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

an efficient isogeometric solid shell formulation for geometrically nonlinear analysis of elastic shells abstract in this work an isogeometric solid shell model for geometrically nonlinear analyses is proposed it is based on a linear interpolation through the thickness and a nurbs interpolation on the middle surface of the shell for both the geometry and the displacement field the green lagrange strains are linearized along the thickness direction and a modified generalized constitutive matrix is adopted to easily eliminate thickness locking without introducing any additional unknowns and to model multi layered composite shells reduced integration schemes which take into account the high continuity of the shape functions are investigated to avoid interpolation locking and to increase the computational efficiency the relaxation of the constitutive equations at each integration point is adopted in the iterative scheme in order to reconstruct the equilibrium path using large steps and a low number of iterations even for very slender structures this strategy makes it possible to minimize the number of stiffness matrix evaluations and decompositions and it turns out to be particularly convenient in isogeometric analyses

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

a reduced integration solid shell finite element based on the eas and the ans concept large deformation problems in this paper we address the extension of a recently proposed reduced integration eight node solid shell finite element to large deformations the element requires only one integration point within the shell plane and at least two integration points over the thickness the possibility to choose arbitrarily many gauss points over the shell thickness enables a realistic and efficient modeling of the non linear material behavior only one enhanced degree of freedom is needed to avoid volumetric and poisson thickness locking one key point of the formulation is the taylor expansion of the inverse jacobian matrix with respect to the element center leading to a very accurate modeling of arbitrary element shapes the transverse shear and curvature thickness locking are cured by means of the assumed natural strain concept further crucial points are the taylor expansion of the compatible cartesian strain with respect to the center of the element as well as the taylor expansion of the second piola kirchhoff stress tensor with respect to the normal through the center of the element copyright 2010 john wiley sons ltd

a new approach to state observation of nonlinear systems with delayed output the article presents a new approach for the construction of a state observer for nonlinear systems when the output measurements are available for computations after a nonnegligible time delay the proposed observer consists of a chain of observation algorithms reconstructing the system state at different delayed time instants chain observer conditions are given for ensuring global exponential convergence to zero of the observation error for any given delay in the measurements the implementation of the observer is simple and computer simulations demonstrate its effectiveness

a robust non linear solid shell element based on a mixed variational formulation the paper is concerned with a geometrically non linear solid shell finite element formulation which is based on the hu washizu variational principle for the approximation of the independent displacement stress and strain fields the strain field is additively decomposed into two parts due to the fact that one part of the strain field is interpolated in the same manner as proposed by the enhanced assumed strain eas method it is denoted as eas field the other strain field is approximated with the same interpolation functions as the stress field in contrast to the eas concept the approximation spaces of the stresses and the enhanced assumed strains are not orthogonal consequently the stress field is not eliminated from the finite element equations for the displacements tri linear shape functions are considered shear locking and curvature thickness locking are treated using assumed natural strain interpolations a static condensation leads to a simple low order hexahedral solid shell element numerical tests show that the present model is very robust and allows larger load steps than an eas solid shell element

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

continuous discrete observer for state affine systems with sampled and delayed measurements the observation of a class of multi input multi output mimo state affine systems with both sampled and delayed output measurements is addressed these two constraints disturb simultaneously the convergence of the observer assuming some persistent excitation conditions to hold and by using lyapunov tools adapted to impulsive systems two classes of global exponential observers are proposed some explicit relations between maximum allowable delay and maximum allowable sampling period are given an extension to some classes of nonlinear systems is also given

selective and reduced numerical integrations for nurbs based isogeometric analysis we propose a new approach to construct selective and reduced integration rules for isogeometric analysis based on nurbs elements the notion of an approximation space that approximates the target space is introduced we explore the use of various approximation spaces associated with optimal patch wise numerical quadratures that exactly integrate the polynomials in approximation spaces with the minimum number of quadrature points patch rules exploit the higher continuity of spline basis functions the tendency of smooth spline functions to exhibit numerical locking in nearly incompressible problems when using a full gauss legendre quadrature is alleviated with selective or reduced integration stability and accuracy of the schemes are examined analyzing the discrete spectrum in a generalized eigenvalue problem we propose a local algorithm which is robust and computationally efficient to compute element by element the quadrature points and weights in patch rules the performance of the methods is assessed on several numerical examples in two dimensional elasticity and reissner mindlin shell structures

a hierarchic family of isogeometric shell finite elements a hierarchic family of isogeometric shell finite elements based on nurbs shape functions is presented in contrast to classical shell finite element formulations inter element continuity of at least c1 enables a unique and continuous representation of the surface normal within one nurbs patch this does not only facilitate formulation of kirchhoff love type shell models for which the standard galerkin weak form has a variational index of 2 but it also offers significant advantages for shear deformable reissner mindlin type shells and higher order shell models for a 5 parameter shell formulation with reissner mindlin kinematics a hierarchic difference vector which accounts for shear deformations is superimposed onto the rotated kirchhoff love type director of the deformed configuration this split into bending and shear deformations in the shell kinematics results in an element formulation which is free from transverse shear locking without the need to apply further remedies like reduced integration assumed natural strains or mixed finite element formulations the third member of the hierarchy is a 7 parameter model including thickness change and allowing for application of unmodified three dimensional constitutive laws the phenomenon of curvature thickness locking coming along with this kinematic extension again is automatically avoided by the hierarchic difference vector concept without any further treatment membrane locking and in plane shear locking are removed by two different approaches firstly elimination via the discrete strain gap dsg method and secondly removal of parasitic membrane strains using a hybrid mixed method based on the hellinger reissner variational principle the hierarchic kinematic structure of the three different shell formulations allows a straightforward combination of these elements within one mesh and is thus the ideal basis for a model adaptive approach

delay robustness of an mathcal l _1 adaptive controller for a class of systems with unknown matched nonlinearities this paper studies the delay robustness of an mathcal l 1 adaptive controller designed for systems with unknown matched nonlinearities and unknown input gain matrices the analysis establishes rigorously the existence of a positive lower bound for the closed loop system s time delay margin tdm provided that a filter bandwidth and an adaptive gain are chosen sufficiently large in this case if the input delay is below a critical value then the state and control input of the control system follow those of a nonadaptive robust reference system closely the analysis also suggests a way to estimate this lower bound for the delay robustness using pade approximants results from forward simulation are consistent with the pade estimate and with an explicit upper bound on the tdm which decays to 0 as the filter bandwidth grows without bound

global stabilisation of nonlinear delay systems with a compact absorbing set predictor based stabilization results are provided for nonlinear systems with input delays and a compact absorbing set the control scheme consists of an inter sample predictor a global observer an approximate predictor and a nominal controller for the delay free case the control scheme is applicable even to the case where the measurement is sampled and possibly delayed the closed loop system is shown to have the properties of global asymptotic stability and exponential convergence in the disturbance free case robustness with respect to perturbations of the sampling schedule and robustness with respect to measurement errors in contrast to existing predictor feedback laws the proposed control scheme utilizes an approximate predictor of a dynamic type which is expressed by a system described by integral delay equations additional results are provided for systems that can be transformed to systems with a compact absorbing set by means of a preliminary predictor feedback

observer design for nonlinear systems under unknown time varying delays the design of observers for nonlinear systems with unknown time varying bounded delays on both state and input still constitutes an open problem in this technical note we show how to solve it for a class of nonlinear systems by combining the high gain observer approach with a lyapunov krasovskii functional suitable choice sufficient conditions are provided to prove the practical stability of the observer it is shown that the observation error is bounded and depends on the size of two parameters the known upper bound delay of the unknown time varying function delay and the instantaneous state dynamic variation furthermore for the particular case of constant known time delay the convergence of the proposed observer becomes exponential the feasibility of the proposed strategy is illustrated by a numerical example

lp estimates of time harmonic maxwell s equations in a bounded domain consider the electromagnetic field scattered by a nonlinear bounded optical medium because of inhomogeneity of the medium the governing equations are maxwell s equation with jump coefficients and a source term by using the sommerfeld radiation condition the model scattering problem may be truncated into a bounded domain in this paper lp estimates for maxwell s equation with jump coefficients are established the solution of maxwell s equation is represented by spherical harmonics an application of the lp estimates gives rise to the well posedness of a linearized model

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

high gain predictor based output feedback control for time delay nonlinear systems this paper designs a high gain predictor for output feedback control of nonlinear systems in the presence of input output and state delays the high gain predictor realizes the states appearing in the output feedback control in terms of predictive state delayed state and current state the system includes internal and external dynamics and the closed loop system under state feedback is required to be asymptotically stable and locally exponentially stable positively invariant sets are found to verify boundedness exponential stability and performance recovery in the simulation a saturated sliding mode control is applied to demonstrate the performance recovery of the closed loop system and the fact that the high gain predictor parameter has a lower bound related to time delays

higher order mitc general shell elements two mixed interpolated general shell finite elements for non linear analysis a 9 node element and a 16 node element are presented the elements are based on the mixed interpolation of tensorial components mitc approach in which the covariant strain component fields for the in plane and shear actions are interpolated and tied to the also interpolated displacement field both the 9 node element referred to as the mitc9 element and the 16 node element referred to as the mitc16 element are tested numerically and found to have high predictive capabilities

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

robustness of nonlinear predictor feedback laws to time and state dependent delay perturbations much recent progress has been achieved for stabilization of linear and nonlinear systems with input delays that are long and dependent on either time or the plant state provided the dependence is known in this paper we consider the delay variations as unknown and study robustness of nominal constant delay predictor feedbacks under delay variations that depend on time and the state we show that when the delay perturbation and its rate have sufficiently small magnitude the local asymptotic stability of the closed loop system under the nominal predictor based design is preserved for the special case of linear systems and under only time varying delay perturbations we prove robustness of global exponential stability of the predictor feedback when the delay perturbation and its rate are small in any one of four different metrics we present two examples one that is concerned with the control of a dc motor through a network and one of a teleoperation like system

high gain observer for a class of time delay nonlinear systems this article proposes a high gain observer design for a class of nonlinear systems with multiple known time varying delays intervening in the states and the inputs in the free delay case the class of systems under consideration coincides with a canonical form characterising a class of multi output nonlinear systems which are observable for any input the underlying high gain design has been mainly motivated by its inherent simplicity from both design and implementation points of view indeed the observer gain is determined from an explicit resolution of a time invariant lyapunov algebraic equation up to the specification of a single design parameter an academic observation problem is addressed to illustrate the effectiveness of the proposed observer

frequency domain results for systems with slow and fast dynamics the mathematical treatment of systems with slow and fast dynamics has traditionally involved singular perturbation theory for differential equations this paper suggests a set of conditions to be placed on a frequency domain description of a system to guarantee two time scale behavior some basic stability and approximation results are presented

output transformations and separation results for feedback linearisable delay systems abstractthe class of strict feedback systems enjoys special properties that make it similar to linear systems this paper proves that such a class is equivalent under a change of coordinates to the wider class of feedback linearisable systems with multiplicative input when the multiplicative terms are functions of the measured variables only we apply this result to the control problem of feedback linearisable nonlinear mimo systems with input and or output delays in this way we provide sufficient conditions under which a separation result holds for output feedback control and moreover a predictor based controller exists when these conditions are satisfied we obtain that the existence of stabilising controllers for arbitrarily large delays in the input and or the output can be proved for a wider class of systems than previously known

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

nonlinear observer design in the presence of delayed output measurements the present work proposes a new approach to the nonlinear observer design problem in the presence of delayed output measurements the proposed nonlinear observer possesses a state dependent gain which is computed from the solution of a system of first order singular partial differential equations and in particular consists of a chain of state observation algorithms that reconstruct the unmeasurable state vector at different delayed time instants within the time delay window introduced by the available output measurements therefore the proposed nonlinear observer exhibits a chain like structure that explicitly reflects and takes into account the magnitude of the output delay furthermore a set of conditions is derived under which convergence of the estimation error to zero is established finally the performance of the proposed observer and its convergence properties are evaluated in an illustrative biological reactor example

hybrid hexahedral element for solids plates shells and beams by selective scaling a robust two field hexahedral element capable of handling plate shell beam and nearly incompressible material analyses without locking are presented starting with the assumed stress element of pian and tong 7 parasitic strain components leading to locking in plate shell and beam analyses are first identified locking can be alleviated by scaling down selectively the parasitic strain components in the leverage matrix unfortunately the element then fails the patch test however patch test correction and reduction in computation can be achieved by the recently proposed admissible matrix formulation the resulting element is lock free and very efficient all matrices involved in constructing the stiffness matrix can be derived explicitly the accuracy of the element is tested by popular bench mark problems