the finite deformation theory for beam plate and shell part v the shell element with drilling degree of freedom based on biot strain due to the facts that the spatial moment force is non conservative and the three components of the finite rotation pseudo vector are not independent the ordinary variational principle based on a functional achieving its stationary value is not suitable for the problem subject to non conservative loading the finite element method proposed in this paper is based on the virtual work principle rigid normal assumption polar decomposition and total lagrangian formulation

a systematic development of solid shell element formulations for linear and non linear analyses employing only displacement degrees of freedom in the present contribution we propose a so called solid shell concept which incorporates only displacement degrees of freedom thus some major disadvantages of the usually used degenerated shell concept are overcome these disadvantages are related to boundary conditions the handling of soft and hard support the need for special co ordinate systems at boundaries the connection with continuum elements and in geometrically non linear analyses to a complicated update of the rotation vector first the kinematics of the so called solid shell concept in analogy to the degenerated shell concept are introduced then several modifications of the solid shell concept are proposed to obtain locking free solid shell elements leading also to formulations which allow the use of general three dimensional material laws and which are also able to represent the normal stresses and strains in thickness direction numerical analyses of geometrically linear and non linear problems are finally performed using solely assumed natural shear strain elements with a linear approximation in in plane direction although some considerations are needed to get comparable boundary conditions in the examples analysed the solid shell elements prove to work as good as the degenerated shell elements the numerical examples show that neither thickness nor shear locking are present even for distorted element shapes 1998 john wiley sons ltd

on the physical significance of higher order kinematic and static variables in a three dimensional shell formulation abstract in recent years considerable attention has been given to the development of higher order plate and shell models these models are able to approximately represent three dimensional effects while pertaining the efficiency of a two dimensional formulation due to pre integration of the structural stiffness matrix across the thickness especially the possibility to use unmodified complete three dimensional material laws within shell analysis has been a major motivation for the development of such models while the theoretical and numerical formulation of so called 7 parameter shell models including a thickness stretch of the shell has been discussed in numerous papers no thorough investigation of the physical significance of the additional kinematic and static variables coming along with the extension into three dimensions is known to the authors however realization of the mechanical meaning of these quantities is decisive for both a proper modeling of shell structures e g concerning loading and kinematic boundary conditions and a correct interpretation of the results in the present paper the significance of kinematic and static variables appearing in a 7 parameter model proposed by buchter and ramm 1992a are discussed it is shown how these quantities refine the model behavior and how they can be related to the classical variables such as curvatures and stress resultants furthermore the special role of the material law within such a formulation is addressed it is pointed out that certain requirements must hold for the variation of kinematic and static variables across the thickness to ensure correct results in this context it is found that the considered 7 parameter model can be regarded as optimal with respect to the number of degrees of freedom involved

numerical implementation of multiplicative elasto plasticity into assumed strain elements with application to shells at large strains alternative formulations of isotropic large strain elasto plasticity are presented which are especially well suited for the implementation into assumed strain elements based on the multiplicative decomposition of the deformation gradient into elastic and plastic parts three distinct eigenvalue problems related to the reference intermediate and current configuration are investigated these eigenvalue problems are connected by similarity transformations which preserve the eigenvalues they play an important role in the subsequent development of alternative constitutive formulations and the corresponding finite element implementation the developed constitutive procedures rely on the right cauchy green tensor or equivalently on the green lagrangian strain tensor rather than the deformation gradient consequently they can be applied directly to assumed strain elements specifically we are concerned with efficient low order shell elements for which the assumed strain method has proven to be extremely powerful to overcome spurious locking effects

self replicating spots in reaction diffusion systems in this article we discuss the self replicating spot a particlelike phenomenon that occurs in reaction diffusion rd systems 1 the spots consist of localized regions in which the concentrations of the reactants differ from the surrounding concentration fields they grow reaching a critical size at which time they divide in two the two resulting spots again grow and divide this process which is visually similar to cell division continues indefinitely the long time behavior depends on the precise values of the external control parameters but typically consists of a chaotic soup in which many spots compete for resources as illustrated in fig 1 those spots that find adequate resources continue to grow and divide those that are unable to find adequate resources decay into the background the spots observed in 1 were found during an attempt to model labyrinthine patterns in the ferrocyanide iodate sulfate fis reaction 2 since then replicating spot patterns have been observed both numerically and experimentally in the fis reaction 3 4 there are obvious differences in the gaspar showalter model of the fis reaction 5 and of the models discussed by us and others this fact suggests that replication is a generic feature characterizing a broad class of reaction diffusion systems in 6 we presented some arguments in support of this proposition these arguments included both a heuristic description of the process of replication and demonstrations of analytic features common to several related model rd systems it turns out that replication is more general than our analysis accounts for nevertheless we think it worthwhile to spell out the details of the theory presented in 6 we remark here that various aspects of the replication phenomenon have been discussed by other authors 7 8 kerner and osipov have a large body of work on largeamplitude dissipative structures including an analysis of the static division of one dimensional pulses as the system size is changed gurevich and mints have a body of work on replication of thermal hot spots in composite superconductors in the article by petrov scott and showalter replication

slowly modulated two pulse solutions in the gray scott model i asymptotic construction and stability two pulse solutions play a central role in the phenomena of self replicating pulses in the one dimensional 1 d gray scott model in the present work part i of two parts we carry out an existence study for solutions consisting of two symmetric pulses moving apart from each other with slowly varying velocities this corresponds to a mildly strong pulse interaction problem in which the inhibitor concentration varies on long spatial length scales critical maximum wave speeds are identified and odes are derived for the wave speed and for the separation distance between the pulses in addition the formal linear stability of these two pulse solutions is determined good agreement is found between these theoretical predictions and the results from numerical simulations the main methods used in this paper are analytical singular perturbation theory for the existence demonstration and the nonlocal eigenvalue problem nlep method developed in our earlier work for the stability analysis the analysis of

finite deformation higher order shell models and rigid body motions this paper focuses on the developments of higher order shell models by employing the new concept of interpolation surfaces i surfaces inside the shell body we introduce n n p 3 i surfaces and choose the values of displacements with correspondence to these surfaces as fundamental shell unknowns such choice allows first to develop various higher order shell models in a very compact form and second to derive non linear strain displacement relationships which are completely free for arbitrarily large rigid body motions the general 3n parameter shell model is proposed in the framework of the lagrangian description the special 9 12 and 15 parameters cases corresponding to n 3 4 and 5 have been dealt in detail the proposed shell models account for thickness stretching and the complete 3d constitutive equations are utilized the displacement vectors of equally located i surfaces for each model are represented in a convected curvilinear coordinate system allowing one to develop directly finite deformation geometrically exact shell finite elements which could be discussed in future works 2008 elsevier ltd all rights reserved

non linear exact geometry 12 node solid shell element with three translational degrees of freedom per node this paper presents the finite rotation exact geometry eg 12 node solid shell element with 36 displacement degrees of freedom the term eg reflects the fact that coefficients of the first and second fundamental forms of the reference surface and christoffel symbols are taken exactly at each element node the finite element formulation developed is based on the 9 parameter shell model by employing a new concept of sampling surfaces s surfaces inside the shell body we introduce three s surfaces namely bottom middle and top and choose nine displacements of these surfaces as fundamental shell unknowns such choice allows one to represent the finite rotation higher order eg solid shell element formulation in a very compact form and to derive the strain displacement relationships which are objective that is invariant under arbitrarily large rigid body shell motions in convected curvilinear coordinates the tangent stiffness matrix is evaluated by using 3d analytical integration and the explicit presentation of this matrix is given the latter is unusual for the non linear eg shell element formulation copyright 2011 john wiley sons ltd

an isogeometric continuum shell element for non linear analysis an isogeometric continuum shell formulation is proposed in which nurbs basis functions are used to construct the reference surface of the shell through the thickness behavior is interpolated using a higher order b spline which is in contrast to the standard continuum shell solid like shell formulation where a linear lagrange shape function is typically used in the thickness direction the present formulation yields a complete isogeometric representation of the continuum shell the shell element is implemented in a standard finite element code using bezier extraction which facilitates numerical integration on the reference surface of the shell through the thickness integration is done using a connectivity array which determines the support of a b spline basis function over an element the formulation has been verified using different linear and geometrically non linear examples the ability of the formulation in modelling buckling of static delaminations in composite materials is also demonstrated

the stability of spike solutions to the one dimensional gierer meinhardt model abstract the stability properties of an n spike equilibrium solution to a simplified form of the gierer meinhardt activator inhibitor model in a one dimensional domain is studied asymptotically in the limit of small activator diffusivity e the equilibrium solution consists of a sequence of spikes of equal height the two classes of eigenvalues that must be considered are the o 1 eigenvalues and the o e2 eigenvalues which are referred to as the large and small eigenvalues respectively the spike pattern is stable when the parameters in the gierer meinhardt model are such that both sets of eigenvalues lie in the left half plane for a certain range of these parameters and for n 2 and e 0 it is shown the o 1 eigenvalues are in the left half plane only when d d n where d n is another critical value of d which satisfies d n n thus when n 2 and e 1 the spike pattern is stable only when d n an explicit formula for d n is given for the special case n 1 it is shown that a one spike equilibrium solution is stable when d d1 e an asymptotic formula for d1 e is given finally the dynamics of a one spike solution is studied by deriving a differential equation for the trajectory of the center of the spike

dynamics and stability of spike type solutions to a one dimensional gierer meinhardt model with sub diffusion abstract the dynamics and stability of spike type patterns to a sub diffusive gierer meinhardt reaction diffusion system is studied in a one dimensional spatial domain a differential algebraic system dae is derived to characterise the dynamics of an n spike quasi equilibrium pattern in the presence of sub diffusion with sub diffusive effects it is shown that quasi equilibrium spike patterns exist for diffusivity ratios asymptotically smaller than for the case of regular diffusion and that the spikes approach their equilibrium locations at an algebraic rather than exponential rate in time a new non local eigenvalue problem nlep is derived to examine the stability of an n spike pattern for a two spike pattern sub diffusion has little effect on the competition instability threshold whereas the threshold associated with an oscillatory instability of the spike profile increases significantly furthermore for a multi spike pattern it is shown that an asynchronous oscillatory instability of the spike profile rather than a synchronous oscillatory instability characteristic of the case of regular diffusion is the dominant instability when the anomaly index is below a certain threshold detailed numerical results are presented for the two spike case

self replication of mesa patterns in reaction diffusion systems abstract certain two component reaction diffusion systems on a finite interval are known to possess mesa box like steady state patterns in the singularly perturbed limit of small diffusivity for one of the two solution components as the diffusivity d of the second component is decreased below some critical value d c with d c o 1 the existence of a steady state mesa pattern is lost triggering the onset of a mesa self replication event that ultimately leads to the creation of additional mesas the initiation of this phenomena is studied in detail for a particular scaling limit of the brusselator model near the existence threshold d c of a single steady state mesa it is shown that an internal layer forms in the centre of the mesa the structure of the solution within this internal layer is shown to be governed by a certain core problem comprised of a single nonautonomous second order ode by analysing this core problem using rigorous and formal asymptotic methods and by using the singular limit eigenvalue problem slep method to asymptotically calculate small eigenvalues an analytical verification of the conditions of nishiura and ueyama y nishiura d ueyama a skeleton structure of self replicating dynamics physica d 130 1 1999 73 104 believed to be responsible for self replication is given these conditions include 1 the existence of a saddle node threshold at which the steady state mesa pattern disappears 2 the dimple shaped eigenfunction at the threshold believed to be responsible for the initiation of the replication process and 3 the stability of the mesa pattern above the existence threshold finally we show that the core problem is universal in the sense that it pertains to a class of reaction diffusion systems including the gierer meinhardt model with saturation where mesa self replication also occurs

calculation of impact contact problems of thin elastic shells taking into account geometrical nonlinearities within the contact region abstract during impact of elastic bodies contact stresses are transmitted in time depending contact surfaces in many impact contact problems large displacements and rotations appear only in the contact surface and in a certain neighbourhood therefore it is efficient to consider geometrical nonlinearities only in this region and to describe the remainder of the body within the geometrical linear theory this leads to substructure techniques where only properties of the nonlinear elements need be modified during the impact contact process the principle of virtual work for nonlinear thin shells is expressed using the total lagrangian formulation and the geometrical nonlinearity of thin shells is described in the frame of moderate rotation theory the contact conditions lead to inequalities for the normal stresses and displacements in the contact interfaces therefore the numerical algorithm involves two superposed iterations for the computation of contact forces and contact areas and for the geometrical nonlinearity the iteration procedure has to be carried out in each time step the spatial discretization using finite element techniques leads to a system of ordinary differential equations which is integrated over the time using the newmark algorithm numerical results were obtained for the impact contact problem of spherical shells for these examples the impact forces and the contact pressure distribution are presented for several parameter combinations results are controlled by conservation laws in integral form and compared with results from geometrical linear theory

traveling spike autosolitons in the gray scott model abstract we developed singular perturbation techniques based on the strong separation of time and length scales to construct the solutions in the form of the traveling spike autosolitons self sustained solitary waves in the gray scott model of an autocatalytic reaction we found that when the inhibitor diffusion is sufficiently slow the ultrafast traveling spike autosolitons are realized in a wide range of parameters when the diffusion of the inhibitor is sufficiently fast the slower traveling spike autosolitons with the diffusion precursor are realized we asymptotically calculated the main parameters such as speed and amplitude of these autosolitons as well as the regions of their existence in the gray scott model we also showed that in certain parameter regions the traveling spike autosolitons coexist with static

tracking control for boundary controlled parabolic pdes with varying parameters combining backstepping and differential flatness the combination of backstepping based state feedback control and flatness based trajectory planning and feedforward control is considered for the design of an exponentially stabilizing tracking controller for a linear diffusion convection reaction system with spatially and temporally varying parameters and nonlinear boundary input for this in a first step the backstepping transformation is utilized to determine a state feedback controller which transforms the original distributed parameter system into an appropriately chosen exponentially stable distributed parameter target system of a significantly simpler structure in a second step the flatness property of the target system is exploited in order to determine the feedforward controller which allows us to realize the tracking of suitably prescribed trajectories for the system output this results in a systematic procedure for the design of an exponentially stabilizing tracking controller for the considered general linear diffusion convection reaction system with varying parameters whose applicability and tracking performance is evaluated in simulation studies

anisotropic elastic plastic analysis of shells at large strains a comparison of multiplicative and additive approaches to enhanced finite element design and constitutive modelling the article presents new aspects of large strain anisotropic elastoplastic analyses of shells on the side of computational shell analysis we focus on recently developed brick type mixed finite shell elements based on trilinear displacement interpolations equipped with enhanced strain modes and shell typical assumed strain modifications here we compare two classes of this shell element design based on a multiplicative and an additive definition of an enhanced strain measure respectively furthermore for both types of continuum based shell elements we outline unified interfaces to strain driven constitutive stress update algorithms of anisotropic finite plasticity on the side of computational plasticity we investigate two classes of constitutive models suitable for the description of anisotropic elastoplastic response at finite strains the first framework uses a multiplicative definition of an elastic strain measure based on a plastic map the second an additively defined elastic strain measure based on a plastic metric both constitutive frameworks use hencky type logarithmic strain measures and are specified to a model problem of orthotropic elastic plastic response of a standard material the algorithmic treatment of the two constitutive models is based on an incremental variational formulation that defines the stresses and consistent tangent moduli in terms of a function evaluation we compare the performances of the two finite element formulations and the two constitutive models by means of numerical simulations of sheet drawing processes for the range of metal plasticity at moderate strains it is shown that results obtained with the different approaches are close to each other while the additive approaches provide simpler and more efficient settings copyright 2004 john wiley sons ltd

pattern selection for two breathers this paper is devoted to the study of pattern selection problems among two different types of layer oscillating solutions in phase and out of phase breathers of reaction diffusion systems varepsilon tau u t varepsilon 2 u xx f u upsilon quad upsilon t upsilon xx g u upsilon involving two parameters 0 0 it is shown that the selected pattern i e stable observable solution strongly depends on the location of internal layers especially for sufficiently small varepsilon the shift of pattern selection occurs arbitrarily many times from in phase to out of phase or vice versa when two layersapproach the boundary separately while the only observable oscillation mode is out of phase when twolayers come close

a skeleton structure of self replicating dynamics abstract self replicating patterns srp have been observed in several chemical reaction models such as the gray scott gs model as well as in physical experiments watching these experiments computational and physical is like watching the more familiar coarsening processes but in reverse the number of unit localized patterns increases until they fill the domain completely self replicating dynamics then can be regarded as a transient process from a localized trigger to a stable stationery or oscillating turing pattern since it is a transient process it is very difficult to give a suitable definition to characterize srp it cannot be described in terms of well studied structures such as the attractor or a singular saddle orbit for a dynamical system in this paper we present a new point of view to describe the transient dynamics of srp over a finite interval of time we focus our attention on the basic mechanism causing srp from a global bifurcational point of view and take our clues from two model systems including the gs model a careful analysis of the anatomy of the global bifurcation diagram suggests that the dynamics of srp is related to a hierarchical structure of limit points of folding bifurcation branches in parameter regions where the branches have ceased to exist thus the skeleton structure mentioned in the title refers to the remains of bifurcation branches the aftereffects of which are manifest in the dynamics of srp one of the natural and important problems is about the existence of an organizing center from which the whole hierarchical structure of limit points emerges in our setting the numerics suggests a strong candidate for that i e bogdanov takens turing btt singularity together with the presence of a stable critical point and so this indicates a universality of the above structure in the class of equations sharing this characteristic

on turnpike and dissipativity properties of continuous time optimal control problems this paper investigates the relations between three different properties which are of importance in optimal control problems dissipativity of the underlying dynamics with respect to a specific supply rate optimal operation at steady state and the turnpike property we show in a continuous time setting that if along optimal trajectories a strict dissipation inequality is satisfied then this implies optimal operation at this steady state and the existence of a turnpike at the same steady state finally we establish novel converse turnpike results i e we show that the existence of a turnpike at a steady state implies optimal operation at this steady state and dissipativity with respect to this steady state we draw upon a numerical example to illustrate our findings

cohesive zone models higher order continuum theories and reliability methods for computational failure analysis a concise overview is given of various numerical methods that can be used to analyse localization and failure in engineering materials the importance of the cohesive zone approach is emphasized and various ways to incorporate the cohesive zone methodology in discretization methods are discussed numerical representations of cohesive zone models suffer from a certain mesh bias for discrete representations this is caused by the initial mesh design while for smeared representations it is rooted in the ill posedness of the rate boundary value problem that arises upon the introduction of decohesion a proper representation of the discrete character of cohesive zone formulations which avoids any mesh bias can be obtained elegantly when exploiting the partition of unity property of finite element shape functions the effectiveness of the approach is demonstrated for some examples at different scales moreover examples are shown how this concept can be used to obtain a proper transition from a plastifying or damaging continuum to a shear band with gross sliding or to a fully open crack true discontinuum when adhering to a continuum description of failure higher order continuum models must be used meshless methods are ideally suited to assess the importance of the higher order gradient terms as will be shown finally regularized strain softening models are used in finite element reliability analyses to quantify the probability of the emergence of various possible failure modes

layer oscillations in reaction diffusion systems this paper considers a two component system of reaction diffusion equations involving two parameters varepsilon and tau varepsilon tau u 1 varepsilon 2 u xx f u v qquad v

a model of finite strain viscoplasticity based on unified constitutive equations theoretical and computational considerations with applications to shells abstract a model of multiplicative finite strain viscoplasticity is developed hereby the elastic internal potential is assumed to depend quadratically on the elastic strain measure ce by means of corresponding invariants hence possible extension of the model to take anisotropy into account is straightforward the evolution equation of the unified type due to bodner and partom asme j appl mech 42 1975 385 are modified so as to fit into the framework adopted the numerical treatment of the problem is fully developed specifically the algorithmic aspects of the resulting non additive structure are intensively discussed hereby the treatment of the exponential map of a non symmetric argument is of a central importance two consistent methods are developed various applications to shell problems are considered hereby a shell theory with seven degrees of freedom together with a 4 node enhanced strain finite element formulation are used a central feature of the shell formulation is its eligibility to the application of a three dimensional constitutive law

numerical analysis of rotationally symmetric shells by the modal superposition method the system of differential equations governing the analysis of rotationally symmetric shells under time dependent or static surface loadings is formulated with the transverse meridional and circumferential displacements as the dependent variables the thickness of the shell may vary and four homogeneous boundary conditions may be prescribed at each boundary edge of the shell the governing differential equations for each fourier harmonic are obtained by use of fourier series in the circumferential direction of the shell influence coefficients at each of the node points along the shell meridian are obtained for each fourier component by employing ordinary finite difference representations for the meridional co ordinate derivatives with these influence coefficients a set of homogeneous flexibility equations governing the free vibration characteristics of the shell is obtained and solved for the frequencies and mode shapes for each fourier component the solutions under time dependent or static surface loadings and due to initial displacements and velocities are then obtained by expanding the solutions in terms of the modes of free vibration of the shell for each fourier component the solution for the total shell response is obtained by fourier series summation solutions for typical shells have been found to be in excellent agreement with solutions by the method of temporal and spatial finite differences solutions for a parabolic shell are presented as an example the solution is also presented for a published cylindrical shell example and is seen to be in excellent agreement with the published finite element method results

implications of dissipativity on stability of economic model predictive control the indefinite linear quadratic case abstract in contrast to the conventional model predictive control mpc approach to control of a given system where a positive definite objective function is employed economic mpc employs a generic cost which is related to the economics of the process as the objective function in the regulation layer often stability proofs of the closed loop system are based on strict dissipativity of the system with respect to this objective function in this paper we focus on linear systems with indefinite quadratic costs we show that while strict dissipativity guarantees stability of the closed loop system it is not required hence we formulate a necessary and sufficient condition that guarantees asymptotic stability of the closed loop system this condition comes down to the existence of two distinct storage functions for which the system is dissipative

global bifurcations at the onset of pulse self replication in this work we carried out an extensive numerical exploration of the delicate global dynamics of pulse self replication and analyzed the stability of singular homoclinic stationary solutions and their bifurcations in the one dimensional gray scott model this stability analysis has several implications for understanding the recently discovered phenomena of self replicating pulses the solutions of the ordinary differential equation are organized around a codimension 2 global bifurcation from which two or n branches of homoclinic orbits originate corresponding to solitary pulse solutions in the partial differential equation a careful analysis of the bifurcation scenarios in the global bifurcation diagram suggests that the dynamics of the self replicating system are related to a hierarchy structure of folding bifurcation branches in parameter space the numerical simulation suggests that the bogdanov takens points together with the presence of critical points emanating from a particular codimension 2 homoclinic orbit play a central role for the global bifurcation of periodic orbits the homoclinic solutions and the complex chaotic dynamics the numerical simulation also reveals the existence of a modulating two pulse or multipulse which accompanies the procedure of pulse self replication in reaction diffusion systems

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

stabilization of strictly dissipative discrete time systems with discounted optimal control abstract we consider stabilization of an equilibrium point via infinite horizon discounted optimal control in discrete time in addition to applications in economics and social sciences discounted optimal control is a commonly used numerical technique guaranteeing solvability of certain classes of optimal control problems in this paper we present conditions based on strict dissipativity that ensure that the optimally controlled system is asymptotically stable or practically asymptotically stable these conditions are shown to be complementary to recently proposed conditions based on a detectability property illustrative examples are provided

a continuum based shell theory for non linear applications the paper introduces a non linear shell theory which provides a complete three dimensional state of stress since the theory is derived from simple three dimensional continuum mechanics it is very easy to understand as an example the theory is applied to quadrilateral shell elements which provide only displacement degrees of freedom located at nodes on the outer surfaces and one degree of freedom at the middle surface it is proposed to eliminate this degree of freedom on element level so that the elements have the same layout as the equivalent brick elements but have a better behaviour in bending have stress resultants and are cheaper with respect to computational effort the advantages with respect to implementation in a finite element program as well as in special applications are obvious however well known conditioning problems in thin shell applications must be expected therefore emphasis is put on this issue in the example problems it is shown that the elements can give acceptable answers in engineering applications and offer a potential for material non linear applications which will be considered in a forthcoming paper

a lie backlund approach to equivalence and flatness of nonlinear systems a new system equivalence relation using the framework of differential geometry of jets and prolongations of infinite order is studied in this setting two systems are said to be equivalent if any variable of one system may be expressed as a function of the variables of the other system and of a finite number of their time derivatives this is a lie backlund isomorphism the authors prove that although the state dimension is not preserved the number of input channels is kept fixed they also prove that a lie backlund isomorphism can be realized by an endogenous feedback the differentially flat nonlinear systems introduced by the authors 1992 via differential algebraic techniques are generalized and the new notion of orbitally flat systems is defined they correspond to systems which are equivalent to a trivial one with time preservation or not the endogenous linearizing feedback is explicitly computed in the case of the vtol aircraft to track given reference trajectories with stability

curved shell elements based on hierarchical p approximation in the thickness direction for linear static analysis of laminated composites this paper presents a new curved shell finite element formulation for linear static analysis of laminated composite plates and shells where the displacement approximation in the direction of the shell thickness can be of an arbitrary polynomial order p thereby permitting strains of at least p 1 order this is accomplished by introducing additional nodal variables in the element displacement approximation corresponding to the lagrange interpolating polynomials in the element thickness direction the resulting element displacement approximation has an important hierarchical property i e the approximation functions and the generalized nodal variables corresponding to an approximation order p are a subset of those corresponding to an approximation order p 1 the element formulation ensures c0 continuity or smoothness of displacements across the interelement boundaries the element properties stiffness matrix and equivalent load vectors are derived using the principle of virtual work and the hierarchical element approximation the formulation is extended for generally orthotropic material behaviour where the material directions are not necessarily parallel to the global axes further extension of this formulation for laminated composites is accomplished by incorporating the material properties of each lamina by numerically integrating the element stiffness matrix for each lamina the formulation has no restriction on either the number of laminas or the layup pattern of the laminas each lamina can be generally orthotropic and the material directions and the lamina thicknesses may vary from point to point within each lamina the geometry of the laminated shell element is described by the co ordinates of the nodes lying on the middle surface of the element and the lamina thicknesses at each node the formulation permits any desired order displacement or strain approximation in the shell thickness direction without remodelling numerical examples are presented to demonstrate the accuracy efficiency and overall superiority of the present formulation the results obtained from the present formulation are compared with those available in the literature as well as the analytical solutions

continuous time linear predictive control and flatness a module theoretic setting with examples a general flatness based framework for linear continuous time predictive control is presented the mathematical setting which is valid for multivariable systems is provided by the algebraic theory of modules where a controllable system corresponds to a finitely generated free module over a principal ideal ring any basis of this free module is a flat output which yields an easy calculation of the predicted trajectory this formalism permits one to handle non minimum phase systems system constraints and to deal with additive perturbations three concrete case studies namely a dc motor a flexible system and a cement mill are analysed and simulations are given these examples are written in such a way that any reader who is not familiar with module theory may nevertheless grasp the proposed control strategy

computation of multiple lie derivatives by algorithmic differentiation lie derivatives are often used in nonlinear control and system theory in general these lie derivatives are computed symbolically using computer algebra software although this approach is well suited for small and medium size problems it is difficult to apply this technique to very complicated systems we suggest an alternative method to compute the values of iterated and mixed lie derivatives by algorithmic differentiation

brief on the linearizability of nonisothermal continuous stirred tank reactors in this paper we consider the dynamic feedback linearizability and flatness of chemical processes using an exterior calculus approach the flatness of a large class of nonisothermal continuous stirred tank chemical reactor is demonstrated it is shown that flatness is independent of reaction kinetics and heat transfer considerations for plant models with kinetics relate three chemical species or less we identify linearizing outputs that are common to all members of a given class

one point quadrature shell element with through thickness stretch a general purpose one point quadrature shell element accounting for through thickness deformation is developed in the shell a complete 3 d constitutive law is introduced leading to a 7 parameter theory which explicitly accounts for thickness change and also for a linear variation of thickness stretch an interpolation scheme for the shell director is developed to avoid thickness locking the developed shell element covers flexible warping behavior by using a local nodal coordinate system at each node which is updated with second order accuracy a physical stabilization scheme for zero energy modes is employed based on the decomposition of the strain field into constant and linear terms with respect to the natural coordinates the rigid body projection is applied to treat rigid body rotations effectively linear and nonlinear patch tests including elasto plasticity and contact are performed and the results are compared with analytical or previously reported results the results are also compared with those of 5 parameter shell elements in order to show that there is no significant deterioration in accuracy especially for thin shell applications

an investigation of a finite rotation four node assumed strain shell element the paper presents a shell formulation based on the degenerated solid approach the theory employs covariant strains and performs explicit integration through the shell thickness the rigid body motion is exactly represented the consistent tangent stiffness matrix is evaluated for the four node quadrilateral it is shown in the final part that this type of element which distinguishes itself by a very simple and easily understandable theory gives good answers for linear as well as non linear applications

flatness based control of a nonlinear chemical reactor model the nonlinear model of a continuous stirred tank reactor is shown to be flat the flatness permits the design of suitable trajectories on the basis of the explicit stationary solution and the tracking of these trajectories asymptotically using quasi static state feedback linearization a nonlinear local observer with a time varying gain is designed allowing the realisation of the state feedback in the case of partial measurement of the state simulation results illustrate the tracking behavior of the closed loop with the observer

constrained reachability and trajectory generation for flat systems we consider the problem of trajectory generation for constrained differentially flat systems based on the topological properties of the set of admissible steady state values of a flat output we derive conditions which allow for an a priori verification of the feasibility of constrained set point changes we propose to utilize this relation to generate feasible reference trajectories to this end we suggest to split the trajectory generation problem into two stages a the planning of geometric reference paths in the flat output space combined with b an assignment of a dynamic reference motion to these paths this assignment is based on a reduced optimal control problem the unique feature of the approach is that due to the specific construction of the reference paths the optimal control problem to be solved is guaranteed to be feasible to illustrate our results we consider a van de vusse reactor as an example

a large deformation solid shell concept based on reduced integration with hourglass stabilization in this paper a new eight node brick solid shell finite element formulation based on the concept of reduced integration with hourglass stabilization is presented the work focuses on static problems the starting point of the derivation is the three field variational functional upon which meanwhile established 3d enhanced strain concepts are based important additional assumptions are made to transfer the approach into a powerful solid shell first of all a taylor expansion of the first piola kirchhoff stress tensor with respect to the normal through the centre of the element is carried out in this way the stress becomes a linear function of the shell surface co ordinates whereas the dependence on the thickness co ordinate remains non linear secondly the jacobian matrix is replaced by its value in the centre of the element these two assumptions lead to a computationally efficient shell element which requires only two gauss points in the thickness direction and one gauss point in the plane of the shell element additionally three internal element degrees of freedom have to be determined to avoid thickness locking one important advantage of the element is the fact that a fully three dimensional stress state can be modelled without any modification of the constitutive law the formulation has only displacement degrees of freedom and the geometry in the thickness direction is correctly displayed copyright 2006 john wiley sons ltd

on the modelling of smooth contact surfaces using cubic splines in this paper a new strategy for the smooth representation of 2d contact surfaces is developed and implemented the contact surfaces are modelled using cubic splines which interpolate the nite element nodes these splines provide a unique surface normal vector and do not require prior knowledge of surface tangents and normals c continuous cubic splines are suitable for representing rigid contact surfaces while c continuous overhauser splines are shown to be most suitable for representing exible contact surfaces a consistent linearization of the kinematic contact constraints based on the spline interpolation is derived the new spline based contact surface interpolation scheme does not in uence the element calculations consequently it can be easily implemented in standard fe codes several numerical examples are used to illustrate the advantages of the proposed smooth representation of contact surfaces the results show a signi cant improvement in accuracy compared to traditional piecewise element based surface interpolation the predicted contact stresses are also less sensitive to the mismatch in the meshes of the di erent contacting bodies this property is useful for problems where the contact area is unknown a priori and when there is signi cant tangential slip copyright 2001 john wiley sons ltd

canonical form observer design for non linear time variable systems an observer of canonical phase variable form for non linear time variable systems is introduced the development of this non linear time variable form requires regularity of the non linear time variable observability matrix of the system from the relationships derived during the development it follows that a non linear time variable observer can be dimensioned by an eigenvalue assignment with respect to the canonical state coordinates if a linearization of system non linearities about the reconstructed state trajectories is permissible this is an assumption similar to that of the extended kalman filter based on a linearization about the current estimate

flatness and defect of non linear systems introductory theory and examples we introduce flat systems which are equivalent to linear ones via a special type of feedback called endogenous their physical properties are subsumed by a linearizing output and they might be regarded as providing another nonlinear extension of kalman s controllability the distance to flatness is measured by a non negative integer the defect we utilize differential algebra where flatness and defect are best defined without distinguishing between input state output and other variables many realistic classes of examples are flat we treat two popular ones the crane and the car with n trailers the motion planning of which is obtained via elementary properties of plane curves the three non flat examples the simple double and variable length pendulums are borrowed from non linear physics a high frequency control strategy is proposed such that the averaged systems become flat

large deformation analysis of contact in degenerate shell elements a new formulation is presented for the analysis of contact in degenerate shell elements this formulation accounts for the transverse stress and strain through the shell thickness and can accommodate double sided shell contact the kinematic contact conditions are expressed accurately in terms of the physical shell contacting surfaces and the problem is formulated in terms of variational inequalities vi large deformations and rotations are accounted for by invoking the appropriate stress and strain measures the solution of the variational inequality is obtained using lagrange multipliers this guarantees that the kinematic contact constraints are accurately satisfied and that the solution is free from user defined parameters two examples involving three beams in contact and ring compression are simulated to establish the validity of the developed formulations and the solution technique 1998 john wiley sons ltd

isogeometric thickness stretchable shell efficient formulation for nonlinear dynamic problems an isogeometric shell element with through thickness stretch is introduced and applied to quasi static and dynamic problems the shell element supports full three dimensional constitutive laws ie the plane stress assumption is not required an updated lagrangian rate formulation is adopted and biquadratic spline based interpolation functions are used for in plane interpolation the concept of fiber mass scaling is proposed to lower the highest eigenfrequencies to improve the performance of the formulation clamped and unclamped knot vectors are compared and the advantages of using unclamped knot vectors are demonstrated the shell element is validated using several benchmark tests which indicate good performance of the proposed formulation

continuous time non linear flatness based predictive control an exact feedforward linearisation setting with an induction drive example a general flatness based framework for non linear continuous time predictive control is presented it extends the results of fliess and marquez 2000 to the non linear case the mathematical setting which is valid for multivariable systems is provided by the theory of flatness based exact feedforward linearisation introduced by the authors hagenmeyer and delaleau 2003b thereby differential flatness does not only yield an easy calculation of the predicted trajectories considering the respective system constraints but allows to use simple linear feedback parts in a two degree of freedom control structure moreover this formalism permits one to handle non minimum phase systems and furthermore to deal with parameter uncertainties and exogenous perturbations respective robustness analysis tools are available finally an induction drive example is discussed in detail and experimental results for this fast electro mechanical system are presented

homoclinic bifurcations at the onset of pulse self replication we establish a series of properties of symmetric n pulse homoclinic solutions of the reduced gray scott system u uv 2 v v uv 2 which play a pivotal role in questions concerning the existence and self replication of pulse solutions of the full gray scott model specifically we establish the existence and study properties of solution branches in the plane that represent multi pulse homoclinic orbits where and are the central values of u x and v x respectively we prove bounds for these solution branches study their behavior as and establish a series of geometric properties of these branches which are valid throughout the plane we also establish qualitative properties of multi pulse solutions and study how they bifurcate i e how they change along the solution branches

the existence and stability of spike equilibria in the one dimensional gray scott model the pulse splitting regime abstract the existence stability and pulse splitting behavior of spike patterns in the one dimensional gray scott model on a finite domain is analyzed in the semi strong spike interaction regime this regime is characterized by a localization of one of the components of the reaction near certain spike locations while the other component exhibits a more global spatial variation across the domain the method of matched asymptotic expansions is then used to construct k spike equilibria in terms of a certain core problem this core problem is studied numerically and asymptotically for each integer k 1 it is shown that there are two branches of k spike equilibria that meet at a saddle node bifurcation value for small values of the diffusivity d of the second component these saddle node bifurcation points occur at approximately the same value a combination of asymptotic and numerical methods is used to analyze the stability of these branches of k spike equilibria with respect to both drift instabilities associated with the small eigenvalues and oscillatory instabilities of the spike profile in this way the key bifurcation and spectral conditions of ei et al s ei y nishiura k ueda 2 n splitting or edge splitting a manner of splitting in dissipative systems jpn j ind appl math 18 2001 181 205 believed to be essential for pulse splitting behavior in a reaction diffusion system are verified by having verified these conditions a simple analytical criterion for the occurrence of pulse splitting is then formulated and confirmed with full numerical simulations of the gray scott model this criterion verifies a conjecture based on numerics and topological arguments reported in a doelman r a gardner t j kaper stability analysis of singular patterns in the 1d gray scott model a matched asymptotics approach physica d 122 1 4 1998 1 36 the analytical results are compared with previously obtained results for pulse splitting behavior

spatio temporal chaos for the gray scott model abstract a new geometrical criterion for the transition to spatio temporal chaos stc arising in the gray scott model is presented this is based on the inter relationship of global bifurcating branches of ordered patterns with respect to supply and removal rates contained in the model this viewpoint not only gives us a new criterion for the onset of stc but also clarifies how the orbit itinerates among several ordered patterns in infinite dimensional space moreover the geometrical characterization gives us a universal viewpoint about the onset and termination of stc there are at least two different mechanisms that cause re injection dynamics and drive the stc one is a generalized heteroclinic cycle consisting of self replication and self destruction processes and the other involves annihilation of colliding waves instead of self destruction

the dynamics of multispike solutions to the one dimensional gierer meinhardt model the dynamical behavior of spike type solutions to a simplified form of the gierer meinhardt activator inhibitor model in a one dimensional domain is studied asymptotically and numerically in the limit of small activator diffusivity varepsilon in the limit varepsilon to 0 a quasi equilibrium solution for the activator concentration that has n localized peaks or spikes is constructed asymptotically using the method of matched asymptotic expansions for an initial condition of this form a differential algebraicsystem of equations describing the evolution of the spike locations is derived the equilibrium solutions for this system are discussed the spikes are shown to evolve on a slow time scale tau varepsilon 2 t towards a stable equilibrium provided that the inhibitor diffusivity d is below some threshold and that a certain stability criterion on the quasi equilibrium solution is satisfied throughout the slow dynamics if this stability condition is not satisfied initially or else is no l

generalized state variable representation for a simplified crane description recent theoretical advances in nonlinear systems theory insist on the relevance of dynamics where control derivatives appear we discuss here a simplified model of a crane which exhibits such a description

slowly modulated two pulse solutions in the gray scott model ii geometric theory bifurcations and splitting dynamics with great sadness we note the passing away of our mentor and colleague wiktor abstract in this second paper we develop a geometrical method to systematically study the singular perturbed problem associated to slowly modulated two pulse solutions it enables one to see that the characteristics of these solutions are strongly determined by the flow on a slow manifold and hence also to identify the saddle node bifurcations and bifurcations to classical traveling waves in which the solutions constructed in part i are created and annihilated moreover we determine the geometric origin of the critical maximum wave speeds discovered in part i in this paper we also study the central role of the slowly varying inhibitor component of the two pulse solutions in the pulse splitting bifurcations finally the validity of the quasi stationary approximation is established here and we relate the results of both parts of this work to the literature on self replication

generalized energy momentum method for non linear adaptive shell dynamics in the present study a generalization of the energy momentum method denoted by generalized energy momentum method applied to the non linear dynamics of shells will be developed within the framework of the generalized a method this algorithmic environment contains the unconditionally stable energy momentum method and its numerically damped version as well as the classical newmark and a methods as special cases in order to control the size of the time steps of the integration scheme with respect to accuracy and eaciency an adaptive time stepping procedure based on local a posteriori error estimation will be improved for non linear dynamical systems and applied to the proposed class of algorithms the spatial discretization is realized by an eight noded finite shell element of reissner mindlin type including an extensible shell director field permitting the application of three dimensional material laws the original formulation of this finite element will be developed for non linear dynamic analysis and adapted for the employment within the introduced energy conserving decaying time integration scheme 1999 elsevier science s a all rights reserved

stability of the static spike autosolitons in the gray scott model we performed an asymptotic linear stability analysis of the static spike autosolitons ass self sustained solitary inhomogeneous states in the gray scott model of an autocatalytic chemical reaction we found that in one dimension these ass destabilize with respect to pulsations or the onset of traveling motion when the inhibitor is slow enough in higher dimensions the one dimensional static spike ass are always unstable with respect to corrugation and wriggling the higher dimensional radially symmetric static spike ass may destabilize with respect to the radially nonsymmetric fluctuations leading to their splitting when the inhibitor is fast or with respect to pulsations when the inhibitor is slow

on best fit corotated frames for 3d continuum finite elements summary we discuss a strategy to construct corotated frames for three dimensional continuum finite elements by minimizing deformations within the frame we find that irrespective of the type of element and the number of nodes using a quaternion parametrization of rotations this minimization is naturally stated as computing the smallest eigenvalue of a 4 4 matrix the simplicity of this smallest eigenvalue plays a crucial role when linearizing the kinematics ensuant quaternion algebra although lengthy results in remarkably simple formulas for projections that arise in the linearized kinematics the exact stiffness matrix does not require computation of the second derivative of the rotation function and is also given by a simple formula as a result the implementation of this corotational formulation becomes particularly straightforward furthermore in contrast to other results in the literature the stiffness matrix for elements with translational dofs is symmetric for illustration this corotational formulation is applied to a solid shell finite element and numerical results are presented copyright 2014 john wiley sons ltd received 25 april 2013 revised 15 october 2013 accepted 10 december 2013

a stress resultant shell theory based on multiscale homogenization in this paper we propose a multiscale method based on computational homogenization for simulating the mechanical response of a thin walled porous structure due to the inhomogeneous nature of the porous material in the thickness direction the length scale of the deformation field variations in the thickness direction is in the same order of magnitude as in the microstructure to resolve this issue a higher order stress resultant shell formulation with linear variation of the thickness stretch based on multiscale homogenization is considered the microscale is accounted for by calculating the micro fluctuations from a boundary value problem over the domain of a 3d representative volume element rve the breadth and width of the rve are determined by the representative microstructure of the porous material whereas in the thickness direction of the shell the rve completely resolves the microscopic variation as a result the macroscopic stress resultants are obtained as volume averages through the entire thickness of the shell the nested solution scheme is quite computationally demanding and it should only be applied where it is needed the paper is concluded by a couple of numerical examples that illustrate the method and support the arguments put forward in the paper comparison is made to a 2d plane strain reference solution with complete resolution of the microstructure over the domain also a 3d case is considered showing the significance of resolving the microscopic fluctuations

stability analysis of singular patterns in the 1d gray scott model a matched asymptotics approach abstract in this work we analyze the linear stability of singular homoclinic stationary solutions and spatially periodic stationary solutions in the one dimensional gray scott model this stability analysis has several implications for understanding the recently discovered phenomena of self replicating pulses for each solution constructed in a doelman et al nonlinearity 10 1997 523 563 we analytically find a large open region in the space of the two scaled parameters in which it is stable specifically for each value of the scaled inhibitor feed rate there exists an interval whose length and location depend on the solution type of values of the activator autocatalyst decay rate for which the solution is stable the upper boundary of each interval corresponds to a subcritical hopf bifurcation point and the lower boundary is explicitly determined by finding the parameter value where the solution disappears i e below which it no longer exists as a solution of the steady state system explicit asymptotic formulae show that the one pulse homoclinic solution gains stability first as the second parameter is decreased and then successively the spatially periodic solutions with decreasing period become stable moreover the stability intervals for different solutions overlap these stability results are derived via the reduction of a fourth order slow fast eigenvalue problem to a second order nonlocal eigenvalue problem nlep explicit determination of these stability intervals plays a central role in understanding pulse self replication numerical simulations confirm that the spatially periodic stationary solutions are attractors in the pulse splitting regime and moreover whenever for a given solution the value of the activator decay rate was taken to lie in the regime below that solution s stability interval initial data close to that solution were observed to evolve toward a different spatially periodic stationary solution one whose stability interval inclucded the parameter value the main analytical technique used is that of matched asymptotic expansions

axisymmetric ring solutions of the 2d gray scott model and their destabilization into spots this article concerns annular ring solutions of the gray scott model in the monostable regime annular rings are far fromequilibrium patterns supported on annuli inside of which the activator is concentrated the diffusive flux of inhibitor over long length scales toward such an annulus feeds the production of activator there and the interaction is semi strong numerical and experimental observations show that annular rings often split into spots and the main result presented in this article is a method to predict the number of spots that an annular ring unstable to angular disturbances will split into this method is an extension to 2d circular geometries of the nonlocal eigenvalue problem nlep method developed for pulse solutions of the 1d gray scott problem in which the full eigenvalue problem a pair of second order nonautonomous coupled equations is recast as a single second order equation with a nonlocal term we also continue the results for the monostable regime into the bistable regime of the gray scott model where target patterns exist and their rings are observed to destabilize into rings of spots as may be shown using a classical turing ginzburg landau analysis thus for these 2d circular geometries the nlep method is to the instability of annular rings in the monostable regime what the turing analysis is to the instability of target patterns in the bistable regime near criticality 2004 elsevier b v all rights reserved

a consistent tangent stiffness matrix for three dimensional non linear contact analysis a consistent tangent stiffness matrix for the analysis of non linear contact problems is presented the associated element has three or four nodes and establishes contact between three dimensional structures like solids and shells it accounts for the non linear kinematics of large deformation analysis and guarantees a quadratic convergence rate two formulations the penalty method and the lagrange multiplier method are investigated

flatness and quasi static state feedback in non linear delay systems two notions from the theory of non linear systems without time delays are generalized to non linear delay systems flatness and quasi static state feedback depending on the generality of the relations considered flatness properties of increasing generality are obtained flatness flatness flatness and difference differential flatness it is then shown that difference differentially flat delay systems are linearizable by a certain class of predictive quasi static state feedback i e that they are equivalent by such feedback to a linear controllable system the mathematical framework is difference differential algebra

flatness of semilinear parabolic pdes a generalized cauchy kowalevski approach a generalized cauchy kowalevski approach is proposed for flatness based trajectory planning for boundary controlled semilinear systems of partial differential equations pdes in a one dimensional spatial domain for this the ansatz presented in trajectory planning for boundary controlled parabolic pdes with varying parameters on higher dimensional spatial domains t meurer and a kugi ieee trans autom control vol 54 no 8 pp 1854 1868 aug 2009 using formal integration is generalized towards a unified design framework which covers linear and semilinear pdes including rather broad classes of nonlinearities arising in applications in addition an efficient semi numerical solution of the implicit state and input parametrizations is developed and evaluated in different scenarios simulation results for various types of nonlinearities and a tubular reactor model described by a system of semilinear reaction diffusion convection equations illustrate the applicability of the proposed method

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

finite element concepts for finite elastoplastic strains and isotropic stress response in shells theoretical and computational analysis this paper presents appropriate finite element concepts accounting for finite elastoplastic strains and isotropic stress response in arbitrary shells three parameterization strategies for the calculation of thin and thick smooth shells as well as shell intersections are discussed in detail in this context the importance of the deformation gradient for an efficient implementation is especially emphasized according to the parameterizations the computational plasticity algorithms are derived in general three dimensional 3 d form for thick shell structures and a restricted 2 d form satisfying the plane stress state underlying thin shells in order to describe arbitrary shell geometries the isoparametric concept is applied to all proposed finite element formulations these are based on quadrilateral 4 node mixed finite shell elements the variational approaches of the enhanced assumed strain method the assumed natural strain concept and the reduced integration technique are accurately considered by means of representative numerical examples the performance of the three different finite element concepts is demonstrated furthermore their individual properties are addressed with respect to efficiency and numerical accuracy thus crucial consequences for an optimal modelling of finite plastic strains in shells can be outlined

non linear behaviour of the rfns element large displacements and rotations the reformulated four node shell element has been shown to exhibit an excellent behaviour with respect to a well known set of benchmark tests for shell elements recently the performance of the rfns element was re confirmed in terms of its asymptotic behaviour by means of classical and new limit tests in the present paper the rfns formulation is extended to incorporate geometric non linear behaviour the total lagrangian formulation is employed the rfns element non linear formulation allows for large displacements and large rotations an efficient performance of the non linear rfns element formulation is confirmed for the applications investigated

the finite deformation theory for beam plate and shell part iv the fe formulation of mindlin plate and shell based on green lagrangian strain using the kinematic description of the revised mindlin model the lagrangian strain derived by li and the fe formulation of the degenerated 3 d solid we propose an exact finite deformation theory for plate and shell the theory eliminates the need for the restrictions imposed by the existing simplified theories such as small strains small rotations or small loading steps numerical examples are presented to demonstrate the validity and accuracy of the theory compared with 3 d continuum theory

trajectory planning for boundary controlled parabolic pdes with varying parameters on higher dimensional spatial domains the flatness based design of a feedforward tracking control is considered for the solution of the trajectory planning problem for a boundary controlled diffusion convection reaction system with spatially and temporally varying parameters defined on a 1 les m dimensional parallelepipedon with the nonlinear input being restricted to a m 1 dimensional hyperplane for this an implicit state and input parametrization in terms of a basic output is determined via a volterra type integral equation with operator kernel by recursively computing successive series coefficients a series solution of the integral equation is obtained whose absolute and uniform convergence is verified by restricting the system parameters and the basic output to a certain but broad gevrey class hence prescribing an admissible desired trajectory for the basic output directly yields the feedforward control by evaluating the input parametrization this results in a systematic procedure for trajectory planning and feedforward control design for boundary controlled parabolic distributed parameter systems defined on higher dimensional domains

dynamic three dimensional computations for solids with variable nodal connectivity for severe distortions this paper presents a three dimensional algorithm for dynamic lagrangian computations for solids with variable nodal connectivity to allow for severe distortions the nodes are analogous to flexible spheres when they move closer together than their equilibrium distance they generate compressive repulsive forces conversely when they move apart they generate tensile attractive forces material strength effects are also included because a node can be affected only by its neighbour nodes the approach has been designated the nabor approach the distinguishing feature of this technique is that it is possible to have variable connectivity a node can acquire new neighbours thus allowing all forms of distortion the three dimensional nabor algorithm has been incorporated as an option into the explicit finite element code epic 3 by using both the nabor grid and the traditional epic 3 finite element grid together it is possible to perform lagrangian computations for a wider range of problems

an algorithm for orbital feedback linearization of single input control affine systems feedback linearization is an effective design and analysis tool used in the study of nonlinear control systems however cases arise where linearizability conditions cannot be met for systems that are not linearizable by classical techniques orbital feedback linearization or feedback linearization by state dependent time scaling has been proposed to relax these conditions unfortunately approaches proposed to date have led to conditions that tend to be more difficult to check then conditions for state feedback linearization in this paper necessary and sufficient conditions for orbital feedback linearizability is presented for a class of single input nonlinear systems the conditions are simple and can be checked directly from the data of the problem using an exterior calculus approach a simple algorithm is developed to compute state dependent time scaling that yield state feedback linearizable systems it is shown that orbital feedback linearizability generalizes the concept state feedback linearizability to deal with locally weakly accessible control systems

a linear differential operator approach to flatness based tracking for linear and non linear systems this contribution presents a flatness based solution to the tracking for linear systems in differential operator representation since the differential operator representation is a flat system representation tracking controllers can easily be designed using dynamic output feedback then the differential operator approach for flatness based tracking of linear systems is extended to non linear systems the design of the resulting linear time varying dynamic output feedback controller is based on a linearization about the trajectory which directly yields the differential operator representation different from the non linear flatness based controller design the new approach uses linear methods both in stabilizing the tracking and in computing the output feedback controller the proposed design procedure assures exact tracking in the steady state when no disturbances are present a simple example demonstrates the design of a dynamic output feedback controller for the tracking of a non linear system

efficient isogeometric nurbs based solid shell elements mixed formulation and b method abstract in this work solid shell nurbs elements are developed in order to address static problems of slender structures under small perturbations a single layer of elements is considered through the thickness of the shell and the degree of approximation in that direction is chosen to be equal to two a full 3d constitutive relation is assumed the objective is to obtain highly accurate low degree elements to be used in coarse meshes in order to do that we propose a mixed method from which we derive a b projection to deal with locking the main idea is to modify the interpolation of the average stresses and strains through the thickness more precisely we develop two finite elements the first element which is based on the mixed method or equivalently on the b projection is extremely accurate but leads to a fully populated global stiffness matrix to improve the efficiency the second element uses a local least squares type procedure to define a new b projection leading to a sparse global stiffness matrix the quality and efficiency of the methods are assessed through several usual test cases and by comparison with other published techniques

kinematics of finite rotation shells with in plane twist parameter abstract the paper concerns shell equations derived from a 3d mixed formulation with explicit rotations the constitutive equation is postulated in terms of the relaxed biot stress and right stretch strain the shell kinematics is based on the reissner hypothesis and on a constant linear approximation of the rotation tensor with respect to the thickness coordinate the rotation around the shell director is parametrized by the drill and in plane twist parameters with the latter one associated with the linear approximation the in plane twist parameter is new and hence consequences of its presence for the shell rotation constrains and strain measures are examined and compared to the formulation with the drill rotation only in the presented formulation the drill rotation is retained explicitly and can be recovered from the drill rotation constraint while the in plane twist parameter is an internal parameter of the theory in this way the enhanced shell kinematics does not increase the number of degrees of freedom of a discrete model

a mathematical mechanism for instabilities in stripe formation on growing domains abstract a cascade process involving stripe splitting in reaction diffusion systems with isotropically growing one dimensional domains is studied such cascades propagating from a smaller domain to a larger domain have been proposed as an answer to the criticism that the turing mechanism lacks robustness because many stable patterns can coexist on a large domain and therefore the final state is very sensitive to the initial conditions in contrast if the system starts with a small domain very few stable patterns are possible which limits the sensitivity to the initial conditions in order to show the validity and limitations of this scenario we clarify the underlying mathematical mechanism that drives various types of stripe splitting via a reduction from partial differential equations to ordinary differential equations as well as investigating global arrangements of the set of n mode stripe branches with d n symmetry of the stripe locations the mathematical simplification above allows us to reveal how each n mode stripe branch is destabilized as the domain grows and to characterize the associated eigenprofiles that actually determine the manner of splitting at the infinitesimal level we find that all the d n symmetry breaking instabilities typically occur simultaneously up to leading order before the saddle node point of the n mode stripe branch is reached the instability with the largest real part is of the alternate type every other peak splits at the infinitesimal level a symmetry preserving instability appears at the saddle node point which drives the simultaneous type of splitting i e mode doubling due to competition between these two types of instabilities the problem depends subtly on the growth speed alternate splitting typically arises for slow growth and simultaneous splitting for fast growth for intermediate growth rates the manner of splitting becomes mixed and sensitive to fluctuations

dynamical hysteresis without static hysteresis scaling laws and asymptotic expansions we study dynamical hysteresis in a simple class of nonlinear ordinary differential equations namely first order equations subject to sinusoidal forcing the assumed nonlinearities are such that the area of the hysteresis loop vanishes as the forcing frequency tends to zero in other words there is no static hysteresis using regular and singular perturbation techniques we derive the first term in the asymptotic expansion for the loop area as a function of the driving frequency in the limit of both large and small frequency although the theory was originally motie have expanded ents on bistable semiconductor lasers it is applied here to explain and in some cases to correct the scaling laws that were recently reported in numerical studies of mean field kinetic ising models of ferromagnets

brief paper some examples and remarks on quasi static feedback of generalized states three simple nonlinear examples with physical background are considered they illustrate how generalized state representations which depend on time derivatives of the input occur it is shown with these examples how quasi static feedback of such generalized states may be used for input output decoupling disturbance rejection and linearization and thus for trajectory tracking