isometric dilations for infinite sequences of noncommuting operators this paper develops a dilation theory for t n l an infinite sequence of noncommuting operators on a hilbert space when the matrix t1 t2 is a contraction a wold decomposition for an infinite sequence of isometries with orthogonal final spaces and a minimal isometric dilation for tn i are obtained some theorems on the geometric structure of the space of the minimal isometric dilation and some consequences are given this results are used to extend the sz nagy foia lifting theorem to this noncommutative setting this paper is a continuation of 5 and develops a dilation theory for an infinite sequence tn n of noncommuting operators on a hilbert space when en 1 tn tn i i is the identity on s many of the results and techniques in dilation theory for one operator 8 and also for two operators 3 4 are extended to this setting first we extend wold decomposition 8 4 to the case of an infinite sequence vn i of isometries with orthogonal final spaces in 2 we obtain a minimal isometric dilation for tn 1 by extending the schaffer construction in 6 4 using these results we give some theorems on the geometric structure of the space of the minimal isometric dilation finally we give some sufficient conditions on a sequence t7 n to be simultaneously quasi similar to a sequence rn n i of isometries on a hilbert space x with en rnrn n ix in 3 we use the above mentioned theorems to obtain the sz nagy foia5 lifting theorem 7 8 1 4 in our setting in a subsequent paper we will use the results of this paper for studying the characteristic function associated to a sequence tn lo 1 with ez 1 t t i throughout this paper a stands for the set 1 2 k k e n or the set n 1 2 received by the editors september 1 1987 1980 mathematics subject classification 1985 revision primary 47a20 secondary 47a45

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

nonparametric fuzzy regression k nn and kernel smoothing techniques abstract fuzzy regression without predefined functional form or nonparametric fuzzy regression is investigated the two most basic nonparametric regression techniques in statistics namely k nearest neighbor smoothing and kernel smoothing are fuzzified and analyzed algorithms are proposed to obtain the best smoothing parameters based on the minimization of cross validation criteria

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

fuzzy nonparametric regression based on local linear smoothing technique in a great deal of literature on fuzzy regression analysis most of research has focused on some predefined parametric forms of fuzzy regression relationships especially on the fuzzy linear regression models in many practical situations it may be unrealistic to predetermine a fuzzy parametric regression relationship in this paper a fuzzy nonparametric model with crisp input and lr fuzzy output is considered and based on the distance measure for fuzzy numbers suggested by diamond p diamond fuzzy least squares information sciences 46 1988 141 157 the local linear smoothing technique in statistics with the cross validation procedure for selecting the optimal value of the smoothing parameter is fuzzified to fit this model some simulation experiments are conducted to examine the performance of the proposed method and three real world datasets are analyzed to illustrate the application of the proposed method the results demonstrate that the proposed method works quite well not only in producing satisfactory estimate of the fuzzy regression function but also in reducing the boundary effect significantly

updated lagrangian formulation of a flat triangular element for thin laminated shells an updated lagrangian formulation of a three node flat triangular shell element is presented for geometrically nonlinear analysis of laminated plates and shells the flat shell element is obtained by combining the discrete kirchhoff theory plate bending element and a membrane element that is similar to the allman element but a derivative of the linear strain triangular element results are presented for large rotation static response analysis of a cantilever beam under end moment cylindrical shell under pinching and stretching loads a hemispherical shell under pinching and stretching loads and a ring plate under a line load for dynamic response analysis of a cylindrical panel and for thermal postbuckling analysis of an imperfect square plate and a cylindrical panel to estimate the accuracy of the present formulation in predicting the nonlinear response of large flexible structures static analysis of an apex loaded circular arch is performed the arch is a building block of a large inflatable structure the results are in good agreement with those available in the existing literature and those obtained using the commercial finite element software abaqus demonstrating the accuracy of the present formulation he two most widely adopted approaches in the finite element analysis of shells are use of curved shell elements based on a suitable shell theory and approximation of the curved structure by an assemblage of flat shell elements in which the membranebending coupling is brought about as a result of material anisotropy and transformation of the element stiffness matrices computed in a local coordinate system to the global coordinate system prior to assembly the curved shell elements can be computationally very expensive especially in the case of nonlinear analysis because of the complexity of the formulation and the need to compute the curvature information flat shell elements are more attractive because of their simplicity and the ease with which they can be built from alreadyexisting familiar membrane and plate bending elements though a large number of elements are required to accurately model curved structures the analysis is computational ly less expensive because of extremely simple formulation updated lagrangian formulations have been predominantly used in the flat shell formulations available in the existing literature in an updated lagrangian formulation all of the variables are referred to a known configuration the reference configuration which is updated continuously during the deformation process if the rigid body modes are removed from the total or incremental displacements the resulting deformational translations and rotations are very small and hence a linearized incremental formulation1 can be used in a linearized incremental formulation the stresses are computed using linear strain displacement relations the tangent stiffness matrix contains only the linear stiffness matrix and the initial stress matrix the stiffness matrices resulting from the nonlinear terms in the strain displacement relations are neglected resulting in very economical analysis if the rigid body modes are not removed all nonlinear terms in the strain displacement relations will have to be considered for computing the stresses and the tangent stiffness matrix a three node flat triangular shell element was introduced by argyris et al 2 for nonlinear elastic stability problems this formula

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

a simultaneous projections method for linear inequalities abstract an iterative method for solving general systems of linear inequalities is considered the method a relaxed generalization of cimmino s scheme for solving linear systems was first suggested by censor and elfving each iterate is obtained as a convex combination of the orthogonal projections of the previous iterate on the half spaces defined by the linear inequalities the algorithm is particularly suitable for implementation on computers with parallel processors we prove convergence from any starting point for both consistent and nonconsistent systems to a feasible point in the first case and to a weighted least squares type solutions in the second

parallel projection methods and the resolution of ill posed problems abstract in this paper we consider a modification of the parallel projection method for solving overdetermined nonlinear systems of equations introduced recently by diniz ehrhardt and martinez 1 this method is based on the classical cimmino s algorithm for solving linear systems the components of the function are divided into small blocks as an attempt to correct the intrinsic ill conditioning of the system and the new iteration is a convex combination of the projections onto the linear manifolds defined by different blocks the modification suggested here was motivated by the application of the method to the resolution of a nonlinear fredholm first kind integral equation we prove convergence results and we report numerical experiments

free holomorphic functions and interpolation in this paper we obtain a noncommutative multivariable analogue of the classical nevanlinna pick interpolation problem for analytic functions with positive real parts on the open unit disc given a function f lambda to mathbb c where lambda is an arbitrary subset of the open unit ball mathbb b n z in mathbb c n z 1 we find necessary and sufficient conditions for the existence of a free holomorphic function g with complex coefficients on the noncommutative open unit ball b mathcal h n 1 such that rm re g geq 0 quad rm and quad g z f z quad z in lambda where b mathcal h is the algebra of all bounded linear operators on a hilbert space mathcal h the proof employs several results from noncommutative multivariable operator theory and a noncommutative cayley transform introduced and studied in the present paper acting from the set of all free holomorphic functions with positive real parts to the set of all bounded free holomorphic functions all the results of this paper are obtained in the more general setting of free holomorphic functions with operator valued coefficients as consequences we deduce some results concerning operator valued analytic interpolation on the unit ball mathbb b n

free pluriharmonic majorants and commutant lifting in this paper we initiate the study of sub pluriharmonic curves and free pluriharmonic majorants on the noncommutative open ball b h n 1 x1 xn b h n x1x1 xnxn 1 2 1 where b h is the algebra of all bounded linear operators on a hilbert space h several classical results from complex analysis have analogues in this noncommutative multivariable setting we present basic properties for sub pluriharmonic curves characterize the class of sub pluriharmonic curves that admit free pluriharmonic majorants and find in this case the least free pluriharmonic majorants we show that for any free holomorphic function on b h n 1 the map 0 1 c r1 rn r rr1 rrn rr1 rrn is a sub pluriharmonic curve in the cuntz toeplitz algebra generated by the right creation operators r1 rn on the full fock space with n generators we prove that is in the noncommutative hardy space hball2 if and only if has a free pluriharmonic majorant in this case we find herglotz riesz and poisson type representations for the least pluriharmonic majorant of moreover we obtain a characterization of the unit ball of hball2 and provide a parametrization and concrete representations for all free pluriharmonic majorants of when is in the unit ball of hball2 in the second part of this paper we introduce a generalized noncommutative commutant lifting gncl problem which extends to our noncommutative multivariable setting several lifting problems including the classical sz nagy foias commutant lifting problem and the extensions obtained by treil volberg foias frazho kaashoek and biswas foias frazho as well as their multivariable noncommutative versions we solve the gncl problem and using the results regarding sub pluriharmonic curves and free pluriharmonic majorants on noncommutative balls we provide a complete description of all solutions in particular we obtain a concrete schur type description of all solutions in the noncommutative commutant lifting theorem

formulation and analysis of conserving algorithms for frictionless dynamic contact impact problems this paper presents the formulation of conserving time stepping algorithms for frictionless dynamic contact of solids a new class of finite element methods is proposed for the solution of these problems that exhibit the same conservation laws as the underlying continuum dynamical system the proposed methods are based on a penalty regularization of the constrained contact problem and lead to full conservation of the total energy of the system including the regularization penalty potential during persistent contact and restoration of the original energy upon release both linear and angular momenta are conserved by the scheme furthermore the newly developed methods have the ability to enforce the associated constraints in the velocity besides the impenetrability constraint in the displacements while preserving the conservation restoration properties of the final numerical scheme a modification of these schemes is described that assures positive energy dissipation if desired even in the highly nonlinear setting of contact impact problems leading to contact schemes with high frequency energy dissipation representative numerical simulations are presented illustrating the performance of the proposed numerical schemes

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

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

a new energy and momentum conserving algorithm for the non linear dynamics of shells a numerical time integration scheme for the dynamics of non linear elastic shells is presented that simultaneously and independent of the time step size inherits exactly the conservation laws of total linear total angular momentum as well as total energy the proposed technique generalizes to non linear shells recent work of the authors on non linear elastodynamics and is ideally suited for long term large scale simulations the algorithm is second order accurate and can be immediately extended with no modification to a fourth order accurate scheme the property of exact energy conservation induces a strong notion of non linear numerical stability which manifests itself in actual simulations

noncommutative transforms and free pluriharmonic functions abstract in this paper we study free pluriharmonic functions on noncommutative balls b h n 0 and their boundary behavior these functions have the form f x 1 x n k 1 k b x a 0 i k 1 k a x a b c where the convergence of the series is in the operator norm topology for any x 1 x n b h n and b h denotes the algebra of all bounded linear operators on a hilbert space h the main tools used in this study are certain noncommutative transforms which are introduced in the present paper and which generalize the classical transforms of berezin poisson fantappie herglotz and cayley several classical results from complex analysis have free analogues in our noncommutative multivariable setting

central intertwining lifting suboptimization and interpolation in several variables in this paper we obtain an explicit central intertwining lifting for row contractions this is used to prove kaftal larson weiss and foias frazho h h2 suboptimization type results for the noncommutative resp commutative analytic toeplitz algebra f n resp w n the algebra f n resp w n can be viewed as a multivariable noncommutative resp commutative analogue of the hardy space h similar results are provided for f n b k k and w n b k k where b k k is the set of all bounded linear operators acting on hilbert spaces new extensions of the sarason caratheodory and nevanlinna pick type interpolation results are obtained for f n b k k and some consequences to the operator valued analytic interpolation in the unit ball of cn are considered

on commutant lifting with finite defect ii in the lifting theorem of b sz nagy c foias and d sarason the intertwining operator a the operator that is lifted is a contraction from one hilbert space to another j a ball and j w helton showed that a kind of lifting theorem still holds if the negative spectral subspace of the operator i a a is finite dimensional in this paper we prove that this result remains valid if the hilbert spaces are replaced by spaces with an indefinite metric c 1997 academic press

multivariable nehari problem and interpolation abstract in this paper we obtain a multivariable nehari type theorem for hankel operators extending the classical result as well as treil volberg generalization the result is based on a new generalization of the noncommutative commutant lifting theorem which extends to several variables the commutant lifting result obtained by treil and volberg and recently generalized by biswas foias and frazho an extension of i s iokhvidov ky fan theorem is obtained and used to prove a multivariable adamian arov krein type theorem for generalized hankel operators as consequences we obtain caratheodory and nevanlinna pick type interpolation results for meromorphic operators on fock spaces resp operator valued meromorphic functions on the unit ball of c n the nehari type results are used to obtain descriptions of hankel operators acting on fock spaces or weighted fock spaces multivariable dirichlet type spaces and to solve new weighted interpolation problems e g sarason for noncommutative analytic toeplitz algebras which have consequences to the operator valued analytic interpolation in the unit ball of c n moreover using central intertwining liftings we obtain explicit formulas for certain solutions of the weighted interpolation problems as another application of the generalized noncommutative commutant lifting theorem we derive an abstract interpolation problem for multipliers this is used to solve a left tangential nevanlinna pick type interpolation problem with operatorial argument for noncommutative analytic toeplitz algebras

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

on the choice of the regularization parameter in nonlinear inverse problems this paper focuses on regularization techniques for nonlinear ill posed inverse problems tikhonov regularization and regularization due to the use of norm constraints are analyzed a model function technique is proposed to iteratively determine an optimal regularization parameter or the parameter characterizing the norm constraint and to estimate the error in the data if it is not known a priori

spectral lifting in banach algebras and interpolation in several variables let a be a unital banach algebra and let j be a closed two sided ideal of a we prove that if any invertible element of a j has an invertible lifting in a4 then the quotient homomorphism 1 a a4 j is a spectral interpolant this result is used to obtain a noncommutative multivariable analogue of the spectral commutant lifting theorem of bercovici foia and tannenbaum this yields spectral versions of sarason nevanlinna pick and caratheodory type interpolation for fn 3b 1c the wot closed algebra generated by the spatial tensor product of the noncommutative analytic toeplitz algebra f and b ac the algebra of bounded operators on a finite dimensional hilbert space kc a spectral tangential commutant lifting theorem in several variables is considered and used to obtain a spectral tangential version of the nevanlinna pick interpolation for f n03b kc in particular we obtain interpolation theorems for matrix valued bounded analytic functions on the open unit ball of cn in which one bounds the spectral radius of the interpolant and not the norm

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

a parallel subgradient projections method for the convex feasibility problem abstract an iterative method to solve the convex feasibility problem for a finite family of convex sets is presented the algorithm consists in the application of a generalization of an acceleration procedure introduced by de pierro in a parallel version of the subgradient projections method proposed by censor and lent the generated sequence is shown to converge for any starting point some numerical results are presented

corotational total lagrangian formulation for three dimensional beamelement a corotational total lagrangian formulation of beam element is presented for the nonlinear analysis of three dimensional beam structures with large rotations but small strains the nonlinear coupling among the bending twisting and stretching deformations is considered all of the element deformations and equations are defined in body attached element coordinates three rotation parameters are proposed to determine the orientation of the element cross section two sets of element nodal parameters termed explicit nodal parameters and implicit nodal parameters are introduced the explicit nodal parameters are used in the assembly of the system equations from the element equations and chosen to be three components of the incremental translation vector and three components of the incremental rotation vector the implicit nodal parameters are used to determine the deformations of the beam element and chosen to be three components of the total displacement vector and nodal values of the three rotation parameters the element internal nodal forces corresponding to the implicit nodal parameters are obtained from the virtual work principle numerical examples are presented and compared with the numerical and experimental results reported in the literature to demonstrate the accuracy and efficiency of the proposed method hree dimensional beams are very important structural elements in all types of engineering systems in many applications these beam elements undergo finite rotations that require a nonlinear formulation to their structural analysis the development of new and efficient formulations for nonlinear analysis of beam structures has attracted the study of many researchers in recent years based on different kinematic assumptions different alternative formulation strategies and procedures to accommodate large rotation capability during the large deformation process have been presented 1 20 the kinematic assumptions used in refs 4 5 7 11 and 17 19 are based on timoshenko s hypothesis the effect of stretching bending torsion and transverse shear are taken into account

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

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

hardy algebras w correspondences and interpolation theory given a von neumann algebra m and a w correspondence e over m we construct an algebra h e that we call the hardy algebra of e when m open image in new window e h e is the classical hardy space h open image in new window of bounded analytic functions on the unit disc when m open image in new window and e open image in new window h e is the free semigroup algebra studied by popescu davidson and pitts and many others we show that given any faithful normal representation of m on a hilbert space h there is a natural correspondence e over the commutant m called the dual of e and that h e can be realized in terms of b h valued functions on the open unit ball open image in new window e in the space of adjoints of elements in e we prove analogues of the nevanlinna pick theorem in this setting and discover other aspects of the value distribution theory for elements in h e we also analyze the boundary behavior of elements in h e and obtain generalizations of the sz nagy foias functional calculus and the functional calculus of popescu for c n c row contractions the correspondence e has a dual that is naturally isomorphic to e and the commutants of certain so called induced representations of h e can be viewed as induced representations of h e for these induced representations a double commutant theorem is proved

a constrained least squares regularization method for nonlinear ill posed problems this paper deals with a method for solving ill posed nonlinear hilbert space operator equations f x y regularization is obtained by solving a constrained least squares regularization problem min f x y 2 quad text subject to j x leqq beta 2 beta serves as a regularization parameter and j x is a quadratic penalty functional to robustly and efficiently solve this regularization problem we apply a trust region method at each iteration the quadratic penalty constraint is retained a gauss newton approximation to the objective functional is taken and we add a quadratic trust region constraint the resulting quadratic subproblem is then reformulated as a nonlinear complementarily problem and solved using newton s method this paper applies methods to find approximate solutions to a severely ill posed nonlinear first kind integral equation arising in geophysics the method of generalized cross validation gcv is used to pick the regularization parameter when random er

interpolation problems in several variables abstract we obtain a noncommutative nudel man type interpolation theorem in several variables and a commutative analogue forh b n the hardy space of bounded analytic functions in the open ball of c n using this result we obtain an operatorial analogue in several variables of the rosenblum rovnyak restriction theorem as well as an extension to the noncommutative analytic toeplitz algebraf we provide new extensions of the caratheodory fejer and nevanlinna pick interpolation theorems forf

a unified co rotational framework for solids shells and beams abstract the paper describes a unified framework for applying the co rotational method to the analysis of solids shells and beams the general method stems from an unusual application of the technique which involves solid elements the proposed framework allows a formulation that is simpler than many of the earlier procedures and in addition gives a direct indication of the terms in the tangent stiffness which may be ignored

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

row action methods for huge and sparse systems and their applications this paper brings together and discusses theory and applications of methods identified and labelled as row action methods for linear feasibility problems find x in bf r n such that ax leqq b linearly constrained optimization problems minimize f x subject to ax leqq b and some interval convex programming problems minimize f x subject to c leqq ax leqq b the main feature of row action methods is that they are iterative procedures which without making any changes to the original matrix a use the rows of a one row at a time such methods are important and have demonstrated effectiveness for problems with large or huge matrices which do not enjoy any detectable or usable structural pattern apart from a high degree of sparaseness fields of application where row action methods are used in various ways include image reconstruction from projection operations research and game theory learning theory pattern recognition and transportation theory a row action method for the

finite rotation analysis and consistent linearization using projectors abstract a systematic procedure is presented that may be used to extend the capabilities of an existing linear finite element to accomodate finite rotation analysis this procedure is a generalization of the work presented in computers and structures volume 30 pp 257 267 the basis of our approach is the element independent co rotational algorithm where the element rigid body motion translations and rotations is separated from the deformational part of its total motion the variation of this co rotational relation results in a projector matrix with the property that a consistent internal force vector is invariant under its action the consistent tangent stiffness matrix is shown to depend on this invariance condition through the derivative of the projector this results in an unsymmetric tangent matrix whose anti symmetric part depends on the out of balance force vector in this paper we prove that using the symmetric part of the tangent matrix the newton iteration retains its quadratic rate of convergence this approach has been used to solve a number of large rotation test example problems the results demonstrate that it is possible to analyze structures undergoing large rotations within a general co rotational framework using simple and economical finite elements the resulting improvements in the performance of these simple elements are brought about through the use of convenient software utilities as pre and post processors to the element routines

a co rotational element time integration strategy for non linear dynamics new procedures are proposed for implicit dynamic analysis using the finite element method the main aim is to give stable solutions with significant rigid body motions in particular rotations in contrast to most conventional approaches the time integration strategy is closely linked to the element technologies with the latter involving a form of co rotational procedure for the undamped situation one of the solution procedures leads to an algorithm that exactly conserves energy when constant external forces are applied i e with gravity loading

on the choice of the linear element for corotational triangular shells the corotational formulation for triangular thin shell elements presented in a eriksson c pacoste element formulation and numerical techniques for stability problems in shells comput methods

poisson transforms on some c algebras generated by isometries abstract a noncommutative poisson transform associated to a certain class of sequences of operators on hilbert spaces with property p is defined on some universal c algebras resp nonselfadjoint algebras generated by isometries its properties are described and used to study these universal algebras and their representations as consequences we obtain a functional calculus isometric resp unitary dilations and commutant lifting theorem for the class of sequences of operators with property p our geometrical approach leads also to new and elementary proofs as well as extensions of some classical results

on the choice of finite rotation parameters in this work we discuss some aspects of the three dimensional finite rotations pertinent to the formulation and computational treatment of the geometrically exact structural theories among various possibilities to parameterize the finite rotations special attention is dedicated to a choice featuring an incremental rotation vector some computational aspects pertinent to the implementation of the newton iterative scheme and the newmark time stepping algorithm applied to solving these problems are examined representative numerical simulations are presented in order to illustrate the performance of the proposed formulation

fixed point quasi newton methods this article studies iterative methods defined by x k 1 phi x k e k where x k in mathbb r n and e k lie on a space of parameters sufficient conditions are established for local convergence and for convergence at an ideal linear or superlinear rate a theory of least change secant update methods for this class of processes is developed several examples are given showing a wide range of applications of the new theory key words quasi

co rotational flat facet triangular elements for shell instability analyses abstract this paper investigates the formulation of co rotational flat facet triangular elements for the numerical analysis of instability phenomena in shell structures the elements have three nodes with six degrees of freedom at each node the term co rotational relates here to the provision of a local system that continuously rotates and translates with the element following mainly nour omid and rankin b nour omid and c c rankin finite rotation analysis and consistent linearization using projectors comput methods appl mech engrg 93 1991 353 384 the definition of an element resorts to a change of variables from the local frame to the global one this is done through the use of a projector matrix which relates the variations of the local displacements to the variations of the global ones by extracting the rigid body modes from the latter the main difference from the original formulation lies in the parameterization of 3d finite rotations in contrast to the paper by nour omid and rankin a parameterization based on the rotational vector is here adopted and thus an additional change of variables has to be performed as a result the rotational variables become additive and the necessity of a special updating procedure is avoided the main feature of the adopted formulation is its independence of the local assumptions used to derive the internal forces and tangent stiffness in local coordinates for a certain class of elements i e elements with the same number of nodes and degrees of freedom the main co rotational framework is the same using this property three types of local formulations are considered a set of carefully chosen test problems is used in order to assess the performances of the three element types