rigid body concept for geometric nonlinear analysis of 3d frames plates and shells based on the updated lagrangian formulation abstract in the nonlinear analysis of elastic structures the displacement increments generated at each incremental step can be decomposed into two components as the rigid displacements and natural deformations based on the updated lagrangian ul formulation the geometric stiffness matrix kg is derived for a 3d rigid beam element from the virtual work equation using a rigid displacement field further by treating the three node triangular plate element tpe as the composition of three rigid beams lying along the three sides the kg matrix for the tpe can be assembled from those of the rigid beams the idea for the ul type incremental iterative nonlinear analysis is that if the rigid rotation effects are fully taken into account at each stage of analysis then the remaining effects of natural deformations can be treated using the small deformation linearized theory the present approach is featured by the fact that the formulation is simple the expressions are explicit and all kinds of actions are considered in the stiffness matrices the robustness of the procedure is demonstrated in the solution of several benchmark problems involving the postbuckling response

aggregating local image descriptors into compact codes this paper addresses the problem of large scale image search three constraints have to be taken into account search accuracy efficiency and memory usage we first present and evaluate different ways of aggregating local image descriptors into a vector and show that the fisher kernel achieves better performance than the reference bag of visual words approach for any given vector dimension we then jointly optimize dimensionality reduction and indexing in order to obtain a precise vector comparison as well as a compact representation the evaluation shows that the image representation can be reduced to a few dozen bytes while preserving high accuracy searching a 100 million image data set takes about 250 ms on one processor core

some exact solutions for the bending of beams with spatially stochastic stiffness to the best of the knowledge of the authors there are no exact solutions available for the bending of beams with spatially stochastic stiffness investigators are therefore utilizing various approximate techniques in the present study a new method is developed to obtain exact solutions for first and second moments of displacements for statically determinate beams that have spatially random stiffness the method is based on the full probabilistic characterization of the random stiffness so that the solutions are valid for any value of the coefficient of variation of the stiffness the deterministic governing equations and boundary conditions derived for both first and second moments allow apparently for the first time in the literature the exact solutions for the mean and covariance functions of the displacements to be determined two governing equations are uncoupled from each other and can be solved separately several exact solutions for the mean and covariance functions are obtained to illustrate the application of the method it is hoped that the exact solutions determined will serve as benchmark solutions to enable the researchers to check the accuracy of various approximate analytical and numerical techniques on the test solutions presented in this study

element formulation and numerical techniques for stability problems in shells in the context of instability problems in shells or shell like structures the objective of the present paper is twofold primarily the paper describes how quasi static conservative instability problems can be considered in a multi parametric context where generalized path following procedures for augmented equilibrium problems are used as computational tools these allow systematic treatment of the higher dimensional solution sets generated under the variations of certain parameters deemed relevant for the given problem the efficient implementation of the above mentioned procedures requires however as an essential ingredient a non linear finite element which is not only accurate but also inexpensive to this end a systematic view on a corotational total lagrangian formulation is described the tric element of argyris and coworkers is slightly modified and introduced as core element formulation special emphasis is given to the alternative methods for treatment of finite three dimensional rotations with reference to both the element definition and solution algorithms numerical examples verify the element capabilities and the possibility to completely describe instability phenomena of large discretized models

response variability of stochastic frame structures using evolutionary field theory the integral form for the variance of the response of stochastic statically indeterminate structural systems involving the so called variability response function vrf and the spectral density function of the stochastic field modelling the uncertain system properties is established for the first time in this paper using evolutionary spectra theory the vrf is a function depending on deterministic parameters related to the geometry boundary conditions mean material properties and loading of the structural system no approximations are involved in the derivation of the integral form however a conjecture has to be made that is validated using monte carlo simulations the uncertain system property considered is the inverse of the elastic modulus flexibility closed form expressions can be derived in principle for the vrf of any statically determinate or indeterminate frame system using a flexibility based formulation alternatively a fast monte carlo simulation approach is provided to numerically evaluate the vrf it is shown in closed form and numerically that the vrf for statically indeterminate structures is a function of the standard deviation ff of the stochastic field modeling the inverse of the elastic modulus although the vrf depends on ff it appears to be independent of the functional form of the spectral density function of the stochastic field modeling the uncertain system properties for statically determinate structures the vrf is independent of ff the integral form can be used to compute the variance of the system response as well as its upper bound with minimal computational effort it also provides an excellent insight into the mechanisms controlling the response variability the upper bounds for the response variance are spectral and probability distribution free requiring knowledge of only the variance of the inverse of the elastic modulus the proposed bounds are realizable in the sense that it is possible to determine the probabilistic characteristics of the stochastic field that produces them several numerical examples are provided demonstrating the capabilities of the methodology

comparison of dynamic response of structures with uncertain but bounded parameters using non probabilistic interval analysis method and probabilistic approach abstract now by combining the finite element analysis and interval mathematics a new non probabilistic set theoretical models that is interval analysis method is being developed in scientific and engineering communities to predict the variability or uncertainty resulting from the unavoidable scatter in structural parameters and the external excitations as an alternative to the classical probabilistic approaches interval analysis methods of uncertainty were developed for modeling uncertain parameters of structures in which bounds on the magnitude of uncertain parameters are only required not necessarily knowing the probabilistic distribution densities instead of conventional optimization studies where the minimum possible response is sought here an uncertainty modeling is developed as an anti optimization problem of finding the least favorable response and the most favorable response under the constraints within the set theoretical description in this study we presented the non probabilistic interval analysis method for the dynamical response of structures with uncertain but bounded parameters under the condition of the interval vector which contains the uncertain but bounded parameters determined from probabilistic statistical information or stochastic sample test through comparing between the non probabilistic interval analysis method and the probabilistic approach in the mathematical proof and the numerical examples we can see that the region of the dynamical response of structures with uncertain but bounded parameters obtained by the interval analysis method contains that produced by the probabilistic approach in other words the width of the maximum or upper and minimum or lower bounds on the dynamical responses yielded by the probabilistic approach is tighter than those produced by the interval analysis method this kind of results is coincident with the meaning of the probabilistic theory and interval mathematics

class dependent discretization for inductive learning from continuous and mixed mode data inductive learning systems can be effectively used to acquire classification knowledge from examples many existing symbolic learning algorithms can be applied in domains with continuous attributes when integrated with a discretization algorithm to transform the continuous attributes into ordered discrete ones in this paper a new information theoretic discretization method optimized for supervised learning is proposed and described this approach seeks to maximize the mutual dependence as measured by the interdependence redundancy between the discrete intervals and the class labels and can automatically determine the most preferred number of intervals for an inductive learning application the method has been tested in a number of inductive learning examples to show that the class dependent discretizer can significantly improve the classification performance of many existing learning algorithms in domains containing numeric attributes

q oscillator realizations of the quantum superalgebras slq m n andospq m 2n realizations of the quantum superalgebras corresponding to thea m n b m n c n 1 andd m n series are given in terms of the creation and annihilation operators ofq deformed bose and fermi oscillators

generalized variability response functions for two dimensional elasticity problems the ability to determine probabilistic characteristics of response quantities in structural mechanics e g displacements stresses as well as effective material properties is restricted due to lack of information on the probabilistic characteristics of the uncertain system parameters the concept of the variability response function vrf has been proposed as a means to systematically capture the effect of the stochastic spectral characteristics of uncertain system parameters modeled by homogeneous random fields on the uncertain structural response the key property of the vrf in its classical sense is its independence from the marginal probability distribution function pdf and the spectral density function sdf of the uncertain system parameters it depends only on the deterministic structural configuration and boundary conditions proofs have been provided for the existence of vrfs for linear and some nonlinear statically determinate beams for statically indeterminate structures the monte carlo based generalized variability response function gvrf methodology has been proposed recently as a generalization of the vrf concept to indeterminate linear and some nonlinear beams the methodology computes gvrfs which are analogous to vrfs for statically determinate structures and evaluates their dependence or lack thereof on the pdf and sdf of the random field thereby providing an estimate of the accuracy of the gvrf in this paper the gvrf methodology is extended to problems involving two dimensional linear continua whose stochasticity is characterized by statistically homogeneous random fields after detailing the gvrf methodology for two dimensional random fields two numerical examples are provided gvrfs are computed for the displacement response and for the effective compliance of linear plane stress systems

assumed strain stabilization procedure for the 9 node lagrange shell element an assumed strain strain interpolation method is used to construct a stabilization matrix for the 9 node shell element the stabilization procedure can be justified based on the hellinger reissner variational method it involves a projection vector which is orthogonal to both linear and quadratic fields in the local co ordinate system of each quadrature point all terms in the development involve 2 2 quadrature in the 9 node element example problems show good accuracy and an almost optimal rate of convergence

finite element analysis with uncertain probabilities this paper presents a general method for the finite element analysis of linear mechanical systems by taking into account probability density functions whose parameters are affected by fuzziness within this framework the standard perturbation based stochastic finite element method is relaxed in order to incorporate uncertain probabilities in static dynamic and modal analyses general formulae are provided for assessing the fuzzy structural reliability and several typologies of optimization problems reliability based design robust design robust reliability based design are formalized in doing this the credibility theory is extensively used to extract qualified crisp data from the available set of fuzzy results so that standard optimizers can be adopted to solve the most important design problems it is shown that the proposed methodology is a general and versatile tool for finite element analyses because it is able to consider both probabilistic and non probabilistic sources of uncertainties such as randomness vagueness ambiguity and imprecision

the tric shell element theoretical and numerical investigation the tric facet triangular shell element which is based on the natural mode method is seen under the light of the non consistent formulation proposed by bergan and co workers under this formulation the convergence requirements are fulfilled even with relaxed conditions on the conformity demands of the displacement shape functions the intrinsic connection between the non consistent formulation and the natural mode method is demonstrated establishing thus a rigorous theoretical foundation for the tric element under the perspective of the non consistent formulation tric s convergence characteristics are established by satisfying apriori the patch test due to its inherent properties and thus guaranteeing convergence to the exact solution furthermore the element s accuracy robustness and efficiency are tested in a number of judiciously selected numerical examples on benchmark plate and shell problems while a cpu time comparison with a pure displacement based isoparametric shell element demonstrates its computational merits

a simple nonlinear triangular plate element and strategies of computation for nonlinear analysis according to the rigid body rule for a solid member subjected to rigid body rotations the initial forces acting on the member that form an equilibrating set must rotate following the rigid body rotations while remaining unchanged in magnitude such a rule is physically intuitive and is employed in this paper to derive an approximate geometric stiffness matrix for a three node triangular plate element tpe containing three translational and three rotational degrees of freedom dofs at each node an element such as this is attractive since it can be easily used along with the 12 dof beam element to simulate various plate and shell assemblies another advantage with the geometric stiffness matrix derived is that it can be explicitly given which renders numerical integrations unnecessary finally the element and procedure proposed are demonstrated to be robust in that solutions of good accuracy can always be obtained if a practically fine mesh has been used and that the solutions converge rapidly to the exact one upon mesh refinement

bec a 2 node fast converging shear deformable isotropic and composite beam element based on 6 rigid body and 6 straining modes abstract we present a 2 node isotropic and composite shear deformable beam element in space the element bec the formulation is based on the natural mode finite element method whereby the 12 cartesian degrees of freedom 6 per node are transformed to 6 natural rigid body and 6 natural straining modes which describe the element s kinematics only a sparse 6 6 natural stiffness matrix needs to be formed while congruent transformations performed on the computer transform the natural stiffness to the local and global cartesian coordinates with significant impact on computational efficiency and economy initial load due to temperature is also given in addition simplified and partly simplified geometrical stiffnesses are established which permit the study of nonlinear phenomena such as buckling and large displacements throughout the formulation no locking or any other parasitic phenomena were encountered although a general formulation is adopted the model is applied here to a solid beam section the theory is implemented in our structural analysis code sani structural analysis and information following validation with reference solutions applications are made to isotropic and composite beams frames and three dimensional composite beam structures the theory presented indicates a new direction in finite element analysis and structural mechanics in general

nonlinear dynamic analysis of shells with the triangular element tric abstract tric is a facet triangular shell element which is based on the natural mode method it has been shown that the tric shell element satisfies the individual element test and in the framework of the nonconsistent formulation the convergence requirements are fulfilled while it has been proved to be very efficient in linear and nonlinear static problems moreover another major advantage in the formulation of this element is the incorporation of the transverse shear deformations in a way that defies the shear locking phenomenon in this work the derivation of the consistent and lumped mass matrices of the tric element is presented so that it can be used in linear and nonlinear dynamic problems both translational and rotational inertia are included in the consistent mass matrix which is conceived using kinematical and geometrical arguments consistent with the assumed natural rigid body and straining modes of the element all the kinematical and geometrical arguments that are invoked for the derivation of the consistent mass matrix are briefly presented moreover two formulations of the lumped mass matrix of tric are derived the first formulation is based entirely on geometrical considerations whereas the second is based on lumping the consistent mass matrix of tric finally the element s robustness and accuracy will be shown by applying it to properly selected benchmark examples of nonlinear shell dynamics while its computational efficiency will be demonstrated by comparing the cpu performance of the element with the other available shell elements

twisted quantum affine superalgebra invariant r matrices and a new integrable electronic model we describe the twisted affine superalgebra sl 2 2 2 and its quantized version u q sl 2 2 2 we investigate the tensor product representation of the four dimensional grade star representation for the fixed point sub superalgebra u q osp 2 2 we work out the tensor product decomposition explicitly and find that the decomposition is not completely reducible associated with this four dimensional grade star representation we derive two u q osp 2 2 invariant r matrices one of them corresponds to u q sl 2 2 2 and the other to u q osp 2 2 1 using the r matrix for u q sl 2 2 2 we construct a new u q osp 2 2 invariant strongly correlated electronic model which is integrable in one dimension interestingly this model reduces in the q 1 limit to the one proposed by essler et al which has a larger sl 2 2 symmetry

fuzzy based robust structural optimization robust optimization is conventionally defined as the collection of the possible problem solutions that can ensure acceptable performances and sufficient immunity against the effects of uncertain parameter variability methods proposed until now use a probabilistic way to model uncertainty and to quantify the final sensitivity in this work a fuzzy uncertainty modellization is adopted for structural engineering in particular to define solution performance scattering the fuzzy entropy is used as a global measure of variable dispersion the final formulation of the problem deals with two antithetical objective functions the fuzzy expected value of structural performance and its fuzzy entropy this fuzzy based approach in robust design is able to give a set of pareto optimal solutions in terms of structural efficiency and sensitivities regarding uncertainty and represents a suitable tool in supporting the decision maker finally different applications have been developed to demonstrate the applicability of the proposed method

on zamolodchikov s solution of the tetrahedron equations the tetrahedron equations arise in field theory as the condition for thes matrix in 2 1 dimensions to be factorizable and in statistical mechanics as the condition that the transfer matrices of three dimensional models commute zamolodchikov has proposed what appear from numerical evidence and special cases to be non trivial particular solutions of these equations but has not fully verified them here it is proved that they are indeed solutions

multispecies tasep and the tetrahedron equation we introduce a family of layer to layer transfer matrices in a three dimensional 3d lattice model which can be viewed as partition functions of the q oscillator valued six vertex model on an m n square lattice by invoking the tetrahedron equation we establish their commutativity and bilinear relations mixing various boundary conditions at q 0 and m n they ultimately yield a new proof of the steady state formula for the n species totally asymmetric simple exclusion process obtained recently by the authors revealing the 3d integrability in the matrix product construction

a class of linear differential dynamical systems with fuzzy initial condition this paper investigates linear first order fuzzy differential dynamical systems where the initial condition is described by a fuzzy number we use a complex number representation of the a level sets of the fuzzy system and prove theorems that provide the solutions under such representation which is applicable to practical computations and also has some implications for theory then the paper shows some properties of the two dimensional dynamical systems and their phase portraits are described by means of examples there may be a significant difference between the solutions according to whether the matrix is nonnegative or not finally the paper points out future research on the fuzzy dynamical systems

the vertex formulation of the bazhanov baxter model in this paper we formulate an integrable model on the simple cubic lattice then valued spin variables of the model belong to edges of the lattice the boltzmann weights of the model obey the vertex type tetrahedron equation in the thermodynamic limit our model is equivalent to the bazhanov baxter model in the case whenn 2 we reproduce korepanov s and hietarinta s solutions of the tetrahedron equation as special cases

tric a simple but sophisticated 3 node triangular element based on 6 rigid body and 12 straining modes for fast computational simulations of arbitrary isotropic and laminated composite shells tric is a simple but sophisticated 3 node shear deformable isotropic and composite flat shell element suitable for large scale linear and nonlinear engineering computations of thin and thick anisotropic plate and complex shell structures its stiffness matrix is based on 12 straining modes but essentially requires the computation of a sparse 9 by 9 matrix the element formulation departs from conventional cartesian mechanics as well as previously adopted physical lumping procedures and contains a completely new implementation of the transverse shear deformation it naturally circumvents all previously imposed constraints the methodology is based on physical inspirations of the natural mode finite element method nm fem formalized through appropriate geometrical trigonometrical and engineering mathematical relations and it involves only exact integrations its stiffness mass and geometrical matrices are all explicitly derived the kinematics of the element are hierarchically decomposed into 6 rigid body and 12 straining modes of deformation a simple congruent matrix operation transforms the elemental natural stiffness matrix to the local and global cartesian coordinates the modes show explicitly how the element deforms in axial straining symmetrical and antisymmetrical bending as well as in transverse shearing the latter has only become clear in the formulation presented here and has brought about a completion of the understanding of natural modes as they apply to the triangular shell element a wide range of numerical examples substantiate the conception and purpose of the element tric fast convergence is observed in many examples

an adaptive spectral galerkin stochastic finite element method using variability response functions a methodology is proposed in this paper to construct an adaptive sparse polynomial chaos pc expansion of the response of stochastic systems whose input parameters are independent random variables modeled as random fields the proposed methodology utilizes the concept of variability response function vrf in order to compute an a priori low cost estimate of the spatial distribution of the second order error of the response as a function of the number of terms used in the truncated karhunen lo eve kl expansion this way the influence of the response variance to the spectral content correlation structure of the random input is taken into account through a spatial variation of the truncated kl terms the criterion for selecting the number of kl terms at different parts of the structure is the uniformity of the spatial distribution of the second order error this way a significantly reduced number of pc coefficients with respect to classical pc expansion is required in order to reach a uniformly distributed target second order error this results in an increase of sparsity of the coefficient matrix of the corresponding linear system of equations leading to an enhancement of the computational efficiency of the spectral stochastic finite element method ssfem copyright c 2014 john wiley sons ltd

new formulation of fem for deterministic and stochastic beams through generalization of fuchs approach this paper proposes an alternative way of constructing the global stiffness matrix of the finite element method for bending beams it also applies the new formulation to first and second moment analysis of stochastic beams which involve spatially uncertain bending stiffness originating from fuchs idea of decoupling the shear and bending components in the bending beam the element level stiffness matrix is diagonalized the generalized stress strain strain displacement and equilibrium relationships are assembled respectively and then are combined to form the global stiffness matrix the advantage of the new formulation is that the bending stiffness explicitly appears in the global stiffness matrix the mean vector and covariance matrix of the displacement of the beam are then obtained in terms of probabilistic characteristics of the uncertain bending stiffness this is in contrast to the conventional finite element method in stochastic setting which is based on the perturbation technique the example is given to illustrate the efficacy of the new formulation and its application to bending of stochastic beams

fuzzy behavior of mechanical systems with uncertain boundary conditions the problem of structures sensitivities to uncertain boundary conditions is presented in this paper and the effect of uncertain prescribed displacements on the static response of structures is discussed the imprecise or uncertain prescribed displacements are treated as fuzzy quantities with known membership functions for numerical computations a fuzzy quantity can be approximated by sets of closed intervals with respect to specified cuts this transforms the problem into a set of interval equations at each level a numerical method is developed to solve the system of fuzzy equations simple stress analysis is also used to establish and illustrate the method a numerical example is presented to demonstrate the capability of the method

new solvable lattice models in three dimensions in this paper we establish a remarkable connection between two seemingly unrelated topics in the area of solvable lattice models the first is the zamolodchikov model which is the only nontrivial model on a three dimen sional lattice so far solved the second is the chiral potts model on the square lattice and its generalization associated with theu q sl n algebra which is of current interest due to its connections with high genus algebraic curves and with representations of quantum groups at roots of unity we show that this last sl n generalized chiral potts model can be interpreted as a model on a threedimensional simple cubic lattice consisting ofn square lattice layers with ann valued n 2 spin at each site further in then 2 case this three dimen sional model reduces after a modification of the boundary conditions to the zamolodchikov model we mentioned above

zn n 1 generalization of the chiral potts model we show that ther matrix which intertwines twon by nn 1 state cyclicl operators related with a generalization ofuq sl n algebra can be considered as a boltzmann weight of four spin box for a lattice model with two spin interaction just as ther matrix of the checkerboard chiral potts model the rapidity variables lie on the algebraic curve of the genusg n2 n 1 n 1 n n 1 defined by 2n 3 independent moduli this curve is a natural generalization of the curve which appeared in the chiral potts model factorization properties of thel operator and its connection to the sos models are also discussed

generalized chiral potts models and minimal cyclic representations of u_q widehat mathfrak g mathfrak l n c finite dimensional cyclic representations of the quantized universal enveloping algebra u q g exist only when the deformation parameter q is a root of unity q n 1 in such representations the n th power of each chevalley generator acts as a non zero scalar these values of e i n f i n and t i n are part of a continuous family of parameters upon which the cyclic representations depend

a hyperspectral image classification framework and its application a new descriptor called lrp is proposed to describe subtle texture for 2d image texture enhancement is built to extend lrp to represent hsi a supervised manifold learning method called dlpp is proposed to reduce dimension the proposed framework outperforms other methods with experiments classification is a critical step to make full use of the hyperspectral data the most current approaches perform well for analyzing the macro texture but they often fail to deal with the micro texture thus this study proposes a general framework for the material with micro texture based on hyperspectral image hsi technique in this framework local response pattern lrp is firstly proposed to describe 2d image texture to preserve more structural information and keep less sensitive to image conditions then lrp is extended to represent hsi with texture enhancement te by considering opponent relationships between pairs of bands after that discriminated locality preserving projection dlpp is proposed to reduce data dimension in a linearizing nonlinear manifold way finally experiments on the hyperspectral images of fresh and frozen thawed fish fillets are conducted the results demonstrate that the proposed framework is efficient in terms of both recognition rates and robustness

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

phenomenological invariants and their application to geometrically nonlinear formulation of triangular finite elements of shear deformable shells abstract a phenomenological definition of classical invariants of strain and stress tensors is considered based on this definition the strain and stress invariants of a shell obeying the assumptions of the reissner mindlin plate theory are determined using only three normal components of the corresponding tensors associated with three independent directions at the shell middle surface the relations obtained for the invariants are employed to formulate a 15 dof curved triangular finite element for geometrically nonlinear analysis of thin and moderately thick elastic transversely isotropic shells undergoing arbitrarily large displacements and rotations the question of improving nonlinear capabilities of the finite element without increasing the number of degrees of freedom is solved by assuming that the element sides are extensible planar nearly circular arcs the shear locking is eliminated by approximating the curvature changes and transverse shear strains based on the solution of the timoshenko beam equations the performance of the finite element is studied using geometrically linear and nonlinear benchmark problems of plates and shells

fuzzy multiobjective optimization of mechanical structures this paper proposes a method that takes imperfections in multiobjective optimization problems into account the main objective is to determine a feasible design space for fuzzy design variables that respects fuzzy restriction rules and optimizes the defuzzified objective functions the proposed method uses the fuzzy finite element method ffem to calculate fuzzy solutions namely displacements and frequencies and genetic algorithms for exploring the design space of fuzzy design variables these elements are explained in detail and then applied to design a drop tower impactor sled defined with imperfections

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

a new approach to fuzzy finite element analysis in this paper a new finite element analysis method for fuzzy structure is proposed by using the information entropy concept according to this method the fuzzy variables can be transferred into random variables so that the fuzzy structure can be treated as random structure when the random variables transferred from fuzzy structure are small the perturbation finite element method can be used to obtain the mean values and the variances of the structural responses

using fem rvt technique for solving a randomly excited ordinary differential equation with a random operator the technique of stochastic finite element sfem which is the finite element technique fem adapted to stochastic problems can be re described to use random variable transformation technique rvt a new fem rvt technique was successfully used in solving stochastic problems with random excitation m el tawil w el tahhan a hussein a proposed technique of sfem on solving ordinary random differential equation j appl math comput 161 2005 35 47 in this paper the technique is adapted to solve a randomly excited differential equation with a random operator the technique shows high accuracy when solving a case study compared with the exact solution finally a problem with unknown exact solution is solved using this technique

improving the computational efficiency in finite element analysis of shells with uncertain properties this work is concerned with improving the computational efficiency of the most time consuming tasks performed in monte carlo simulation based finite element analysis fea of shell structures with uncertain properties for this purpose stochastic field values are generated on a coarse mesh and then interpolated onto the fine mesh used for the standard fea computations the cost effective tric shell element is used to ensure the formation of stiffness matrices in reasonable processing times the solution of finite element equations is efficiently handled with hybrid schemes combining both iterative and direct solution concepts additional computational gains are achieved with the use of parallel computing through the straightforward partitioning of the overall monte carlo simulation process the adoption of such advanced computational approaches allows simulation based probabilistic or stochastic fea of shells to be performed in affordable computing times and therefore become more tractable in structural engineering practice the computational procedures described in this work are evaluated on a cluster of 16 networked pcs using three linear elastic test problems with uncertain material and or geometric parameters a the scordelis lo shell b a pinched cylinder and c a 3d steel frame discretized with shell elements

a survey of non probabilistic uncertainty treatment in finite element analysis the objective of this paper is to critically review the emerging non probabilistic approaches for uncertainty treatment in finite element analysis the paper discusses general theoretical and practical aspects of both the interval and fuzzy finite element analysis first the applicability of the non probabilistic concepts for numerical uncertainty analysis is discussed from a theoretical viewpoint the necessary conditions for a useful application of the non probabilistic concepts are determined and are proven to be complementary rather than competitive to the classical probabilistic approach the second part of the paper focuses on numerical aspects of the interval finite element method it describes two principal strategies for the implementation i e the anti optimisation and the interval arithmetic approach and gives a state of the art of the interval finite element algorithms available from literature it is shown how the application of the interval arithmetic approach to the classical finite element procedure can result in a severe overestimation of the uncertainty on the output and the main sources of this conservatism are identified a numerical example in the final part of the paper illustrates the capabilities of the different strategies on an eigenfrequency analysis of a built up benchmark structure

flexibility based upper bounds on the response variability of simple beams spectral and probability distribution free upper bounds on the response variability of both statically determinate and indeterminate beams are established in the present paper based on exact closed form analytic expressions derived for the variance of the response displacement a conjecture has to be made in the case of statically indeterminate beams in order to establish these bounds the conjecture is supported through an argument postulating the existence of an integral form for the variance of the response displacement and through a brute force optimization procedure providing numerical validation such bounds require knowledge of only the variance of the stochastic field modeling the inverse of the elastic modulus and are realizable in the sense that it is possible to fully determine the probabilistic characteristics of the stochastic field modeling the inverse of the elastic modulus that produces them furthermore it is possible to fully determine also the corresponding stochastic field modeling the elastic modulus that produces these bounds these spectral and probability distribution free bounds can also be computed numerically using a so called fast monte carlo simulation procedure that does not require a closed form analytic expression for the response displacement making this approach much more general numerical examples are provided involving a statically determinate and a statically indeterminate beam

the stochastic finite element method past present and future a powerful tool in computational stochastic mechanics is the stochastic finite element method sfem sfem is an extension of the classical deterministic fe approach to the stochastic framework i e to the solution of static and dynamic problems with stochastic mechanical geometric and or loading properties the considerable attention that sfem received over the last decade can be mainly attributed to the spectacular growth of computing power rendering possible the efficient treatment of large scale problems this article aims at providing a state of the art review of past and recent developments in the sfem area and indicating future directions as well as some open issues to be examined by the computational mechanics community in the future

extension of field consistence approach into developing plane stress elements in this research paper the possibilities for extending the field consistence approach l yunhua on shear locking in finite elements licentiate thesis stockholm 1997 l yunhua explanation and elimination of shear locking and membrane locking with field consistence approach comput methods appl mech engrg in press starting from different variational principles to plane stress elements are investigated in the extension two main difficulties are explicitly solving a set of coupled partial differential equations and satisfying inter element compatibility the first one is alleviated by constructing element interpolations from a set of quasi general solutions rather than the real general solutions to the euler lagrangian equations the second one is solved by combining the field consistence approach with the iso parametric interpolation technique the traditional assumed stress method is improved and an efficient plane stress element is obtained it seems that the relations between the three commonly used variational principles can be more reasonably established in the framework of the field consistence approach

stochastic finite element analysis of shells in the present paper the stochastic formulation of the triangular composite tric facet shell element is presented using the weighted integral and local average methods the elastic modulus of the structure is considered to be a two dimensional homogeneous stochastic field which is represented via the spectral representation method as a result of the proposed derivation and the special features of the element the stochastic stiffness matrix is calculated in terms of a minimum number of random variables of the stochastic field giving a cost effective stochastic matrix under the assumption of a pre specified power spectral density function of the stochastic field it is possible to compute the response variability of the shell structure numerical tests are provided to demonstrate the applicability of the proposed methodologies

risk assessment system of natural hazards a new approach based on fuzzy probability this paper presents a system for assessing the risk of natural disasters particularly under highly uncertain conditions i e where neither the statistical data nor the physical knowledge required for a purely probabilistic risk analysis are sufficient the theoretical foundation of this study is based on employing fuzzy set theory to complement the probability theory with an additional dimension of uncertainty this would allow for expressing the likelihood of natural hazards by fuzzy probability the fuzzy probability is characterized in terms of possibility probability distributions for which a new approach has been developed the new approach has been compared with an alternative approach moreover uncertainties about the correlation of the parameters of hazard intensity damage and loss i e vulnerability relations have been considered by means of fuzzy relations the composition of fuzzy probability of hazard and fuzzy vulnerability relation yields the fuzzy probability of damage or loss the system has been applied for assessing the earthquake risk in istanbul metropolitan area

the effect of material and thickness variability on the buckling load of shells with random initial imperfections abstract the effect of material and thickness imperfections on the buckling load of isotropic shells is investigated in this paper for this purpose the concept of an initial imperfect structure is introduced involving not only geometric deviations of the shell structure from its perfect geometry but also a spatial variability of the modulus of elasticity as well as the thickness of the shell the initial geometric imperfections are described as a two dimensional uni variate 2d 1v stochastic field with statistical properties that are either based on an available data bank of measured initial imperfections or assumed in cases where no experimental data is available in order to describe the non homogeneous characteristics of the initial imperfections the spectral representation method is used in conjunction with an autoregressive moving average model with evolutionary power spectra based on a statistical analysis of the experimentally measured imperfections in cases where no experimental results is available the initial imperfections are assumed to be homogeneous and their impact on the buckling load is investigated on the basis of worst case scenarios with respect to the correlation length parameters of the stochastic fields the elastic modulus and the shell thickness are described as 2d 1v non correlated homogeneous stochastic fields while the stochastic stiffness matrix of the shell elements is formulated using the local average method the monte carlo simulation method is used to calculate the variability of the buckling load while for the determination of the limit load of the shell a stochastic formulation of the elastoplastic and geometrically non linear tric facet triangular shell element is implemented

probabilistic interval reliability of structural systems the probabilistic reliability approach is the most widely used method for reliability analysis the recent research shows that the reliabilities of structural systems strongly depend on the parameters of the probability model it is possible that the little error in the estimation of the parameters may lead to the remarkable error of the resulting probability in this study we introduce the interval approach into the conventional reliability theory we present a novel approach which allows us to obtain the system failure probability interval from the statistical parameter intervals of the basic variables this approach is a combination of the two techniques namely the classical reliability theory and the interval analysis in the end of this paper we show the feasibility of the proposed approach through two examples of the truss systems

on the classification of finite dimensional pointed hopf algebras we classify finite dimensional complex hopf algebras a which are pointed that is all of whose irreducible comodules are one dimensional and whose group of group like elementsg a is abelian such that all prime divisors of the order of g a are 7 since these hopf algebras turn out to be deformations of a natural class of generalized small quantum groups our result can be read as an axiomatic description of generalized small quantum groups

higher order weighted integral stochastic finite element method and simplified first order application it is well known that expansion based stochastic methods are approximate schemes as they are based on a first or at most second order series expansion on the basic variable e g displacement therefore expansion based stochastic analysis schemes are bound to show small response variability when compared with monte carlo simulation mcs results and application of these schemes is limited to stochastic problems with relatively small variability in order to overcome these general drawbacks of the expansion methods we suggest a higher order stochastic field function that can be employed in the expansion based stochastic analysis scheme of the weighted integral method we then propose a new weighted integral formulation using the higher order stochastic field function the new formulation is not only applicable to stochastic problems with a high degree of uncertainty but also can reproduce the phenomenon of accelerated increase in the response variability when the coefficient of variation of the stochastic field increases as observed in the mcs in order to show the validity of the proposed formulation we provide two numerical examples and the results are discussed in detail

stochastic finite element analysis of shells with combined random material and geometric properties abstract in this work an extended stochastic formulation of the triangular composite facet shell element tric is presented for the case of combined uncertain material young s modulus poisson s ratio and geometric thickness properties these properties are assumed to be described by uncorrelated two dimensional homogeneous stochastic fields the stochastic finite element analysis of shell structures is performed using the spectral representation method for the description of the random fields in conjunction with monte carlo simulation mcs for the computation of the response variability useful conclusions regarding the influence of each one of the structural parameters on the response variability are derived from the numerical tests examined

classification of arithmetic root systems arithmetic root systems are invariants of nichols algebras of diagonal type with a certain finiteness property they can also be considered as generalizations of ordinary root systems with rich structure and many new examples on the other hand nichols algebras are fundamental objects in the construction of quantized enveloping algebras in the noncommutative differential geometry of quantum groups and in the classification of pointed hopf algebras by the lifting method of andruskiewitsch and schneider in the present paper arithmetic root systems are classified in full generality as a byproduct many new finite dimensional pointed hopf algebras are obtained

the bird s eye view on finite element method for structures with large stochastic variations abstract extensive motivation to do an additional work in the finite element method in stochastic problems femsp is discussed the qualitative comparison of femsp with the state of the art of the deterministic fem is given these observations and thoughts are then realized in several manners we first present the exact inverse femsp which however cannot serve as a general tool for stochastic analysis of complex structures the new variational principles for stochastic beams for the mean response function as well as response s auto correlation function are formulated and the fem based on the variational principles is presented finally a general non perturbative fem for stochastic problems with large variations is developed based on the element level flexibility it is concluded that much work needs to be done in order femsp to be at the level compared to that of the deterministic fem the advantage of the main methods presented here over the conventional ones lies in their non perturbational nature numerical examples are presented

analysis of mean and mean square response of general linear stochastic finite element systems a general finite element based formulation is presented for the analysis of the mean and mean square response of stochastic structural systems whose material properties are described by random fields a flexibility based formulation is followed that does not involve any approximations closed formed integral expressions for the mean and mean square value of the response displacement of statically indeterminate stochastic structures are introduced in this paper these integral expressions involve the spectral density function of a stochastic field modeling the uncertain material properties and two new quantities named the mean response function mrf and the variability response function for the mean square response vrf1 the mrf and the vrf1 have many similarities with the classical variability response function vrf used to estimate the variance of the response displacement the existence of the mrf and the vrf1 depends on a conjecture that is validated numerically using a brute force monte carlo simulation approach a so called finite element method based fast monte carlo simulation procedure fem fmcs is introduced for the accurate and efficient numerical evaluation of the mrf and the vrf1 this methodology is established for the analysis of stochastic beam frame structures as well as for more general stochastic finite element systems i e plane stress and shell problems numerical examples are provided including a statically indeterminate beam a plane stress problem and a shell structure the mrf and vrf1 are used to perform sensitivity parametric analyses with respect to various probabilistic characteristics involved in the problem i e correlation distance standard deviation and to establish realizable upper bounds on the mean value of the response displacement throughout this paper the vrf is computed in parallel to the mrf and the vrf1 it should be noted that although the concept of the vrf has been introduced in an earlier work this is the first time that a flexibility based approach has been used to estimate the vrf for two dimensional problems

clip4 hybrid inductive machine learning algorithm that generates inequality rules the paper describes a hybrid inductive machine learning algorithm called clip4 the algorithm first partitions data into subsets using a tree structure and then generates production rules only from subsets stored at the leaf nodes the unique feature of the algorithm is generation of rules that involve inequalities the algorithm works with the data that have large number of examples and attributes can cope with noisy data and can use numerical nominal continuous and missing value attributes the algorithm s flexibility and efficiency are shown on several well known benchmarking data sets and the results are compared with other machine learning algorithms the benchmarking results in each instance show the clip4 s accuracy cpu time and rule complexity clip4 has built in features like tree pruning methods for partitioning the data for data with large number of examples and attributes and for data containing noise data independent mechanism for dealing with missing values genetic operators to improve accuracy on small data and the discretization schemes clip4 generates model of data that consists of well generalized rules and ranks attributes and selectors that can be used for feature selection

elasto plastic analysis of shells with the triangular element tric tric is a simple but sophisticated three node shear deformable isotropic and composite facet shell element suitable for large scale linear and nonlinear engineering computations of thin and moderately thick anisotropic plate and complex shell structures in the present work an elasto plastic constitutive model based on the von mises yield criterion with isotropic hardening is incorporated into the element the characteristic feature of this formulation is that the nonlinear material behaviour is taken into account entirely in the natural system of the element this is achieved by transforming quantities such as equivalent plastic strain equivalent stress the expression of the yield surface and the components of flow vector from the material coordinate system to the natural coordinate system these transformations lead to simple and elegant expressions for the respective quantities in the natural system which eventually result to an efficient and cost effective treatment of the nonlinear analysis of arbitrary shells including material and geometrical nonlinearities

generalized chiral potts models and minimal cyclic representations of u_q widehat germ g germ l n bf c we present for odd n a construction of the n 1 state generalization of the chiral potts model proposed recently by bazhanov et al the yang baxter equation is proved

tetrahedron equations and the relativistic s matrix of straight strings in 2 1 dimensions the quantums matrix theory of straight strings infinite one dimensional objects like straight domain walls in 2 1 dimensions is considered thes matrix is supposed to be purely elastic and factorized the tetrahedron equations which are the factorization conditions are investigated for the special two colour model the relativistic three strings matrix which apparently satisfies this tetrahedron equation is proposed

effect of multiple uncertain material properties on the response variability of in plane and plate structures abstract in the majority of research works on stochastic finite element analysis the main concern is put on the effect of uncertain elastic modulus on the response variability this is mainly due to the importance of this parameter in the stochastic response of structures but also to the difficulties in introducing other material and or geometrical uncertain parameters in the stochastic formulation in this paper a formulation is suggested in order to determine the response variability of in plane and plate structures with multiple uncertain material parameters i e elastic modulus and poisson s ratio to accomplish this use is made of the general equation for n th joint moment and a polynomial expansion on the coefficients of constitutive matrix for computational purposes the infinite series of stochastic sub stiffness matrices is truncated preserving sufficient accuracy to demonstrate the validity of the proposed formulation some numerical examples are provided and the results are compared with those obtained by means of classical monte carlo simulation combined with the local average scheme

exact bounds for the static response set of structures with uncertain but bounded parameters abstract the numerical estimation of the static displacement bounds of structures with uncertain but bounded parameters is considered in this paper by representing each uncertain but bounded parameter as an interval number or vector a static response analysis problem for the structure can be expressed in the form of a system of linear interval equations in which the coefficient matrix and the right hand side term are respectively the interval matrix and the interval vector in this study we present two new simple mathematical proofs of the vertex solution theorem using cramer s rule for solving linear interval equations different from the other proof methods to find the upper and lower bounds on the set of solutions the first takes advantage of optimization theory while the second is based on interval extension by means of a typical example considered first by hansen it can be seen that the result calculated by the vertex solution theorem is the same as one predicted by the oettli prager criterion examples of a three stepped beam and a 10 bar truss are presented to illustrate the computational aspects of the vertex solution theorem in comparison with the interval perturbation method

tetrahedron equation and generalized quantum groups we construct families of solutions of the yang baxter equation from n products of three dimensional r and l operators satisfying the tetrahedron equation they are identified with the quantum r matrices for the hopf algebras known as generalized quantum groups depending on the number of r s and l s involved in the product the trace construction interpolates the symmetric tensor representations of and the antisymmetric tensor representations of whereas a boundary vector construction interpolates the q oscillator representation of and the spin representation of the intermediate cases are associated with an affinization of quantum superalgebras

an effective discretization method for disposing high dimensional data abstract feature discretization is an extremely important preprocessing task used for classification in data mining and machine learning as many classification methods require that each dimension of the training dataset contains only discrete values most of discretization methods mainly concentrate on discretizing low dimensional data in this paper we focus on discretizing high dimensional data that frequently present the nonlinear structures firstly we present a novel supervised dimension reduction algorithm to map high dimensional data into a low dimensional space which ensures to keep intrinsic correlation structure of the original data this algorithm overcomes the deficiency that the geometric topology of the data is easily distorted when mapping data that present an uneven distribution in high dimensional space to the best of our knowledge this is the first approach to solve high dimensional nonlinear data discretization with a dimension reduction technique secondly we propose a supervised area based chi square discretization algorithm to effectively discretize each continuous dimension in the low dimensional space this algorithm overcomes the deficiency that existing methods do not consider the possibility of being merged for each interval pair from the view of probability finally we conduct the experiments to evaluate the performance of the proposed method the results show that our method achieves higher classification accuracy and yields a more concise knowledge of the data especially for high dimensional datasets than existing discretization methods in addition our discretization method has also been successfully applied to computer vision and image classification

phenomenological invariant based finite element model for geometrically nonlinear analysis of thin shells abstract a kirchhoff love type curved triangular finite element is proposed for geometrically nonlinear analysis of elastic isotropic shells undergoing small strains but large displacements the finite element formulation is based on the expression of the strain energy in terms of invariants of the strain and curvature change tensors of the shell middle surface the element sides are chosen as three independent directions for determining the strains and curvature changes the emphasis is put on improvement of the bending behavior of the element so that the element is able to undergo finite curvature changes recursive relations are obtained for exactly calculating the coefficients of the first and second order variations of the strain energy of the finite element which are necessary to formulate the equilibrium and stability conditions of the discrete model of a shell a shell finite element with 15 degrees of freedom is developed and tested numerical examples are presented to demonstrate the accuracy and mesh convergence of the finite element solutions

laplacian eigenmaps for dimensionality reduction and data representation one of the central problems in machine learning and pattern recognition is to develop appropriate representations for complex data we consider the problem of constructing a representation for data lying on a low dimensional manifold embedded in a high dimensional space drawing on the correspondence between the graph laplacian the laplace beltrami operator on the manifold and the connections to the heat equation we propose a geometrically motivated algorithm for representing the high dimensional data the algorithm provides a computationally efficient approach to nonlinear dimensionality reduction that has locality preserving properties and a natural connection to clustering some potential applications and illustrative examples are discussed

zamolodchikov s tetrahedron equation and hidden structure of quantum groups the tetrahedron equation is a three dimensional generalization of the yang baxter equation its solutions define integrable three dimensional lattice models of statistical mechanics and quantum field theory their integrability is not related to the size of the lattice therefore the same solution of the tetrahedron equation defines different integrable models for different finite periodic cubic lattices obviously any such three dimensional model can be viewed as a two dimensional integrable model on a square lattice where the additional third dimension is treated as an internal degree of freedom therefore every solution of the tetrahedron equation provides an infinite sequence of integrable 2d models differing by the size of this hidden third dimension in this paper we construct a new solution of the tetrahedron equation which provides in this way the two dimensional solvable models related to finite dimensional highest weight representations for all quantum affine algebra where the rank n coincides with the size of the hidden dimension these models are related to an anisotropic deformation of the sl n invariant heisenberg magnets they were extensively studied for a long time but the hidden 3d structure was hitherto unknown our results lead to a remarkable exact rank size duality relation for the nested bethe ansatz solution for these models note also that the above solution of the tetrahedron equation arises in the quantization of the resonant three wave scattering model which is a well known integrable classical system in 2 1 dimensions

stochastic second order perturbation approach to the stress based finite element method abstract the paper is devoted to the application of the second order perturbation second probabilistic moment method to the stress based finite element method fem the approach is introduced for the linear elastic heterogeneous medium up to the second order variational equations of the complementary energy principle are presented together with an additional stochastic finite element discretization based on airy and prandtl stress functions the numerical examples shown in this paper illustrate the probabilistic stress and strain tensors in the cantilever beam under shear loading and torsioned square beam with randomly defined material and geometrical parameters the results obtained in the tests can be applied in probabilistic analyses of the boundary value problems having any closed form mathematical solutions as well as in the stress based stochastic fem analysis of solids and structures

fuzzy modal finite element analysis of structures with imprecise material properties this paper extends the fuzzy set theory to a dynamic finite element analysis of engineering systems which have uncertainties in material properties a general algorithm which resolves the uncertain eigenvalue problem by using a reanalysis approach is considered this algorithm is applied to the study of the modal behaviour of structures presenting uncertain material properties some indexes which determine the more sensitive eigenvalue to several uncertainty sources are also put forward finally a plate structure as numerical path test is analysed the results of such a calculation determine the sensitivity of the modal behaviour to multiple simultaneous material parameters

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

an alternative assumed strain method in this paper an alternative assumed strain aas method is put forward on the basis of a previous work the method has two main features the stresses are eliminated from the finite element form

the r matrix of quantum doubles of nichols algebras of diagonal type let h be the quantum double of a nichols algebra of diagonal type we compute the r matrix of 3 tuples of modules for general finite dimensional highest weight modules over h we also calculate a multiplicative formula for the universal r matrix when h is finite dimensional we show the unicity of a pbw basis or a lusztig type poincare birkhoff witt basis with a given convex order

solving processes for a system of first order fuzzy differential equations abstract in this third paper of a series of reports on fuzzy differential equations we consider the system of first order inhomogeneous fuzzy differential equations d d t x t a t x t f t 1 with x 0 x 0 where d x t t is an n dimensional vector of first same order or reverse order derived functions of an n dimensional vector x t x 1 t x n t t of unknown fuzzy set valued functions that is d dt x t d dt x 1 t d dt x n t t f t is an n dimensional vector f 1 t f n t t of known fuzzy set valued functions a t is an n n matrix of known real functions we introduce the time domain and frequency domain methods for the solutions of the system of first order fuzzy differential equations 1 the solving processes of time domain and frequency domain for the system of first order fuzzy differential equations with constant coefficients and variable coefficients are put forward one example is considered in order to demonstrate the rationality and validity of the methods the work provides an indispensable mathematical tool for setting up the theories of fuzzy stochastic differential equations 7 fuzzy dynamical systems 3 fuzzy random vibration 8 fuzzy stochastic dynamical systems 10 11 14 16 and fuzzy stochastic systems 17 19

exact and approximate solutions and variational principles for stochastic shear beams under deterministic loading probabilistic response of shear beams with stochastic flexibility and subjected to deterministic static loads is studied in this paper the differential equations governing the probabilistic responses as well as the variational principles for the probabilistic responses are formulated apparently for the first time new exact solutions are also derived for specific cases stochastic versions of galerkin and rayleigh ritz method are then applied to obtain approximate solutions when exact solution is unfeasible to derive both the exact and the approximate solutions possess a unique characteristic they are applicable to any value of the coefficient of variation previous investigations were unable to capture this remarkable characteristic

spectral stochastic finite element analysis for laminated composite plates abstract a spectral stochastic finite element formulation with consideration of multi layer effect and spatial variability of material properties is developed for probabilistic analysis of laminated composite plates the material properties of each lamina are modeled as a set of random fields and represented by the karhunen loeve expansion the expansion is incorporated into a spatial discretization in accordance with a standard finite element procedure based on the first order shear deformation theory a spectral expansion with use of polynomial chaos is employed to represent the stochastic nodal displacements in terms of standard normal random variables a preconditioning matrix is then proposed for the solution of spectral stochastic finite element equations with use of a preconditioning conjugate gradient technique the various statistics of interest of the system responses are finally obtained by means of the coefficients of the spectral expansion the numerical accuracy and the computational efficiency of the method are demonstrated by comparison with monte carlo simulation

principal manifolds and nonlinear dimensionality reduction via tangent space alignment we present a new algorithm for manifold learning and nonlinear dimensionality reduction based on a set of unorganized data points sampled with noise from a parameterized manifold the local geometry of the manifold is learned by constructing an approximation for the tangent space at each data point and those tangent spaces are then aligned to give the global coordinates of the data points with respect to the underlying manifold we also present an error analysis of our algorithm showing that reconstruction errors can be quite small in some cases we illustrate our algorithm using curves and surfaces both in two dimensional three dimensional 2d 3d euclidean spaces and in higher dimensional euclidean spaces we also address several theoretical and algorithmic issues for further research and improvements

response variability due to randomness in poisson s ratio for plane strain and plane stress states summary in the ordinary structural materials one of the parameters that can be assumed to have spatial uncertainty is poisson s ratio therefore the independent evaluation of the effects of this parameter on the response variability is of importance the difficulties in obtaining the response variability due to randomness in poisson s ratio lie in the fact that the poisson s ratio enters the stiffness matrix as a non linear parameter in this paper a formulation to determine the response variability in plane strain and plane stress states due to the randomness in the poisson s ratio is given the formulation is accomplished by means of the stochastic decomposition of the constitutive matrix into several sub matrices taking into consideration of the polynomial expansion on the coefficients of constitutive relation to demonstrate the validity of the proposed formulation some example structures are chosen and the results are compared with those obtained by means of monte carlo simulation through the formulation proposed in this study it becomes possible for the weighted integral stochastic finite element analysis to consider all the uncertain material parameters in its application