robustness of the proposed technique to noise and stability to changes in regularization parameter then we focus on nonlocal tomographic examples where we consider limited angle data problems we compare our technique with state of the art discrete and continuous image reconstruction techniques experiments show that the proposed method outperforms state of the art techniques in challenging scenarios involving discrete valued unknowns

a hybrid mixed model for non linear shell analysis and its applications to large rotation problems adopting an updated lagrange approach the general framework for the fully non linear analysis of curved shells is developed using a simple quadrilateral c0 model hmsh5 the governing equations are derived based on a consistent linearization of an incremental mixed variational principle of the modified hellinger reissner type with independent assumptions for displacement and strain fields emphasis is placed on devising effective solution procedures to deal with large rotations in space finite stretches and generalized rate type material models in particular a geometrically exact scheme for configuration update is developed by making use of the so called exponential mapping algorithm and the resulting element was shown to exhibit a quadratic rate of asymptotic convergence in solving practical shell problems with newton raphson type iterative schemes for the purpose of updating the spatial stress field of the element an objective generalized midpoint integration rule is utilized which relies crucially on the concept of polar decomposition for the deformation gradient and is in keeping with the underlying mixed method finally the effectiveness and practical usefulness of the hmsh5 element are demonstrated through a number of test cases involving beams plates and shells undergoing very large displacements and rotations

newton krylov method for computing the cyclic steady states of evolution problems in nonlinear mechanics this work is focused on the newton krylov technique for computing the steady cyclic states of evolution problems in non linear mechanics with space time periodicity conditions this kind of problems can be faced for instance in the modeling of a rolling tyre with a periodic tread pattern where the cyclic state satisfies rolling periodicity condition including shifts both in time and space the newton krylov method is a combination of a newton nonlinear solver with a krylov linear solver looking for the initial state which provides the space time periodic solution the convergence of the krylov iterations is proved to hold in presence of an adequate preconditioner after preconditioning the newton krylov method can be also considered as an observer controller method correcting the transient solution of the initial value problem after each period using information stored while computing the residual the krylov solver computation time becomes negligible with respect to the residual computation time the method has been analyzed and tested on academic applications and compared to the standard evolution fixed point method finally it has been implemented into the michelin industrial code applied to a full 3d rolling tyre model

buehler confidence bounds for a reliability maintainability measure this article presents an upper confidence bound for a measure of reliability maintainability of a series system in which component repair is assumed to restore the system to its original status under exponentiality of component repair time and survival time distributions the measure m is the ratio of expected system repair time to expected system survival time moreover under this exponentiality assumption the bound is uniformly minimum among all bounds of specified level that are nondecreasing functions of the maximum likelihood estimator of m as a matter of practical interest the measure m has been incorporated into military standard mil std 470b and is an official statistic of the air force reliability maintainability information system

decomposition of images by the anisotropic rudin osher fatemi model the total variation based image denoising model of rudin osher and fatemi can be generalized in a natural way to favor certain edge directions we consider the resulting anisotropic energies and study properties of their minimizers 2004 wiley periodicals inc

disease prediction based on functional connectomes using a scalable and spatially informed support vector machine substantial evidence indicates that major psychiatric disorders are associated with distributed neural dysconnectivity leading to a strong interest in using neuroimaging methods to accurately predict disorder status in this work we are specifically interested in a multivariate approach that uses features derived from whole brain resting state functional connectomes however functional connectomes reside in a high dimensional space which complicates model interpretation and introduces numerous statistical and computational challenges traditional feature selection techniques are used to reduce data dimensionality but are blind to the spatial structure of the connectomes we propose a regularization framework where the 6 d structure of the functional connectome defined by pairs of points in 3 d space is explicitly taken into account via the fused lasso or the graphnet regularizer our method only restricts the loss function to be convex and margin based allowing non differentiable loss functions such as the hinge loss to be used using the fused lasso or graphnet regularizer with the hinge loss leads to a structured sparse support vector machine svm with embedded feature selection we introduce a novel efficient optimization algorithm based on the augmented lagrangian and the classical alternating direction method which can solve both fused lasso and graphnet regularized svm with very little modification we also demonstrate that the inner subproblems of the algorithm can be solved efficiently in analytic form by coupling the variable splitting strategy with a data augmentation scheme experiments on simulated data and resting state scans from a large schizophrenia dataset show that our proposed approach can identify predictive regions that are spatially contiguous in the 6 d connectome space offering an additional layer of interpretability that could provide new insights about various disease processes

on steplength algorithms for a class of continuation methods the continuation methods considered here are algorithms for the computational analysis of the regular parts of the solution field of equations of the form fx b f d subset r n 1 to r n for given b in r n while these methods are similar in structure to those used for ode solvers their errors are independent of the history of the process and are solely determined by the termination criterion of the corrector at the current step this suggests the use of a posteriors estimates of the convergence radii of the corrector it is proved here that such estimates cannot be obtained from the sequence of corrector iterates alone but that they require some global information about f however it is shown that a finite sequence of corrector iterates does allow for the computation of effective estimates of the convergence quality of certain types of correctors this is used for the design of various step algorithms for continuation processes two of them are based on a newton corrector while the third o

une methode numerique pour le calcul des points de retournement application a un probleme aux limites non lineaire an iterative method is presented for determining a turning point in a branch of solutions of an algebraic system of equations depending on a parameter one shows that the convergence is superlinear and that this method may constitute a complement for the newton method with a finite element method numerical results are given testing the process on the discrete version of a mildly nonlinear boundary value problem to determine the turning point in the positive solution branch

compatibility condition and existence results in discrete finite incompressible elasticity abstract a theory on the existence of solutions of the discretized equilibrium equations in incompressible finite elasticity is given a compatibility condition between the space of displacements and the space of pressures is introduced and is studied in a particular case of finite element spaces using q 1 and q 0 isoparametric elements an original assembling of these elements is presented which leads to discrete spaces satisfying the compatibility condition

branch switching for pitchfork bifurcation in nonlinear finite element method a general branch switching approach is proposed based on pseudo arc length continuation in the nonlinear finite element method fem to trace the branch solution curve at the pitchfork bifurcation point in parameter space by this approach branch direction can be determined without derivatives of tangent stiffness matrix this approach is proved mathematically and is inserted into a general fem code stability of equilibrium corresponding to each solution curve is estimated by the lagrange dirichlet criteria as an example the whole process of the elastic mode jumping for rectangular thin plates in which there are many pitchfork bifurcations in parameter space in loading and unloading is simulated by the improved fem code the numerical results are identical with that of an experiment done by previous researchers

computing finite rotations of shells by an asymptotic numerical method abstract we present an asymptotic numerical algorithm for the computation of elastic shells with large rotations the theoretical formulation involves a three field hu washizu functional which allows us to put the problem into a quadratic framework the spatial discretization is based on geometrically exact element recently presented by buchter et al buchter et al three dimensional extension of non linear shell formulation based on the enhanced assumed strain concept int j numer methods engrg 37 1994 2551 1568 several classical benchmarks are discussed to define the best strategy and to assess the validity and the efficiency of the present method as compared to more classical iterative algorithms

improvement of the scaled corrector method for bifurcation analysis using symmetry exploiting block diagonalization in the nonlinear bifurcation analysis for large scaled structures the standard eigenanalysis of the tangent stiffness matrix yields important information but at the same time demands a large amount of computational cost the scaled corrector method was developed as a numerically efficient eigenanalysis free bifurcation analysis strategy which exploits byproducts of the numerical iteration for path tracing this method however has a problem in its accuracy especially when eigenvalues are nearly or exactly coincidental as a remedy for this we propose a new bifurcation analysis method through the implementation of bifurcation mechanism of a symmetric structure into the scaled corrector method the bifurcation mode is accurately approximated by decomposing a scaled corrector vector into a number of vectors by means of block diagonalization method in group theoretic bifurcation theory and in turn by choosing the predominant one among these vectors in order to demonstrate the usefulness of this method it is applied to the bifurcation analysis of reticulated regular hexagonal truss domes to compute accurately the locations of double bifurcation points and nearly coincidental bifurcation points and associated bifurcation modes

an algebraic geometric method to calculate branches near a bifurcation point abstract systems of nonlinear algebraic equations with a parameter arises in many branches of mathematics and engineering computation of the solution curve is usually hindered by the existence of a bifurcation point where the rank of the corresponding matrix is not full and usually there is another branch curve passing it we introduce a method from algebraic geometry to find the branch curve a computational example is provided

a unifying approach to isotropic and anisotropic total variation denoising models total variation minimisation is a well established method for digital image restoration its implicit preservation of edges permits the derivation of anisotropic models for a qualitative improvement at corners this paper is a synopsis of anisotropic models with state of the art insights into the numerics of isotropic models we generalise two representative models from both branches of research this formulation leads to a general convergent algorithm and a general highly efficient algorithm which apply for both cases a transfer of the discretisation from the anisotropic model to the isotropic setting results in an improvement of rotational invariance

existence and approximation results for nonlinear mixed problems application to incompressible finite elasticity this paper considers the problems of minimizing gateaux differentiable functionals over subsets of real banach spaces defined by a non linear equality constraint the existence of a lagrange multiplier is proved together with approximation results on the constrained subset provided a nonlinear compatibility condition generalizing the classical inf sup condition is satisfied these ideas are applied to equilibrium problems in incompressible finite elasticity and lead to convergence results for these problems

on the interaction of frictional formulations with bifurcation phenomena in hyperelastic steady state rolling calculations a finite element formulation for hyperelastic steady state rolling of inflated tires is analyzed in particular numerical difficulties associated with enforcing frictional conditions within such a framework are discussed we focus in this work on adherent i e no slip friction formulations and in addition to analyzing the numerical difficulties associated with such problems we also study the interaction of frictional conditions with bifurcation phenomena such phenomena are observed in the context of multiple solutions both stable and unstable of the discretized system and are also manifested in the behavior of the iterative map used to solve the nonlinear algebraic system of equations

some computational aspects of a group theoretic finite element approach to the buckling and postbuckling analyses of plates and shells of revolution abstract progress in the application of group theoretic methods to the nonlinear bifurcation analysis of symmetric structures has provided new hope in understanding the global postbuckling behavior of symmetric thin shell structures however what is still lacking in the computational mechanics community is a general purpose fe code with a group theoretic capability designed to take optimal advantage of existing symmetry this paper addresses some of the important issues associated with developing such a code the long term goal being to provide structural analysts with new numerical tools for doing careful global analyses of imperfection sensitive structures which may eventually lead to more accurate predictions of the maximum load carrying capacity of thin imperfection sensitive shell structures

on the adaptive finite element method of steady state rolling contact for hyperelasticity in finite deformations in this paper we present an adaptive finite element method for steady state rolling contact in finite deformations along with a residual based a posteriori error estimator for rolling contact problem with coulomb friction a general formulation of rolling contact geometry is derived from the point of view of differential geometry solvability conditions for the rolling contact problems are discussed we use newton s method to solve variational equations derived from a penalty regularization of the finite element approximation of the rolling contact problem we provide a numerical example to illustrate the method

reduced basis technique for collapse analysis of shells a hybrid finite element rayleigh ritz technique is used to predict the collapse behavior of shells in this hybrid technique the modeling versatility of the finite element method is preserved and a significant reduction in the number of degrees of freedom is achieved by expressing the nodal displacement vector as a linear combination of a small number of basis vectors a rayleigh ritz technique is used to approximate the finite element equations of the discretized shell by a reduced system of nonlinear algebraic equations a scalar function is introduced to measure the degree of nonlinearity of the structure for the case of loading applied by means of axial end shortening also a quantitative measure for the error of the reduced system of equations is proposed some insight is given as to why and when the reduced basis technique works and the effectiveness of the technique for predicting the collapse behavior of shells is demonstrated by means of a numerical example of elastic collapse of an axially compressed pear shaped cylinder

accurate confidence limits for stratified clinical trials for stratified 2 2 tables standard approximate confidence limits can perform poorly from a strict frequentist perspective even for moderate sized samples yet they are routinely used in this paper i show how to use importance sampling to compute highly accurate limits in reasonable time the methodology is very general and simple to implement and orders of magnitude are faster than existing alternatives copyright 2013 john wiley sons ltd

the importance of the designated statistic on buehler upper limits on a system failure probability the upper limits introduced by buehler are constructed to be honest confidence limits that are as small as possible subject to the constraint that they are nondecreasing functions of a designated statistics this methodology has largely been developed for applications in reliability that involve finding an upper limit on the probability of failure p1 pk of a system of k components with probabilities of failure pi for mainly computational reasons it is common to choose the designated statistic s p1 pk where pi is an estimator of pi buehler on the other hand suggested the choice s pu1 puk where pui is a so called exact 1 1 k upper limit for pi in this article we draw attention to existing general theory suggesting that s should be chosen to be an approximate upper limit for the interest parameter not an estimator we also give numerical results suggesting that extreme loss in efficiency typically follows if s is chosen poorly our current recommendation is that s should be an a

exact one sided confidence limits for the difference between two correlated proportions we construct exact and optimal one sided upper and lower confidence bounds for the difference between two probabilities based on matched binary pairs using well established optimality theory of buehler starting with five different approximate lower and upper limits we adjust them to have coverage probability exactly equal to the desired nominal level and then compare the resulting exact limits by their mean size exact limits based on the signed root likelihood ratio statistic are preferred and recommended for practical use

nonlinear analysis based on homogeneous incremental systems abstract the performance of path following techniques depends on so called constraint equations which are used in the augmented incremental systems it is common practice in the literature that these equations are explicitly defined following the arbitrary geometrical or physical ideas in the present paper their role is discussed in order to establish a reliable method of augmentation it is shown that the explicitly defined constraint equation is not necessary the implicit formulation is proposed which is based on the rank analysis performed on the rectangular matrix of the homogeneous incremental system the proposed method allows to solve problems where the well known continuation schemes fail the theoretical considerations are illustrated by the numerical examples

high order predictor corrector algorithms new predictor corrector algorithms are presented for the computation of solution paths of non linear partial differential equations the predictors and the correctors are based on perturbation techniques and pade approximants this extends the asymptotic numerical method anm which is an efficient high order continuation technique without corrector the efficiency and the reliability of the new technique are assessed by several examples within thin shell theory and navier stokes equations many variants have been tested to establish an optimal algorithm

approximation of obstacle problems by continuation methods nonlinear variational inequalities associated with obstacle problems are considered which may exhibit multiple solutions and turning points a predictor corrector continuation method for following a solution branch is presented essentially it is shown that regular or simple singular solutions of the nonlinear eigenvalue problem are regular for an augmented problem the main difficulty here is due to the fact that the equations are not differentiable in the frechet sense the numerical schemes that are used in the implementation of the method are developed for the predictor step a deflated block algorithm is used and for the corrector step algorithms are set up using projected sor projected newton and projected preconditioned conjugate gradients the efficiency of the various algorithms is compared by applying the continuation method to a finite element discretization of a two dimensional problem numerical results are presented

geometrically isolated nonisolated solutions and their approximation a solution x x 0 of f x 0 is said to be isolated if the frechet derivative f x 0 is nonsingular it is said to be geometrically isolated if no other solution is in x x 0 leqq rho for some rho 0 isolated solutions are always geometrically isolated sufficient conditions are obtained to insure that a nonisolated solution is also geometrically isolated we then study the application of approximation methods in the general form f h x h 0 to approximate nonisolated solutions which are geometrically isolated under strong consistency conditions the results are somewhat negative the approximations may have an even number including zero or an odd number of roots near x 0 depending upon the multiplicity cf x 0 as a root if the accuracy is o h p and the multiplicity is n then the approximations have error o h p n the relation of these results to limit and bifurcation points is discussed briefly

a predictor algorithm for fast geometrically nonlinear dynamic analysis an efficient predictor algorithm is presented for fast geometrically nonlinear dynamic analysis the basic concept of this algorithm entails the use of the predicted starting point close to the converged solution point in the iterative procedure of nonlinear dynamics the predicted starting point is much closer to the converged solution than the conventionally adopted starting point i e the previously converged solution point so the number of iterations required for convergence decreases in addition the additional time for prediction is trivial and therefore the total computation time significantly decreases the neural network which is used to predict the starting point characterizes the pattern of the previously converged solution points the mean vector the complementary vector and the slope factor are elements of the present predictor algorithm which work with the neural network to make the prediction in the iterative procedure of nonlinear dynamic analysis numerical tests of structural nonlinear dynamic problems using an 18 node assumed strain solid element demonstrate the validity and the efficiency of the predictor algorithm

a finite element solution method for contact problems with friction a new finite element solution method for the analysis of frictional contact problems is presented the contact problem is solved by imposing geometric constraints on the pseudo equilibrium configuration defined as a configuration at which the compatibility conditions are violated the algorithm does not require any a priori knowledge of the pairs of contactor nodes or segments the contact condition of sticking slipping rolling or tension release is determined from the relative magnitudes of the normal and tangential global nodal forces contact iterations are in general found to converge within one or two iterations the analysis method is applied to selected problems to illustrate the applicability of the solution procedure

numerical models of steady rolling for non linear viscoelastic structures in finite deformations a lagrangian formulation of constitutive laws for a viscoelastic material based on irreversible thermodynamics is first presented these laws are expressed by a non linear differential equation governing the evolution of an internal variable then equations describing the steady rolling of an axisymmetric viscoelastic structure are obtained from the conservation laws of continuum mechanics a finite element approximation and a solution technique of the algebraic system is proposed the eiimination of the internal variable allows one to keep an elastic like algorithm with an independent solution of the viscoelastic equation numerical tests show the feasibility and the efficiency of the proposed methods in large three dimensional situations

computational modelling of thermoforming processes in the case of finite viscoelastic materials abstract in this paper we describe the computational simulation of the inflation phase of a thermoforming process under which a thin polymer sheet is deformed into a mould under the action of applied pressure it is assumed that the sheet undergoes finite viscoelastic deformation which is treated using a hyperelastic model containing internal variables the simplification is adopted that the sheet can be treated as a membrane and also that there is a total sticking contact condition when the sheet comes in contact with the mould the computational model uses finite elements in space and incorporates mesh adaptivity based on a residual estimator in order to simulate the deformation accurately and efficiently the internal variables satisfy an ordinary differential equation in time which is solved using a predictor corrector scheme the constitutive model is a generalisation of that of le tallec and rahier p le tallec c rahier numerical models of steady rolling for non linear viscoelastic structures in finite deformations int j numer methods engrg 37 1994 1159 1186 in the simulation it is demonstrated how effectively the estimator works in controlling the meshes for some demanding mould shapes

elastic postbuckling analysis via finite element and perturbation techniques part ii application to shells of revolution the general theory developed in part 1 of this paper for the finite element stability analysis of structural systems using perturbation expansions in the vicinity of a critical point is applied here to the analysis of shells of revolution the discretization of the shell is performed by means of a semianalytical approximation and the matrices required for the evaluation of critical points and postcritical equilibrium paths are obtained two cases are presented bifurcation in axisymmetric and in asymmetric buckling modes the derivatives required for an imperfection analysis are also obtained a technique of switching between two paths using continuation methods is also discussed in which the switch is performed using derivatives of the perturbation expansion results are presented for bifurcation in axisymmetric and in non axisymmetric modes and compared with known solutions or with results from changing the path using continuation methods good correlation is shown for structures displaying unstable bifurcation the influence of load and geometric imperfections is evaluated

three dimensional incompressible viscoelasticity in large strains formulation and numerical approximation abstract this paper considers viscoelastic incompressible solids in large deformations a three dimensional thermodynamical model is first proposed it leads to a nonlinear variational problem which is approximated in space by mixed finite elements and in time by a first order implicit scheme this approximation is analyzed on the corresponding linearized problem finally an elimination strategy is described which reduces each step of the discrete problem to the solution of a standard hyperelastic problem to be solved by newton s method

the ale formulation of bodies in rolling contact theoretical foundations and finite element approach abstract numerical methods for the analysis of rolling contact problems are of high importance for the optimization of the components car tires for example today finite element methods for the computation of stationary rolling contact have been developed for industrial use however from a review of the scientific literature it has been concluded that the theoretical foundations of the relative kinematic description i e an arbitrary lagrangian eulerian ale formulation seems to be not well understood in detail this presentation is aimed to close this gap starting from the basic kinematic description of the ale formulation of rolling the weak form of the equations of motion are developed by this careful analysis an additional flux contribution is derived which has not been recognized in the scientific literature so far the contact problem is described for the treatment of two deformable bodies in rolling contact within the framework of well established methods for the numerical treatment of contact in the lagrangian picture in general essential differences between the lagrangian description and the ale description of rolling are shown up and discussed in detail for a comprehensive presentation the finite element discretization is restricted to the case of a deformable wheel rolling on a rigid plane surface however the sketched algorithmic approach is valid in general the efficiency of the numerical algorithms developed so far are discussed by the analysis of a simple three dimensional example critical remarks and an outlook to further research in this field concludes this presentation

an effective parametrization for asymptotic extrapolations abstract when considering the range of validity of asymptotic expansions the choice of the expansion parameter plays an essential role in effect with the exception of a posteriori adjustments of the expansion components the definition of this parameter is the only way of improving the approximation at a finite distance from the initial point good parametrization equations are usually obtained by norms that involve all variables of the problem or based on the nature of the mechanical phenomena here this equation is constructed following the criteria of reducing the residual error and at the same time exactly reproducing solutions that admit a polynomial second degree representation that choice is automatic in the analysis and improves the domain of accurate approximations an appropriate predictor corrector scheme was implemented to compare extrapolations obtained by this and several standard parametrizations the solution scheme was used to analyse geometrically nonlinear plane frame structures

path following analysis of thin walled structures and comparison with asymptotic post critical solutions a path following non linear elastic analysis for structures composed of assemblages of flat slender elastic panels is presented the proposed path following method employs fem technology and a kinematical model to analyse these structures using a koiter asymptotic approach as a result it is possible to verify the accuracy achieved by the asymptotic method the proposed mixed path following formulation is both efficient and robust with regards to the locking extrapolation phenomenon that strongly affects compatible formulations the use of an hc finite element makes it possible to avoid the problem of the finite rotations in the space maintaining a high degree of continuity and making the numeric formulation simple and efficient copyright 2002 john wiley sons ltd

on linear constraints for newton raphson corrections and critical point searches in structural f e problems the paper discusses the introduction of constraining equations in the tangential stiffness relation used to calculate the responses to different load cases in solution algorithms for non linear mechanical finite element f e problems an alternative to the normal two phase solution method is discussed this method is used to represent different iteration constraints and in conjunction with the search for critical solution points numerical tests are presented evaluating the efficiency of different iteration constraints for a model problem practically useful criteria for critical points are discussed the basic methods for search of such points and some numerical aspects are discussed and evaluated for three different problems