assumed strain stabilization of the eight node hexahedral element an accurate and robust stabilization based on the assumed strain method and an operator orthogonal to constant strain fields is presented for an eight node hexahedral element with uniform reduced integration the stabilization forces depend only on the element geometry and material properties user specified parameters are not needed yet the assumed strain stabilization is nearly as fast as perturbation type hourglass control in an explicit code it has excellent coarse mesh accuracy for linear elastic bending and is easily incorporated into a nonlinear program the assumed strain field is also used with four point integration which does not require stabilization in addition two forms of the b matrix are studied and it is shown that the mean form is more efficient since it passes the patch test in a simplified form

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

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

applications of cumulants to array processing iv direction finding in coherent signals case for pt iii see ibid vol 45 no 9 p 2253 64 1997 we present a subspace based direction finding method for coherent signal environments using an antenna array our method which uses fourth order statistics is capable of resolving more signals than a comparable second order statistics based subspace method and is applicable to a larger class of arrays the maximum number of signals resolvable with our method may exceed the number of sensors in the array only a uniform linear subarray is needed the rest of the array may have arbitrary and unknown response and does not require calibration on the other hand the comparable second order statistics based method is limited to uniform linear arrays only no search procedure is needed in our method simulation experiments supporting our conclusions are provided

linear prediction approach to direction estimation of cyclostationary signals in multipath environment we investigate the estimation of the directions of arrival doa of closely spaced narrowband cyclostationary signals in the presence of multipath propagation by exploiting the spatial and temporal properties of most communication signals we propose a new cyclic forward backward linear prediction fblp approach for coherent signals impinging on a uniform linear array ula in the proposed algorithm the evaluation of the cyclic array covariance matrix is avoided and the difficulty of choosing the optimal time lag parameter is alleviated as a result the proposed approach has two advantages 1 the computational load is relatively reduced and 2 the robustness of estimation is significantly improved the performance of the proposed approach is confirmed through numerical examples and it is shown that this approach is superior in resolving the closely spaced coherent signals with a small length of array data and at relatively low signal to noise ratio snr

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 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

geometrically non linear enhanced strain mixed methods and the method of incompatible modes a class of assumed strain mixed finite element methods for fully non linear problems in solid mechanics is presented which when restricted to geometrically linear problems encompasses the classical method of incompatible modes as a particular case the method relies crucially on a local multiplicative decomposition of the deformation gradient into a conforming and an enhanced part formulated in the context of a three field variational formulation the resulting class of mixed methods provides a possible extension to the non linear regime of well known incompatible mode formulations in addition this class of methods includes non linear generalizations of recently proposed enhanced strain interpolations for axisymmetric problems which cannot be interpreted as incompatible modes elements the good performance of the proposed methodology is illustrated in a number of simulations including 2 d 3 d and axisymmetric finite deformation problems in elasticity and elastoplasticity remarkably these methods appear to be specially well suited for problems involving localization of the deformation as illustrated in several numerical examples

a support vector machine music algorithm this paper introduces a new support vector machine svm formulation for the direction of arrival doa estimation problem we establish a theoretical relationship between the minimum variance distortionless response mvdr and the multiple signal characterization music methods this leads naturally to the derivation of an svm music algorithm which combines the benefits of subspace methods with those of svm spatially smoothed versions and a recursive form of the algorithms exhibit good performance against coherent signals we test the method s performance in scenarios with noncoherent and coherent signals and in small sample size situations obtaining an improved performance in comparison with existing standard approaches

applications of cumulants to array processing iii blind beamforming for coherent signals for pt ii see ibid vol 43 no 7 p 1663 7 1995 we provide a cumulant based blind beamforming method for recovery of statistically independent narrowband source signals in the presence of coherent or perfectly correlated multipath propagation our method is based on the fact that for a blind beamformer the presence of coherent multipaths is equivalent to the case of independent sources with a different steering matrix our approach is applicable to any array configuration having unknown response signal sources must have nonzero fourth order cumulants there is no need to estimate the directions of arrival our method maximizes signal to interference plus noise ratio sinr a comparable result does not exist using just second order statistics

an improved spatial smoothing technique for bearing estimation in a multipath environment it is well known that signal subspace algorithms perform poorly when coherent or highly correlated signals are present recently the so called spatial smoothing technique was devised to preprocess the array covariance matrix so that signal subspace algorithms can be applied irrespective of the signal correlation unfortunately the application of this technique reduces the effective aperture of the array a modified spatial smoothing technique that is capable of increasing the effective aperture of the array over that of conventional spatial smoothing methods is explored it is shown that under certain conditions the modified algorithm may fail to yield the desired increase in array aperture and some simulation results concerning the sensitivity of the modified spatial smoothing algorithm to these conditions are provided

doa estimation by exploiting the symmetric configuration of uniform linear array a new direction of arrival doa estimation method is proposed for uniform linear array in this paper when both uncorrelated and coherent sources are present the uncorrelated and coherent sources are estimated at two different stages the uncorrelated sources are first estimated using conventional subspace methods and then they are eliminated by exploiting the symmetric configuration of the array finally the remaining coherent sources are estimated by reconstructing a non toeplitz matrix the number of sources resolved by our method can exceed the number of array elements simulation results demonstrate the effectiveness and efficiency of our proposed method

consistent tangent operators for rate independent elastoplasticity abstract it is shown that for problems involving rate constitutive equations such as rate independent elastoplasticity the notion of consistency between the tangent stiffness operator and the integration algorithm employed in the solution of the incremental problem plays a crucial role in preserving the quadratic rate of asymptotic convergence of iterative solution schemes based upon newton s method within the framework of closest point projection algorithms a methodology is presented whereby tangent operators consistent with this class of algorithms may be systematically developed to wit associative j 2 flow rules with general nonlinear kinematic and isotropic hardening rules as well as a class of non associative flow rules are considered the resulting iterative solution scheme preserves the asymptotic quadratic convergence characteristic of newton s method whereas use of the socalled elastoplastic tangent in conjunction with a radial return integration algorithm a procedure often employed results in newton type of algorithms with suboptimal rate of convergence application is made to a set of numerical examples which include saturation hardening laws of exponential type

on the parameterized differential inverse galois problem over k t x abstract in this article we consider the inverse galois problem for parameterized differential equations over k t x with k any field of characteristic zero and use the method of patching over fields due to harbater and hartmann we show that every connected semisimple k t split linear algebraic group is a parameterized differential galois group over k t x

physical stabilization of the 4 node shell element with one point quadrature abstract a new four node shell element for nonlinear analysis which is useful for explicit time integration with single point quadrature is presented an assumed strain method is used to stabilize the zero energy modes of the element the stabilization procedure is based on the hu washizu variational principle and does not require the input of any stabilization parameters example problems show good accuracy and rate of convergence compared with fully integrated 4 node elements however the physically stabilized element is substantially faster than the fully integrated element

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

differential galois theory of linear difference equations we present a galois theory of difference equations designed to measure the differential dependencies among solutions of linear difference equations with this we are able to reprove holder s theorem that the gamma function satisfies no polynomial differential equation and are able to give general results that imply for example that no differential relationship holds among solutions of certain classes of q hypergeometric equations

the differential galois theory of strongly normal extensions differential galois theory the theory of strongly normal extensions has unfortunately languished this may be due to its reliance on kolchin s elegant but not widely adopted axiomatization of the theory of algebraic groups this paper attempts to revive the theory using a differential scheme in place of those axioms we also avoid using a universal differential field instead relying on a certain tensor product we identify automorphisms of a strongly normal extension with maximal differential ideals of this tensor product thus identifying the galois group with the closed points of an affine differential scheme moreover the tensor product has a natural coring structure which translates into the galois group operation composition of automorphisms this affine differential scheme splits i e is obtained by base extension from a not differential not necessarily affine group scheme as a consequence the galois group is canonically isomorphic to the closed or rational points of a group scheme defined over constants we obtain the fundamental theorem of differential galois theory giving a bijective correspondence between subgroup schemes and intermediate differential fields on the way to this result we study certain aspects of differential algebraic geometry e g closed immersions products local ringed space of constants and split differential schemes

a mixed shell formulation accounting for thickness strains and finite strain 3d material models a non linear quadrilateral shell element for the analysis of thin structures is presented the reissner mindlin theory with inextensible director vector is used to develop a three field variational formulation with independent displacements stress resultants and shell strains the interpolation of the independent shell strains consists of two parts the first part corresponds to the interpolation of the stress resultants within the second part independent thickness strains are considered this allows incorporation of arbitrary non linear 3d constitutive equations without further modifications the developed mixed hybrid shell element possesses the correct rank and fulfills the in plane and bending patch test the essential feature of the new element is the robustness in the equilibrium iterations it allows very large load steps in comparison with other element formulations we present results for finite strain elasticity inelasticity bifurcation and post buckling problems copyright 2007 john wiley sons ltd

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

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

two dimensional direction estimation for a mixture of noncoherent and coherent signals this paper deals with the two dimensional 2 d direction of arrival doa estimation of a mixture of noncoherent including uncorrelated and partially correlated and coherent i e fully correlated narrowband signals impinging on a planar sensor array composed of two parallel uniform linear arrays ulas an oblique projection based approach for 2 d direction estimation opade is proposed by using some cross correlations between the received array data in the proposed opade the oblique projection is utilized to isolate the coherent signals from the noncoherent ones and the effect of additive noise is alleviated while the computationally intensive eigendecomposition is avoided and the estimated elevation and azimuth angles are paired automatically further an iterative alternating scheme is presented to improve the estimation accuracy of the oblique projector and hence that of the doas of coherent signals the cramer rao lower bound crb for the mixture of noncoherent and coherent signals is also derived explicitly where the prior knowledge of the signal correlation is incorporated into the 2 d doa estimation of noncoherent signals finally the effectiveness of the opade and the theoretical analysis are substantiated through numerical examples

applications of cumulants to array processing i aperture extension and array calibration an interpretation for the use of cumulants in narrowband array processing problems is proposed it is shown how fourth order cumulants of multichannel observations increase the directional information compared with second order statistics based on the interpretation it is shown how cumulants can be used to increase the effective aperture of an arbitrary antenna array the amount of partial information necessary to jointly calibrate an arbitrary array and estimate the directions of far field sources is also investigated it is proven that the presence of a doublet and use of fourth order cumulants is sufficient to accomplish this task the proposed approach is computationally efficient and more general than covariance based algorithms that have addressed the calibration problem under constraints a class of beamforming techniques is proposed to recover the source waveforms proposed estimation procedures are based on cumulants which bring insensitivity to the spatial correlation structure of additive gaussian measurement noise simulations are provided to illustrate the use of the proposed algorithms

application of cumulants to array signal processing v sensitivity issues for pt iv see ibid vol 45 p 2265 76 1997 virtual esprit vespa imposes a slight constraint on the array i e only a pair of identical sensors are required we follow the classical procedure to define the sensitivity of vespa with respect to each model parameter and derive closed forms for the sensitivity formulas we justify our derivations by comparing the theoretical formulas with the results from monte carlo simulations additionally we demonstrate by simulations that vespa is more robust to model mismatches than esprit in most situations

iterative hos sos ihoss algorithm for direction of arrival estimation and sensor localization a new method for joint direction of arrival doa and sensor position estimation is introduced the sensors are assumed to be randomly deployed except two reference sensors the proposed method exploits the advantages of both higher order statistics hos and second order statistics sos with an iterative algorithm namely iterative higher order second order statistics ihoss a new cumulant matrix estimation technique is proposed for the hos approach by converting the multisource problem into a single source one ihoss performs well even in case of correlated source signals due to the effectiveness of the proposed cumulant matrix estimate a cost function is defined for the joint doa and position estimation the iterative procedure is guaranteed to converge the ambiguity problem in sensor position estimation is solved by observing the source signals at least in two different frequencies the conditions on these frequencies are presented closed form expressions are derived for the deterministic cramer rao bound crb for doa and unknown sensor positions for noncircular complex gaussian noise with unknown covariance matrix simulation results show that the performance of ihoss is significantly better than the hos approaches for doa estimation and closely follows the crb for both doa and sensor position estimations

spatial spectrum estimation in a coherent signal environment using an array in motion spatial spectrum estimation utilizing an array in motion is here investigated for dealing with coherent arrivals in a multiple signal environment the effect of estimating the spatial correlations while the array is moving is studied in terms of the decorrelation it produces the change it causes in the eigenvalues of the correlation matrix and the improvements obtained in the measured spectrum cases of both fixed and varying angle of arrival are investigated the former arises with distant sources and will with a sufficiently long estimation interval emulate uncorrelated sources and given correspondingly sharp spectra the latter arises with nearby sources and will allow them to be distinguished but will be attended by spectral shift and broadening and loss of resolution it is shown that meaningful estimates of the arrival angles can nevertheless be made specific illustrations are worked out using a seven element sparse nonuniformly spaced linear array utilizing the well known superresolution spectral estimators the maximum likelihood ml method the method of linear prediction lp and the method of multiple signal classification music

new classes of parameterized differential galois groups this paper is on the inverse parameterized differential galois problem we show that surprisingly many groups do not occur as parameterized differential galois groups over k x even when k is algebraically closed we then combine the method of patching over fields with a suitable version of galois descent to prove that certain groups do occur as parameterized differential galois groups over k t x this class includes linear differential algebraic groups that are generated by finitely many unipotent elements and also semisimple connected linear algebraic groups

existence of parameterized picard vessiot extensions over fields with algebraically closed constants abstract the purpose of this short note is to establish the existence of parameterized picard vessiot extensions for systems of linear difference differential equations over difference differential fields with an algebraically closed field of constants

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

a uniform strain hexahedron and quadrilateral with orthogonal hourglass control the treatment of zero energy modes which arise due to one point integration of first order isoparametric finite elements is addressed a method for precisely isolating these modes for arbitrary geometry is developed two hourglass control schemes viscous and elastic are presented and examined in addition a convenient one point integration scheme which analytically integrates the element volume and uniform strain modes is presented

compressive music revisiting the link between compressive sensing and array signal processing the multiple measurement vector mmv problem addresses the identification of unknown input vectors that share common sparse support even though mmv problems have been traditionally addressed within the context of sensor array signal processing the recent trend is to apply compressive sensing cs due to its capability to estimate sparse support even with an insufficient number of snapshots in which case classical array signal processing fails however cs guarantees the accurate recovery in a probabilistic manner which often shows inferior performance in the regime where the traditional array signal processing approaches succeed the apparent dichotomy between the probabilistic cs and deterministic sensor array signal processing has not been fully understood the main contribution of the present article is a unified approach that revisits the link between cs and array signal processing first unveiled in the mid 1990s by feng and bresler the new algorithm which we call compressive music identifies the parts of support using cs after which the remaining supports are estimated using a novel generalized music criterion using a large system mmv model we show that our compressive music requires a smaller number of sensor elements for accurate support recovery than the existing cs methods and that it can approach the optimal bound with finite number of snapshots even in cases where the signals are linearly dependent

a multiple quadrature eight node hexahedral finite element for large deformation elastoplastic analysis abstract a multiple quadrature underintegrated hexahedral finite element which is free of volumetric and shear locking and has no spurious singular modes is described and implemented for nonlinear analysis finite element formulations are derived in the corotational coordinate system the use of consistent tangent operators for large deformation elastoplasticity with nonlinear isotropic kinematic hardening rules preserves the quadratic rate of convergence of the newton s iteration method in static analysis test problems studied demonstrate the efficiency and effectiveness of this element in solving a wide variety of problems including sheet metal forming processes

computationally efficient subspace based method for direction of arrival estimation without eigendecomposition a computationally simple direction of arrival doa estimation method with good statistical performance is attractive in many practical applications of array processing in this paper we propose a new computationally efficient subspace based method without eigendecomposition sumwe for the coherent narrowband signals impinging on a uniform linear array ula by exploiting the array geometry and its shift invariance property the coherency of incident signals is decorrelated through subarray averaging and the null space is obtained through a linear operation of a matrix formed from the cross correlations between some sensor data where the effect of additive noise is eliminated consequently the doas can be estimated without performing eigendecomposition and there is no need to evaluate all correlations of the array data furthermore the sumwe is also suitable for the case of partly coherent or incoherent signals and it can be extended to the spatially correlated noise by choosing appropriate subarrays the statistical analysis of the sumwe is studied and the asymptotic mean squared error mse expression of the estimation error is derived the performance of the sumwe is demonstrated and the theoretical analysis is substantiated through numerical examples it is shown that the sumwe is superior in resolving closely spaced coherent signals with a small number of snapshots and at low signal to noise ratio snr and offers good estimation performance for both uncorrelated and correlated incident signals

generalized differential galois theory a galois theory of differential fields with parameters is developed in a manner that generalizes kolchin s theory it is shown that all connected differential algebraic groups are galois groups of some appropriate differential field extension

applications of cumulants to array processing ii non gaussian noise suppression the main motivation of using higher order statistics in signal processing applications has been their insensitivity to additive colored gaussian noise the main objection to those methods is their possible vulnerability to non gaussian noise the authors investigate the effects of non gaussian ambient noise on cumulant based direction finding systems using the interpretation for the information provided by cumulants for array processing applications described in dogan and mendek they first demonstrate the suppression of uncorrelated non gaussian noise that has spatially varying statistics then they indicate methods to suppress spatially colored non gaussian noise using cumulants and an additional sensor whose measurement noise component is independent of the noise components of the original array measurements they also indicate the noise suppression properties of the virtual esprit algorithm proposed in dogan and mendel in addition they propose a method that combines second and fourth order statistics together in order to suppress spatially colored non gaussian noise finally they also illustrate how to suppress spatially colored non gaussian noise when the additional sensor measurement is not available simulations are presented to verify the results

calculating differential galois groups of parametrized differential equations with applications to hypertranscendence the main motivation of our work is to create an efficient algorithm that decides hypertranscendence of solutions of linear differential equations via the parameterized and differential galois theories to achieve this we expand the representation theory of linear differential algebraic groups and develop new algorithms that calculate unipotent radicals of parameterized differential galois groups for differential equations whose coefficients are rational functions berman and singer presented an algorithm calculating the differential galois group for differential equations without parameters whose differential operator is a composition of two completely reducible differential operators we use their algorithm as a part of our algorithm as a result we find an effective criterion for the algebraic independence of the solutions of parameterized differential equations and all of their derivatives with respect to the parameter

improved versions of assumed enhanced strain tri linear elements for 3d finite deformation problems abstract improved three dimensional tri linear elements for finite deformation problems are developed based on an assumed enhanced strain methodology which in the linear regime incorporates the classical method of incompatible modes as a particular case three crucial modifications of a recently proposed element which reduces to wilson s brick in the linear regime are introduced to prevent locking response in distorted configurations and to maintain proper rank while preserving excellent performance in bending dominated and localization problems i a modified quadrature rule ii an additional enhancement of the divergence term and iii a modification of the isoparametric shape function derivatives for the three dimensional problem moreover these modified shape function derivatives are shown to improve the performance of the standard tri linear brick in distorted configurations in addition a strategy is described to circumvent the memory storage requirements in the static condensation procedure of the enhanced strain parameters the excellent performance of the improved methodology is illustrated in representative numerical simulations

oblique projection based enumeration of mixed noncoherent and coherent narrowband signals in many application scenarios the signals impinging on the array of sensors comprise the noncoherent uncorrelated and or partially correlated signals and the coherent signals with several groups due to multipath propagation in this paper we consider the problem of estimating the number of noncoherent narrowband signals and that of coherent narrowband signals with multiple groups impinging on a planar sensor array composed of two parallel uniform linear arrays ulas and an oblique projection based enumerator for the mixed signals opems is proposed by utilizing the qr decomposition based ratio criterion qrrc for rank determination of a matrix in the opems the number of noncoherent signals and that of coherent signals in each group are estimated separately where only the elevation angles of noncoherent signals are estimated to isolate the coherent signals from the noncoherent ones and the computationally intensive and time consuming eigendecomposition procedure is avoided the consistency of the proposed opems is analyzed and its effectiveness is verified through numerical examples

direction finding algorithms based on high order statistics two direction finding algorithms are presented for nongaussian signals which are based on the fourth order cumulants of the data received by the array the first algorithm is similar to music while the second is asymptotically minimum variance in a certain sense the first algorithm requires singular value decomposition of the cumulant matrix while the second is based on nonlinear minimization of a certain cost function the performance of the minimum variance algorithm can be assessed by analytical means at least for the case of discrete probability distributions of the source signals and spatially uncorrelated gaussian noise the numerical experiments performed seem to confirm the insensitivity of these algorithms to the gaussian noise parameters

explicit algorithms for the nonlinear dynamics of shells abstract a finite element formulation and algorithm for the nonlinear analysis of the large deflection materially nonlinear response of impulsively loaded shells is presented a unique feature of this algorithm is the use of a bilinear four node quadrilateral element with single point quadrature and a simple hourglass control which is orthogonal to rigid body modes on an element level and does not compromise the consistency of the equations the geometric nonlinearities are treated by using a corotational description wherein a coordinate system that rotates with the material is embedded at the integration point thus the algorithm is directly applicable to anisotropic materials without any corrections for frame invariance of material property tensors this algorithm can treat about 200 element time steps per cpu second on a cyber 170 730 computer in the explicit time integration mode numerous results are presented for both elastic and elastic plastic problems with large strains that show that the method in most cases is comparable in accuracy with an earlier version of this algorithm employing a cubic triangular plate shell element but substantially faster

linear algebraic groups as parameterized picard vessiot galois groups we show that a linear algebraic group is the galois group of a parameterized picard vessiot extension of k x x 1 for certain differential fields k if and only if its identity component has no one dimensional quotient as a linear algebraic group

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

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

a linear quadrilateral shell element with fast stiffness computation abstract a new quadrilateral shell element with 5 6 nodal degrees of freedom is presented assuming linear isotropic elasticity a hellinger reissner functional with independent displacements rotations and stress resultants is used within the mixed formulation the stress resultants are interpolated using five parameters for the membrane forces as well as for the bending moments and four parameters for the shear forces the hybrid element stiffness matrix resulting from the stationary condition is integrated analytically this leads to a part obtained by one point integration and a stabilization matrix the element possesses the correct rank is free of locking and is applicable within the whole range of thin and thick shells the in plane and bending patch tests are fulfilled and the computed numerical examples show that the convergence behaviour of the stress resultants is very good in comparison to comparable existing elements the essential advantage is the fast stiffness computation due to the analytically integrated matrices

a theoretical and computational model for isotropic elastoplastic stress analysis in shells at large strains the article presents new aspects of large strain isotropic elastoplastic analysis of shells on the shell theory side we consider several possible continuum based parametrizations of the shell deformation and investigate their applicability with respect to the implementation of general three dimensional local constitutive models as an aspect of computational shell analysis we then discuss in detail the numerical implementation of a shell based on the parametrization of the top and bottom surface in terms of a new 8 node brick type mixed finite shell element on the basis of assumed strain and enhanced strain variational approaches on the side of plasticity theory we adopt a recently proposed intermediate configuration free formulation of large strain plasticity based on the notion of a plastic metric and consider its representation with respect to the parameter manifold of the shell this frame is formulated in terms of principal strains and principal stresses with respect to dual co and contra variant eigenvector triads associated with a mixed variant elastic strain tensor the new aspect of computational plasticity is the development of a stress update algorithm for the plasticity model mentioned above which includes a general return mapping in the eigenvalue space the algorithm can be applied to general coordinate charts and is particularly convenient when formulated with respect to the space of the curvilinear coordinates of the shell parametrization we demonstrate the performance of the finite element formulation and constitutive algorithms by means of several numerical examples

a galois theoretic proof of the differential transcendence of the incomplete gamma function abstract we give simple necessary and sufficient conditions for the t transcendence of the solutions to a parameterized second order linear differential equation of the form 2 y x 2 p y x 0 where p f x is a rational function in x with coefficients in a t field f our criteria imply in particular the t transcendence of the incomplete gamma function t x generalizing a result of johnson reinhart and rubel this result is also an important part of an efficient algorithm to compute the parameterized picard vessiot group of an arbitrary parameterized second order linear differential equation over f x

parameterized picard vessiot extensions and atiyah extensions abstract generalizing atiyah extensions we introduce and study differential abelian tensor categories over differential rings by a differential ring we mean a commutative ring with an action of a lie ring by derivations in particular these derivations act on a differential category a differential tannakian theory is developed the main application is to the galois theory of linear differential equations with parameters namely we show the existence of a parameterized picard vessiot extension and therefore the galois correspondence for many differential fields with possibly non differentially closed fields of constants that is fields of functions of parameters other applications include a substantially simplified test for a system of linear differential equations with parameters to be isomonodromic which will appear in a separate paper this application is based on differential categories developed in the present paper and not just differential algebraic groups and their representations

on the modelling of non linear kinematic hardening at finite strains with application to springback comparison of time integration algorithms the paper discusses the derivation and the numerical implementation of a finite strain material model for non linear kinematic and isotropic hardening the kinematic hardening component represents a continuum extension of the classical rheological model of armstrong frederick kinematic hardening in addition a comparison between several numerical algorithms for the integration of the evolution equations is conducted in particular a new form of the exponential map that preserves the plastic volume and the symmetry of the internal variables as well as two modifications of the backward euler scheme are discussed finally the applicability of the model for springback prediction is demonstrated by performing simulations of the draw bending process and a comparison with experiments the results show an excellent agreement between simulation and experiment copyright 2007 john wiley sons ltd

a class of mixed assumed strain methods and the method of incompatible modes a three field mixed formulation in terms of displacements stresses and an enhanced strain field is presented which encompasses as a particular case the classical method of incompatible modes within this frame work incompatible elements arise as particular compatible mixed approximations of the enhanced strain field the conditions that the stress interpolation contain piece wise constant functions and be l2 ortho gonal to the enhanced strain interpolation ensure satisfaction of the patch test and allow the elimination of the stress field from the formulation the preceding conditions are formulated in a form particularly convenient for element design as an illustration of the methodology three new elements are developed and shown to exhibit good performance a plane 3d elastic plastic quad an axisymmetric element and a thick plate bending quad the formulation described herein is suitable for non linear analysis

three dimensional extension of non linear shell formulation based on the enhanced assumed strain concept conventional shell formulations such as 3 or 5 parameter theories or even 6 parameter theories including the thickness change as extra parameter require a condensation of the constitutive law in order to avoid a significant error due to the assumption of a linear displacement field across the thickness this means that the normal stress in thickness direction has to either vanish or be constant in general these extra constraints cannot be satisfied explicitly or they lead to elaborate strain expressions the main objective of the present study is to introduce directly a complete 3 d constitutive law without modification therefore a 7 parameter theory is utilized which includes a linear varying thickness stretch as extra variable allowing also large strain effects

multiple source location a matrix decomposition approach in this paper we present a new method without using the eigenstructure of the sensor covariance matrix for estimating the number of sources d and the direction of arrival of sources based on the matrix decomposition this method uniformly handles coherent and noncoherent sources alike in our procedure a number p is calculated and used for determination of the maximum number of distinguishable sources by a given linear array system