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

co rotational beam elements with warping effects in instability problems the present paper investigates the formulation of 3d co rotational beam elements for the buckling and post buckling analysis of frame structures following pacoste and eriksson comput methods app

julia sets and mandelbrot sets in noor orbit in recent literature researchers have generated julia sets and mandelbrot sets in mann and ishikawa orbits that are examples of two step and three step feedback processes respectively this paper presents further generalization of julia and mandelbrot sets for complex valued polynomials such as quadratic cubic and higher degree polynomials using a noor orbit which is a four step iterative procedure the graphical images of julia and mandelbrot sets have been visualized and certain patterns in mandelbrot sets have been recognized it is fascinating to see that a few mandelbrot sets are akin to a butterfly or a coupled urn or a coupled trident

convergence analysis of a finite element method based on different moduli in tension and compression abstract when analyzing materials that exhibit different mechanical behaviors in tension and compression an iterative approach is required due to material nonlinearities because of this iterative strategy numerical instabilities may occur in the computational procedure in this paper we analyze the reason why iterative computation sometimes does not converge we also present a method to accelerate convergence this method is the introduction of a new pattern of shear modulus that was strictly derived according to the constitutive model based on the bimodular elasticity theory presented by ambartsumyan we test this procedure with a numerical example concerning a plane stress problem results obtained from this example show that the proposed method reduces the cost of computation and accelerates the convergence of the solution

a new 48 d o f quadrilateral shell element with variable order polynomial and rational b spline geometries with rigid body modes a 48 degrees of freedom d o f quadrilateral thin elastic shell finite element using variable order polynomial functions b spline functions and rational b spline functions to model the shell surface is developed this development may allow the stiffness formulation of the shell element to be linked to the geometry data bases created by computer aided design systems the displacement functions are that of bicubic hermitian polynomials the displacement functions and d o f are expressed and investigated in both the curvilinear and cartesian forms the cuivilinear form is simpler and can provide the proper solution for a certain class of shell problems for certain highly curved shells such as bellows however the curvilinear form fails to properly model some rigid body modes even with either the explicit inclusion of rigid body terms or the high order displacement functions it is suggested in this study that such difficulty can be circumvented and the rigid body modes can be properly included if a cartesian form is used for displacement functions the strain displacement equations are expressed in curvilinear co ordinates thus the cartesian displacement functions require a transformation to curvilinear displacement at each numerical integration point examples include a pinched cylinder a translational shell under central load a uniformly loaded hypar shell a pressurized ovel shell a semi toroidal bellows and a u shaped bellows for the first four examples geometric modellings consist of polynomials of second order subparametric third order isoparametric and fourth and fifth order both superparametric as well as b spline functions of fourth and fifth order the geometries of the pinched cylinder the semi toroidal bellows and the u shaped bellows were modelled exactly using rational b spline functions all the results obtained are in good agreement with alternative existing solutions

an adaptive secret image sharing with a new bitwise steganographic property recently numerous studies have been conducted in the area of secret image sharing and steganography the main objective of these schemes is to produce high quality tampering resistant stego images a number of these methods are based on least significant bit embedding and hence the presence of hidden data can be detected by well designed steganalysis algorithms this paper proposes a new sharing scheme for critical images so that stego images are obtained with better visual quality and at the same time the authentication ability can be adjusted to any desired level adaptive in order to achieve these objectives the construction of cellular automata is modified so that visual quality is improved although authentication bits are hidden in cover images furthermore authentication bits are computed in such a way that any tampering with one block affects more than one block for steganographic purposes least significant bit replacement is substituted with a new blockwise xor operation so that the scheme can withstand steganalysis attacks the other interesting property of the proposed method is that the size of blocks is determined dynamically therefore our approach can be adapted with secret cover images of different sizes

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

on the calculation of misiurewicz patterns in one dimensional quadratic maps abstract in this work we give for the first time a table with all misiurewicz points m n p for low values of the preperiod and period 2 n 8 1 p 5 in one dimensional quadratic maps in the particular case of m n 1 important misiurewicz points which are all placed in the period 1 chaotic band the preperiod values are 2 n 11 a brute force algorithm to obtain all the symbolic sequences patterns of the m n p and a more efficient algorithm to obtain the patterns of m n 1 are also shown

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

large displacements of shells including material nonlinearities abstract the paper presents a finite element formulation of shells with large deflections including elastoplastic material behaviour the elements utilized are the so called degenerated shell elements with special emphasis on the simple 4 node quadrilateral both the total lagrangian and the updated lagrangian formulation are considered for the treatment of plastic behaviour the concept of a layered element model is proposed and investigated for both the tangential modulus method and the initial load method in the final section sample problems are presented and compared with reference solutions it is shown that the 4 node element is very well suited to the class of problems under consideration it is characterized by an easy applicability high accuracy and low rates of computer time in appendix a an analytical solution of a cantilever beam subjected to an end load including geometrical and material nonlinearities is presented

implantation of a nonlinear capability on a linear software system the present paper proposes a simple procedure which extends with minor additions an existing linear elastic program system aska to geometrically nonlinear applications involving large displacements but small strains such an attempt is of course not new numerous other techniques related to this subject are documented in a large list of publications which have appeared over the last twenty five years or so for the present purpose it suffices to quote in place of an extensive review a few pertinent papers l 8 at the same time we propose to discuss in what follows certain general principles of a geometrically nonlinear finite element analysis and their relation to the present work clearly an extension of a linear computational capability to nonlinear applications demands in the first instance a suitable incrementation procedure pertinent equations determining the so called incremental equilibrium are well known inherent to the concept of an incremental transition from a given equilibrium state to another is the notion of a tangential stiffness matrix of the structure in this context the elastic material stiffness matrix already established for a linear analysis must be supplemented by the geometrical stiffness matrix which expresses the influence of the existing stress state on the incremental condition of equilibrium of the structure simple incrementation of the nonlinear response leads to a desired linearisation of the computational process but also to inevitable accumulating deviations from the true equilibrium solution in a first attempt to remove the error imposed by the linearisation higher order incremental approximations may be employed in the limit this approach leads to a fully nonlinear formulation of the problem for large deflections and entails as a rule software concepts larstran different from those valid in a linear analysis also important in this context is the development and implementation of numerical methods for the solution of the nonlinear governing equations the literature on the subject is still growing and partial overlapping of the methods is unavoidable the treatment of geometrically nonlinear problems is based on the equilibrium condition between internal stresses and applied loads for the unknown deflected configuration of the structure elastic structures do not require a priori an incremental application of the loading which proves however advantageous in the numerical process on the other hand incremen

julia sets and bifurcation diagrams for exponential maps on decrit certaines des bifurcations qui apparaissent dans la famille des applications entieres e z exp z pour 1 on sait que j e c on montre qu il y a beaucoup d autres valeurs pour lesquelles ceci arrive

a consistent co rotational formulation for non linear three dimensional beam elements abstract this paper describes a co rotational formulation for three dimensional beams in which both the internal force vector and tangent stiffness matrix are consistently derived from the adopted strain measures the latter relate to standard beam theory but are embedded in a continuously rotating frame a set of numerical examples show that the element provides an excellent numerical performance

an algorithm for finite element analysis of partly wrinkled membranes a generalization and numerical implementation is presented of the stein hedgepeth 1961 continuum theory for the analysis of partly wrinkled membranes such as the tensioned membrane surfaces which are found in spacecraft structural components the approach has its basis in experimental observations showing that when wrinkles develop in a membrane parallel to the x direction the associated overall contraction in the y direction exceeds that predicted by the poisson s ratio effect

new numerical method for two dimensional partially wrinkled membranes based on the introduction of a nonnegative adjustable parameter into poisson s ratio a new numerical method is proposed to solve numerically the partially wrinkled membrane problems with arbitrary complex shapes three fundamental issues in this new method are addressed first a nonnegative adjustable parameter is introduced into the constitutive law automatically representing unwrinkled taut and wrinkled states of a membrane second a parametric variational principle is developed for the new membrane model third by the variational principle the original membrane problem is converted to a nonlinear mathematical programming problem the variational principle and the mathematical programming formulation lay a foundation for efficient numerical analysis of wrinkled membrane structures using finite element discretization three typical examples are given to show the effectiveness of this method

a posteriori analysis of penalized and mixed formulations of koiter s shell model we are interested in finite element approximations of a koiter model for linearly elastic shells with little regularity to perform conforming method we present a penalized and a mixed formulations of the model allowing to approximate and to enforce weakly mechanical constraints respectively we establish existence and uniqueness of the solution to the both formulations moreover a posteriori analysis is led yielding an upper bound and a lower bound of the error finally numerical results are presented to illustrate the efficiency of the a posteriori estimators we therefore propose a mesh adaptivity strategy relying on these indicators

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

vibration analysis of bimodulus laminated cylindrical panels this paper deals with the flexural vibration behavior of bimodular laminated composite cylindrical panels with various boundary conditions the formulation is based on first order shear deformation theory and bert s constitutive model the governing equations are derived using finite element method and lagrange s equation of motion an iterative eigenvalue approach is employed to obtain the positive and negative half cycle free vibration frequencies and corresponding mode shapes a detailed parametric study is carried out to study the influences of thickness ratio aspect ratio lamination scheme edge conditions and bimodularity ratio on the free vibration characteristics of bimodulus angle and cross ply composite laminated cylindrical panels it is interesting to observe that there is a significant difference between the frequencies of positive and negative half cycles depending on the panel parameters through the thickness distribution of modal stresses for positive half cycle is significantly different from that for negative half cycle unlike unimodular case wherein the stresses at a particular location in negative half cycle would be of same magnitude but of opposite sign of those corresponding to positive half cycle finally the effect of bimodularity on the steady state response versus forcing frequency relation is studied for a typical case

the generalized mandelbort julia sets from a class of complex exponential map we have generalized the baker devaney and romera s work and constructed a series of generalized mandelbort julia sets in abbreviated form generalized m j sets from the complex exponential map using the experimental mathematics method we have innovated as follows present the theoretic proof about the explosion of the generalized j sets for complex index number theoretically analyze the symmetry and periodicity of the generalized m j sets present a new attaching rule described the distributing of periodicity petal of generalized m sets for complex index number find abundant structure information of the generalized j sets contained in the generalized m sets for complex index number find that the speed of fractal growth in generalized m j sets for complex index number is faster than that of generalized m j sets for real index number the parameter value l 0 decides the speed of the fractal growth and the fractal growth in generalized m sets for complex index number points tends to the multifurcation and misiurewicz point

the generalized mandelbrot set perturbed by composing noise of additive and multiplicative adopting the experimental mathematics method combining complex variable function theory with computer aided drawing this paper researches on the structural characteristic and the fission evolution law of the generalized mandelbrot set generalized m set in short perturbed by composing noise of additive and multiplicative analyzes the effect of random perturbation to the generalized m set

a t n multi secret sharing scheme in the t n multi secret sharing scheme there are n participants in the system at least t or more participants can easily pool their secrets shadows and reconstruct p secrets at the same time chien et al ieice trans fundamentals e83 a 2000 2762 used n p t 1 public values 2 n p t x n p storages and solved n p t simultaneous equations to share p secrets in this article we shall propose an alternative t n multi secret sharing based on shamir s secret sharing we shall use n p t 1 or n 1 public values 2 t 1 or 2 p 1 storages and employ the lagrange interpolation polynomial to share p secrets our scheme will have exactly the same power as chien et al s scheme

a new efficient t n verifiable multi secret sharing vmss based on ych scheme a verifiable multi secret sharing scheme vmss is a multi secret sharing scheme with the verifiable property this paper presents a new efficient verifiable multi secret sharing based on ych c c yang t y chang m s hwang a t n multi secret sharing scheme appl math comput 151 2004 483 490 scheme and the intractability of the discrete logarithm dl and it just needs few public values and low modular exponentiation operation

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

mixed models and reduced selective integration displacement models for nonlinear shell analysis simple mixed models are developed for the geometrically nonlinear analysis of shells a total lagrangian description of the shell deformation is used and the analytical formulation is based on a form of the nonlinear shallow shell theory with the effects of transverse shear deformation and bending extensional coupling included the fundamental unknowns consist of eight stress resultants and five generalized displacements of the shell and the element characteristic arrays are obtained by using the hellinger reissner mixed variational principle the polynomial interpolation or shape functions used in approximating the stress resultants are in general of different degree than those used for approximating the generalized displacements the stress resultants are discontinuous at the element boundaries and are eliminated on the element level the equivalence and near equivalence between the mixed models developed herein and displacement models based on reduced selective integration of both transverse shear and extensional energy terms is discussed the use of reduction methods in conjunction with the mixed models is outlined and the advantages of mixed models over displacement models are delineated analytic expressions are derived for the rigid body and spurious or zero energy models for the various mixed models and their equivalent displacement models also the advantages of mixed models over equivalent displacement models are outlined numerical results are presented to demonstrate the high accuracy and effectiveness of the mixed models developed and to compare their performance with other mixed models reported in the literature

physical meaning for mandelbrot and julia sets abstract we consider the dynamics of a kicked charged particle moving in a double well potential and a time dependent magnetic field in certain cases the stroboscopic dynamics reduces to the complex logistic map thus providing physical meaning for the mandelbrot set in other cases we obtain iterated function systems consisting of the inverse complex logistic map thus providing physical meaning for julia sets our approach can be generalized to complex mappings with a maximum of order q

the geometric stiffness of thick shell triangular finite elements for large rotations this paper is concerned with the development of the geometric stiffness matrix of thick shell finite elements for geometrically nonlinear analysis of the newton type a linear shell element that is comprised of the constant stress triangular membrane element and the triangular discrete kirchhoff mindlin theory dkmt plate element is upgraded to become a geometrically nonlinear thick shell finite element perturbation methods are used to derive the geometric stiffness matrix from the gradient in global coordinates of the nodal force vector when stresses are kept fixed the present approach follows earlier works associated with trusses space frames and thin shells it has the advantage of explicitness and clear physical insight a special procedure tailored to triangular elements is used to isolate pure rotations to enable stress recovery via linear elastic constitutive relations several examples are solved the results compare well with those available in the literature copyright 2005 john wiley sons ltd

new efficient and practical verifiable multi secret sharing schemes in 2006 zhao et al proposed a practical verifiable multi secret sharing based on yang et al s and feldman s schemes in this paper we propose two efficient computationally secure t n and verifiable multi secret sharing schemes based on homogeneous linear recursion the first scheme has the advantage of better performance a new simple construction and various techniques for the reconstruction phase the second scheme requires fewer public values with respect to zhao et al s and shao and cao schemes these schemes are easy to implement and provide great capabilities for many applications

efficient verifiable multi secret sharing scheme based on hash function abstract a verifiable k t n multi secret sharing scheme vmss allows a dealer to share k secrets among n players in particular 1 the secret shadow given by the dealer or some player can be verifiable and 2 t or more players can cooperate to reveal the k secrets while less than t players cannot reveal any secret vmss can be used in many applications such as access control however the existing vmss schemes either require costly computation or miss some important properties of vmss these two weaknesses make the vmss scheme not so good as expected in this paper we propose a novel vmss scheme which does not need any costly computation while holds all properties of vmss

research on fractal structure of generalized m j sets utilized lyapunov exponents and periodic scanning techniques abstract in order to show details of fractal structure of mandelbrot set precisely lyapunov exponents and periodic scanning techniques have been brought forward by shirriff and welstead this paper generalizes these two techniques and puts forward periodicity orbit search and comparison technique which can be used to discuss the relationship of the generalized mandelbrot julia sets the generalized m j sets adopting the techniques mentioned above and the experimental mathematics method of combining the theory of analytic function of one complex variable with computer aided drawing this paper researches on the structure topological inflexibility and the discontinuity evolution law of the generalized m j sets generated from the complex mapping z z c r and explores structure and distributing of periodicity petal and topological law of periodicity orbits of the generalized m sets and finds that the generalized m set contains abundant information of structure of the generalized j sets by founding the whole portray of the generalized j sets based on the generalized m set qualitatively furthermore the physical meaning of the generalized m j sets have been expounded

two aggregate function based algorithms for analysis of 3d frictional contact by linear complementarity problem formulation three dimensional frictional contact is formulated as linear complementarity problem lcp by using the parametric variational principle and quadratic programming method two aggregate function based algorithms called respectively as self adjusting interior point algorithm and aggregate function smoothing algorithm are proposed for the solution of the lcp derived from the contact problems a nonlinear finite element code is developed for numerical analysis of 3d multi body contact problems four numerical examples are computed to demonstrate the applicability and computational efficiency of the methods proposed

two finite element approximations of naghdi s shell model in cartesian coordinates we present a penalized version of naghdi s model and a mixed formulation of the same model in cartesian coordinates for linearly elastic shells with little regularity and finite element approximations thereof numerical tests are given that validate and illustrate our approach

a gradient based algorithm to solve inverse plane bimodular problems of identification abstract this paper presents a gradient based algorithm to solve inverse plane bimodular problems of identifying constitutive parameters including tensile compressive moduli and tensile compressive poisson s ratios for the forward bimodular problem a fe tangent stiffness matrix is derived facilitating the implementation of gradient based algorithms for the inverse bimodular problem of identification a two level sensitivity analysis based strategy is proposed numerical verification in term of accuracy and efficiency is provided and the impacts of initial guess number of measurement points regional inhomogeneity and noisy data on the identification are taken into accounts

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

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

an improvement on the lin wu t n threshold verifiable multi secret sharing scheme lin and wu iee proc comput digit tech 146 1999 264 have proposed an efficient t n threshold verifiable multi secret sharing vmss scheme based on the factorization problem and the discrete logarithm modulo a large composite problem in their scheme the dealer can arbitrarily give any set of multiple secrets to be shared and only one reusable secret shadow is to be kept by every participant on the other hand they have claimed that their scheme can provide an efficient solution to the cheating problems between the dealer and any participant however he and wu iee proc comput digit tech 148 2001 139 have shown that lin and wu s scheme is in fact insecure against a cheating participant in this paper we shall try to improve the security of lin and wu s scheme while providing more efficient performance than other vmss schemes in terms of computational complexity

the modeling and numerical analysis of wrinkled membranes in this paper three fundamental issues regarding modeling and analysis of wrinkled membranes are addressed first a new membrane model with viable young s modulus and poisson s ratio is proposed which physically characterizes stress relaxation phenomena in membrane wrinkling and expresses taut wrinkled and slack states of a membrane in a systematic manner second a parametric variational principle is developed for the new membrane model third by the variational principle the original membrane problem is converted to a non linear complementarity problem in mathematical programming a parametric finite element discretization and a smoothing newton method are then used for numerical solution the proposed membrane model and numerical method are capable of delivering convergent results for membranes with a mixture of wrinkled and slack regions without iteration of membrane stresses three numerical examples are provided

degenerated isoparametric finite elements using explicit integration the kinematics of degenerated finite elements using explicit integration are investigated in particular for geometric nonlinear applications two representations of the nodal rotational degrees of freedom are investigated the first adopts the infinitesimal representation of rotations while the second uses a valid large rotation representation a method of explicit integration is presented which satisfies rigid body rotations under arbitrary large rotations the accuracy and convergence of these formulations are investigated

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 mixed finite element for shell model with free edge boundary conditions part 2 the numerical scheme abstract from the mixed variational formulation which was suggested in part 1 we construct a finite element scheme then a mathematical justification concerning the error estimate is developed the most important point is to justify two compatibility conditions between the approximation of the kinematics and the stresses because of the structure of the shell operator they are not obvious at all and several restrictions on the mesh are necessary therefore the classical result known in fluid mechanics for stokes equations cannot be applied directly

on the symmetries of the julia sets for the process z zp c the self replicating properties of the julia sets jc p for the iterative processes z implies zp c are examined for integers p 1 it is shown that the corresponding mandelbrot sets m p contain p 1 fold symmetries which results in jc p having p fold symmetries

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

on numerical approximations of the area of the generalized mandelbrot sets in the present work the area of the generalized mandelbrot sets is defined as the double limit of the areas of the plotted generalized mandelbrot sets in a given square lattice using the finite escape algorithm while the lattice resolution and the number of iteration counts used to plot them tends to infinity the asymptotic behavior of the areas of the generalized mandelbrot sets in terms of their degree growth is investigated finally numerical approximations of the area of the mandelbrot set are proposed by using tools from regression analysis

quadratic programming method in numerical simulation of metal forming process abstract in this paper a quadratic programming qp model based on a parametric variational principle is proposed for elastic plastic ep finite element analysis of metal forming processes the contact problem with friction between blank and tools is treated in the same way as in plastic analysis the penalty factors which are normally introduced into the algorithm for contact analysis have a direct influence on accuracy of solution there is no available rule for choosing a reasonable value of these factors for simulation of metal forming and they are therefore cancelled through a special technique so that the numerical results can be of high accuracy the algorithms for contact analysis and plastic analysis are established in one frame and consistent with each other compared with the conventional ep fem the newly developed method requires no tedious iterative procedures and has no convergence problems to apply this method easily to simulation of metal forming detailed forms of some key matrices or vectors for 2d fem and 3d fem are presented and a parametric loading algorithm for the qp model is developed which is suitable for qp problem with free variables and can decrease memory cost by avoiding the introduction of additional slack variables and improve the solution efficiency to some extent finally the proposed qp model is validated by two examples analysis of v notched tension test and analysis of the drawing of a square box one of the benchmarks proposed at numisheet93 it can be seen that the accuracy of solution of the new ep fem based on qp is better than that of the conventional ep fem based on iteration to make the new ep fem more applicable to metal forming industries it is necessary to develop a more efficient qp algorithm that is suitable for large scale problems

geometrically nonlinear formulation for the axisymmetric shell elements a geometrically nonlinear formulation using total lagrangian approach is presented for the axisymmetric shell elements the basic element is formulated using the co ordinates of the mid surface nodes and the mid surface nodal point normals an important aspect of the formulation presented here is that the restriction on the magnitude of the nodal rotations is eliminated this is accomplished by retaining true nonlinear nodal rotation terms in the definition of the displacement field and the consistent derivation of the element properties based on this displacement field the element properties are derived and presented in detail numerical examples are also presented to demonstrate the element behaviour and the accuracy

large deflection analysis of shell structure by using corotational total lagrangian formulation abstract a corotational total lagrangian cr tl formulation using the von karman assumption is presented for the analysis of nonlinear shell problems this formulation is applicable for the nonlinear analysis of shell structures with large rotations but moderate deformations the numerical algorithm used here is an incremental iterative method based on the newton raphson method combined with constant arc length of incremental displacement vector in order to improve the convergence properties of the equilibrium iterations special care is taken in the calculation of the geometric stiffness matrix numerical examples are presented and compared with the results reported in the literature to demonstrate the accuracy and efficiency of the proposed method

spectral discretization of a naghdi shell model we consider the naghdi equations which model a thin three dimensional shell we propose a spectral discretization of this problem in the case where the midsurface of the shell is weakly regular we perform the numerical analysis of the discrete problem and prove optimal error estimates

a curved quadrilateral element for static analysis of shells with geometric and material nonlinearities a 48 degrees of freedom quadrilateral element including the effect of both material and geometric nonlinearities is formulated and appropriate numerical procedures are adopted for the development of a systematic and efficient approach for the static nonlinear analysis of general shell structures the element surface is described by a variable order polynomial in curvilinear co ordinates the displacement functions are described by bicubic hermitian polynomials in curvilinear co ordinates without being confined to the assumption of axisymmetry this formulation allows for the treatment of shells with a more general shape and with a complex spread of plastic zones in the formulation for geometric nonlinearity the total lagrangian approach is adopted only small strains and small rotations are allowed in the formulation for plastic deformation the concept of a layered element model is used in the inelastic range the material is assumed to obey the von mises yield criterion and the prandtl reuss flow rule a tangential stiffness formulation is combined with the modified newton raphson iteration method for the solution of nonlinear problems a systematic choice of examples ranging from fiat plates to cylindrical panels and to spherical caps is solved and compared with available solutions to evaluate the recommended formulations and procedures in terms of their accuracy and efficiency

noise perturbed generalized mandelbrot sets adopting the experimental mathematics method of combining the theory of analytic function of one complex variable with computer aided drawing in this paper on the structure characteristics and the discontinuity evolution law of the additive noise perturbed generalized mandelbrot sets m sets was studied on the influence of stochastic perturbed parameters of the structure of generalized m sets was analyzed the physical meaning of the additive noise perturbed generalized m sets was expounded

a new t n multi secret sharing scheme based on shamir s secret sharing in 2000 chien et al proposed a t n multi secret sharing scheme at least t of the n participants can easily reconstruct p secrets at the same time but the secret reconstruction needs to solve simultaneous equations which is a complex process in order to reduce the complexity of the secret reconstruction yang et al proposed an alternative scheme based on shamir s secret sharing in 2004 but there are more public values required in yang s scheme than in chien s scheme when p

complex analytic dynamics on the riemann sphere dichotomie dynamique de fatou et julia points periodiques consequences du theoreme de montel l ensemble de julia est la fermeture de l ensemble des points periodiques repulseurs resultats classiques sur l ensemble de fatou classification de sullivan de l ensemble de fatou une condition pour le developpement sur l ensemble de julia la dynamique des polynomes l ensemble de mandelbrot et le travail de douady et hubbard le theoreme d application de riemann mesurable et la dynamique analytique

a verifiable multi secret sharing scheme based on cellular automata in this paper we propose a verifiable t n threshold multi secret sharing scheme based on one dimensional cellular automata where the number of secrets is not restricted by n or t we show that our scheme can be used to solve an open problem proposed recently in alvarez et al 2008 g alvarez l hernandez encinas a martin del rey a multisecret sharing scheme for color images based on cellular automata information sciences 178 2008 4382 4395

a geometrically non linear tensorial formulation of a skewed quadrilateral thin shell finite element a 48 degree of freedom d o f skewed quadrilateral thin shell finite element including the effect of geometrical non linearity is formulated and appropriate numerical procedures are adopted for the development of an efficient approach for the static and dynamic analysis of general thin shell structures the element surface is described by a variable order polynomial in curvilinear co ordinates the displacement functions are described by bicubic hermitian polynomials in curvilinear co ordinates the directions of the curvilinear co ordinates at each nodal point are uniquely defined to coincide with the directions of the boundaries of the element in the present case of a skewed quadrilateral with non orthogonal curvilinear coordinates the coupling terms of the metric tensor and curvature tensor of the surface no longer vanish such as in the case of orthogonal co ordinates the tensor form is used in the setup of the shape functions geometric derivatives stiffness matrix and computer code this allows for the treatment of shells with irregular shapes and variable curvatures to evaluate the efficiency and accuracy of this formulation a systematic list of examples is chosen i linear and non linear static analysis of square and rhombic plates cylindrical and spherical shells ii linear vibrations of trapezoidal flat and curved plates iii large amplitude vibrations of a rhombic plate for the square plate and cylindrical and spherical shell shewed element meshes with various distortion angles are used to study the effect of the distortion angles on the accuracy of the results and to demonstrate the versatility of the present element all results are compared with alternative available solutions including those obtained using regular rectangular meshes pinched thin cylindrical and spherical shells are studied using different skewed meshes and various gauss integration meshes and no membrane locking phenomenon is observed

a mixed finite element for shell model with free edge boundary conditions part 1 the mixed variational formulation abstract after a very brief recall on general shell theory we construct a mixed variational formulation based on the introduction of a new unknown the rotation of the normal to the medium surface in koiter shell theory for instance this rotation can be expressed with respect to the three components of the displacement field of the medium surface and their derivatives the lagrange multiplier corresponding to this relation known as the kirchhoff love kinematical assumption is also introduced as an independent unknown there are two main difficulties one is due to the differential geometry of surfaces and is rather technical the other is to define correctly the dual space for the kirchhoff love relation the difficulty is similar to the one met in the characterization of the dual space of the sobolev space h 1 being the medium surface of the shell for which a boundary component appears except for clamped shells which is a very restrictive situation

additive perturbed generalized mandelbrot julia sets abstract adopting the experimental mathematics method combining complex variable function theory with computer aided drawing this paper researches on the structural characteristic and the fission evolution law of additive perturbed generalized mandelbrot julia sets generalized m j sets in short the corresponding relationship between point coordinates in generalized m set and the general structure of generalized j sets has been founded qualitatively and the physical meaning of the generalized m j sets has been expounded the following conclusions are deduced 1 chaotic patterns of fractal structure of generalized j sets may emerge out of double periodic bifurcation which shows that brownian movement can be chaotic 2 experimental evidence of li yorke theorem is given out 3 the additive perturbed generalized m set contains abundant information on the construction of generalized j sets 4 resemble logistic map in the process of a series of double periodic bifurcation coming into chaos generalized j sets also present self similarity in parameter space

a new computational framework for materials with different mechanical responses in tension and compression and its applications abstract materials possessing tension compression asymmetric behavior can be simulated by a bi modulus constitutive relation which assumes the materials have different moduli in tension and compression traditional iteration methods struggle for the convergence difficulty for such kind of constitutive model in this paper a new computational framework is established solution procedures under both small and finite deformations which have asymptotically quadratic rate of convergence have also been proposed and implemented in abaqus with umat numerical examples show that the proposed computational framework can be applied successfully to simulate the wrinkling analysis of thin plane membranes and explain some unusual cell mechanosensing phenomena