elastoplastic and contact analysis based on consistent dynamic formulation of co rotational planar elements abstract co rotational formulation is one of the approaches applicable to geometrically nonlinear problems in structural analysis based on the assumptions of small degree of strain and large displacement the cr formulation allows an accurate geometrically nonlinear structural analysis in this paper an improved cr formulation for dynamic nonlinear analysis is developed for the planar element also extension of the local formulation is conducted for an elastoplastic problem a simplified approach for planar elastoplastic analyses is proposed by maintaining the original feature of the cr formulation moreover a modified approach in the local formulation is suggested in order to improve the level of accuracy in the plastic state contact analysis using the lagrange multiplier is then implemented during the present validation procedure of the proposed approaches four different planar elements are employed those elements are investigated with regard to efficiency and accuracy in a general geometrically nonlinear and a geometrically nonlinear elastoplastic problem respectively it is found that the present dynamic formulations gives both accuracy and consistency for all types of the plane element also comparison regarding the choice of the local formulation for the elastoplastic problem is systematically conducted and demonstrated

structural instability analyses based on generalised path following this paper describes how quasi static conservative instability problems can be completely described using generalised path following procedures for augmented equilibrium formulations in particul

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

finite elements with increased freedom in choosing shape functions starting with a mathematical statement of the convergence requirements for an element stiffness matrix the paper discusses displacement shape functions that may be used in connection with the potential energy principle in short these functions must be force orthogonal and energy orthogonal but they need not be conforming satisfy interelement compatibility it is shown that the requirements to the displacement functions may be greatly relaxed through slight modifications of the coupling stiffness between fundamental and higher order displacement modes several alternative formulations are examined in particular a new free formulation is suggested using this form which is very simple the only requirement to the displacement patterns used is that they should contain the fundamental deformation modes and be linearly independent applications of the theory to triangular and rectangular plate bending elements are shown the simple stiffness matrix for the latter is given explicitly the numerical results compare favourably with other types of finite elements

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

an objective 3d large deformation finite element formulation for geometrically exact curved kirchhoff rods the objective of this work is the development of a new finite element formulation for beams according to the kirchhoff theory of thin rods which includes the deformation states of axial tension torsion and bending the proposed formulation accounts for large deformations in three dimensional problem settings consisting of slender prismatic beams with arbitrarily curved initial geometries and arbitrary cross section shapes like in geometrically exact reissner theories the derived deformation measures are geometrically exact in the sense that they are consistent with the strong and weak form of the balance equations and the beam geometry for any configuration and for arbitrarily large translations rotations and strains a novel orthogonal interpolation strategy is applied to the triad field representing the cross section orientation in order to fulfill the kirchhoff constraint of vanishing shear strains in a strong sense and to preserve the objectivity of the spatially discretized problem the continuity requirements resulting from the corresponding weak form are fulfilled by a cubic hermite interpolation thus leading to a c1 continuous representation of the beam centerline fundamental properties such as objectivity path independence consistency and accuracy of the developed beam element are verified by means of suitable numerical examples

universal manifold embedding for geometrically deformed functions assume we have a set of observations for example images of different objects each undergoing a different geometric deformation yet all the deformations belong to the same family as a result of the action of these deformations the set of different observations on each object is generally a manifold in the ambient space of observations in this paper we show that in those cases where the set of deformations admits a finite dimensional representation there is a mapping from the space of observations to a low dimensional linear space the manifold corresponding to each object is mapped to a distinct linear subspace of euclidean space the dimension of the subspace is the same as that of the manifold this mapping which we call universal manifold embedding enables the estimation of geometric deformations using the classical linear theory the universal manifold embedding further enables the representation of the object classification and detection problems in a linear subspace matching framework the embedding of the space of observations depends on the deformation model and is independent of the specific observed object hence it is universal we study two cases of this embedding that of elastic deformations of 1 d signals and the case of affine deformations of n dimensional signals

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

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

numerical analysis of complex instability behaviour using incremental iterative strategies the paper describes how quasi static conservative instability problems can be analysed in a multi parametric space using generalised path following procedures for augmented equilibrium problems

energy conserving algorithms for a corotational formulation standard nonlinear schemes for the the simulation of elastodynamic problems have several shortcomings when considering high speed rotations to tackle these problems we use a corotational framework and a corresponding specific linearization to design new energy conserving numerical schemes in the two dimensional case an algorithm preserving also angular momentum is presented the existence of a solution for the fully discrete setting of this algorithm is established numerical results illustrate the flexibility and efficiency of the proposed algorithms

learning smooth pattern transformation manifolds manifold models provide low dimensional representations that are useful for processing and analyzing data in a transformation invariant way in this paper we study the problem of learning smooth pattern transformation manifolds from image sets that represent observations of geometrically transformed signals to construct a manifold we build a representative pattern whose transformations accurately fit various input images we examine two objectives of the manifold building problem namely approximation and classification for the approximation problem we propose a greedy method that constructs a representative pattern by selecting analytic atoms from a continuous dictionary manifold we present a dc optimization scheme that is applicable to a wide range of transformation and dictionary models and demonstrate its application to the transformation manifolds generated by the rotation translation and anisotropic scaling of a reference pattern then we generalize this approach to a setting with multiple transformation manifolds where each manifold represents a different class of signals we present an iterative multiple manifold building algorithm such that the classification accuracy is promoted in the learning of the representative patterns the experimental results suggest that the proposed methods yield high accuracy in the approximation and classification of data compared with some reference methods while the invariance to geometric transformations is achieved because of the transformation manifold model

a modified corotational framework for triangular shell elements the corotational framework for triangular shell elements has been presented by different authors see the introduction the purpose of this paper is to introduce three modifications in this approach the first one is a simplified definition of the local rotations the second one is a reduction of the number of local degrees of freedom from 18 to 15 the third and principal one concerns the parameterisation of the global finite rotations a new approach based on euler parameters quaternion is proposed in particular it is shown that only three parameters are required the purpose of these three modifications is to obtain a formulation which gives the same numerical results but which is computationally more efficient than the original one this aspect is illustrated in several numerical examples

energy consistent corotational schemes for frictional contact problems in this paper we consider the unilateral frictional contact problem of a hyperelastic body in the case of large displacements and small strains in order to retain the linear elasticity framework we decompose the deformation into a large global rotation and a small elastic displacement this corotational approach is combined with a primal dual active set strategy to tackle the contact problem the resulting algorithm preserves both energy and angular momentum

plastic instability of beam structures using co rotational elements in a previous paper comput methods appl mech engrg 191 2002 1755 the authors have presented a 3d co rotational elastic beam element including warping effects this formulation is now further developed in order to incorporate elasto plastic deformations the element possesses seven degrees of freedom at each node and can be used to model beams with arbitrary cross sections thus within the present approach the centroid and shear center of the cross section are not necessarily coincident the main purpose of this element is to model elasto plastic instability problems in this context two methods of branch switching are tested and discussed in the first one the bifurcation point is isolated by successive bisections and the branch switching is operated by using the eigenvector associated to the negative eigenvalue in the second one introduced by petryk an energy approach is used to select automatically the stable post bifurcation path six examples including large displacement and stability problems are used in order to assess the performances of the element

a fuzzy logic based approach to qualitative modeling this paper discusses a general approach to quali tative modeling based on fuzzy logic the method of qualitative modeling is divided into two parts fuzzy modeling and linguistic approximation it proposes to use a fuzzy clustering method fuzzy c means method to identify the structure of a fuzzy model to clarify the advantages of the proposed method it also shows some examples of modeling among them a model of a dynamical process and a model of a human operator s control action

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

linear estimation of time warped signals we introduce a novel methodology for estimating the time axis deformation between two observations on a time warped signal since the problem of estimating the warping function is nonlinear existing methods iteratively minimize some metric between the observation and a hypothesized deformed template assuming the family of possible deformations the signal may undergo admits a finite dimensional representation we show that there is a nonlinear mapping from the space of observations to a low dimensional linear space such that in this space the problem of estimating the parametric model of the warping function is solved by a linear system of equations we call the family of estimators derived based on this representation linear warping estimators lwe the new representation of the problem enables an analytic analysis of the behavior of the solution in the presence of model mismatches which is prohibitive when iterative methods are employed the ability to achieve this major simplification both in the solution and in analyzing its performance results from the representation of the problem in a new coordinate system which is natural to the properties of the problem instead of representing it in the standard coordinate system imposed by the sampling mechanism the proposed solution is unique and exact as it provides a closed form expression for evaluating each of the parameters of the warping model using only measurements of the amplitude information of the observed and reference signals the solution is applicable to any elastic warping regardless of its magnitude we analyze the behavior of the lwe in the presence of noise and obtain a minimum variance unbiased estimator for the model parameters by finding an optimal set of nonlinear operators for mapping the original problem into a low dimensional linear space

estimation of subspace arrangements with applications in modeling and segmenting mixed data recently many scientific and engineering applications have involved the challenging task of analyzing large amounts of unsorted high dimensional data that have very complicated structures from both geometric and statistical points of view such unsorted data are considered mixed as different parts of the data have significantly different structures which cannot be described by a single model in this paper we propose to use subspace arrangements a union of multiple subspaces for modeling mixed data each subspace in the arrangement is used to model just a homogeneous subset of the data thus multiple subspaces together can capture the heterogeneous structures within the data set in this paper we give a comprehensive introduction to a new approach for the estimation of subspace arrangements this is known as generalized principal component analysis gpca in particular we provide a comprehensive summary of important algebraic properties and statistical facts that are crucial for making the inference of subspace arrangements both efficient and robust even when the given data are corrupted by noise or contaminated with outliers this new method in many ways improves and generalizes extant methods for modeling or clustering mixed data there have been successful applications of this new method to many real world problems in computer vision image processing and system identification in this paper we will examine several of those representative applications this paper is intended to be expository in nature however in order that this may serve as a more complete reference for both theoreticians and practitioners we take the liberty of filling in several gaps between the theory and the practice in the existing literature

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

nonlinear localization strategies for domain decomposition methods application to post buckling analyses abstract in this paper we explore the capabilities of some nonlinear strategies based on domain decomposition for nonlinear analyses and more particularly for post buckling analyses of large slender structures after having recalled the classical newton krylov schur methods chosen here to serve as a reference we propose two versions specifically developed to treat nonlinear phenomena at the most relevant scale through nonlinear localizations per substructure all these different strategies lead to solving similar condensed problems on which we apply classical domain decomposition methods performances are discussed and comparative results in terms of convergence are presented in the case of beam frames with large rotations and local buckling

a co rotational quasi conforming 4 node resultant shell element for large deformation elasto plastic analysis abstract a co rotational quasi conforming formulation of a 4 node stress resultant shell element is presented for non linear analysis of plate and shell structures the tangent stiffness matrix in this quasi conforming formulation is explicitly integrated this makes the element computationally efficient in incremental non linear analysis it includes drilling degrees of freedom which improves membrane behavior and allows the modeling of stiffened plates and shells it is also free of shear locking behavior the formulation of the geometrical stiffness is derived using the full definition of green strain tensor the inclusion of the bending moment and transverse shear resultant forces in the geometric stiffness allows effective analysis of stability problems of moderately thick plates and shells the stresses are accurately taken at the nodal points without extrapolation the plasticity is traced by applying the von mises yield condition and prandtl reuss flow rule to discrete points through the thickness the multi layered approach is based on equally spaced stations including extreme fibers a modified trapezoidal rule is used for the numerical integration of the constitutive relation in the plasticity part numerous tests are carried out for the non linear validation of present 4 node shell element and the results are in good agreement with references

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

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

on the largest principal angle between random subspaces formulas are derived for the probability density function and the probability distribution function of the largest canonical angle between two p dirnensional subspaces of r n chosen from the uniform distribution on the grassmann manifold which is the unique distribution invariant by orthogonal transformations of r n the formulas involve the gamma function and the hypergeometric function of a matrix argument c 2005 elsevier inc all rights reserved

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

asymptotic post buckling fem analysis using corotational formulation finite element asymptotic post buckling analysis being based on fourth order expansions of the strain energy requires that nonlinear structural modeling be accurate to same order at least with respect to the rigid motions of the elements a corotational description is proposed here as a general tool to satisfy this requirement of objectivity by referring each element to a local frame which moves rotates with the element so filtering its rigid motion in this description nonlinearity of the problem derives essentially from the change of reference from the global fixed frame to the local one the strain energy being governed by their relative rotations in finite kinematics this noticeably complicates the algebra for obtaining exact expressions of its variations quite simple basic expressions for the first four corotational derivatives of the strain energy are provided allowing the set up of a fourth order accurate asymptotic analysis starting from standard finite elements based on linear or simplified nonlinear local modelings the formulation is implemented for the analysis of 3d beam assemblages and several numerical results are presented and discussed showing the effectiveness and robustness of the proposed approach in reproducing the nonlinear equilibrium path in both cases of monomodal and coupled multimodal buckling

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

geometrically nonlinear dynamic formulation for three dimensional co rotational solid elements abstract this study presents a three dimensional nonlinear dynamic formulation based on a co rotational cr approach for solid elements the cr formulation is relatively efficient but it is based on the assumption of small strains during large displacement the novel idea of the present formulation involves the use of the cr formulation through a three dimensional solid element for inertial quantities in addition to an internal force vector and a stiffness matrix the present dynamic formulation is derived from lagrange s equation of motion in this procedure the cr formulation i e element independent cr is one of the most attractive features that is strongly manifested in an efficient manner consequently this obtains the governing equation of motion including motion driven inertial components physical quantities induced by the prescribed motion four examples are presented to demonstrate the accuracy of the present dynamic formulation finally the results are compared with those obtained by abaqus and the findings reveal that the proposed dynamic formulation is in good agreement with existing predictions

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

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

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

geometry and radiometry invariant matched manifold detection consider a set of deformable objects undergoing geometric and radiometric transformations as a result of the action of these transformations the set of different realizations of each object is generally a manifold in the space of observations assuming the geometric deformations an object undergoes belong to some finite dimensional family it has been shown that the universal manifold embedding ume provides a set of nonlinear operators that universally maps each of the different manifolds where each manifold is generated by the set all of possible appearances of a single object into a distinct linear subspace of an euclidean space in this paper we generalize this framework to the case where the observed object undergoes both an affine geometric transformation and a monotonic radiometric transformation and present a novel framework for the detection and recognition of the deformable objects applying to each of the observations an operator that makes it invariant to monotonic amplitude transformations but is geometry covariant with the affine transformation the set of all possible observations on that object is mapped by the ume into a single linear subspace invariant with respect to both the geometric and radiometric transformations the embedding of the space of observations is independent of the specific observed object hence it is universal the invariant representation of the object is the basis of a matched manifold detection and tracking framework of objects that undergo complex geometric and radiometric deformations the observed surface is tessellated into a set of tiles such that the deformation of each one is well approximated by an affine geometric transformation and a monotonic transformation of the measured intensities since each tile is mapped by the radiometry invariant ume to a distinct linear subspace the detection and tracking problems are solved by evaluating distances between linear subspaces classification in this context becomes a problem of determining which labeled subspace in a grassmannian is closest to a subspace in the same grassmannian where the latter has been generated by radiometry invariant ume from an unlabeled observation

a co evolving framework for robust particle swarm optimization particle swarm optimization pso as an efficient and powerful problem solving strategy has been widely used but appropriate adjustment of its parameters usually requires a lot of time and labor so a co evolving framework is proposed to improve the robustness of the pso in this paper within this framework the fuzzy rules for the manipulation of the inertia weights are co evolved with the particles and the simulation results on a suite of test functions show that the use of this co evolving framework improves the performance of the pso especially the robustness against the dimensional variation of the test functions

dynamic context cooperative quantum behaved particle swarm optimization based on multilevel thresholding applied to medical image segmentation this paper proposes a dynamic context cooperative quantum behaved particle swarm optimization algorithm the proposed algorithm incorporates a new method for dynamically updating the context vector each time it completes a cooperation operation with other particles we first explain how this leads to enhanced search ability and improved optimization over previous methods and demonstrate this empirically with comparative experiments using benchmark test functions we then demonstrate a practical application of the proposed method by showing how it can be applied to optimize the parameters for otsu image segmentation for processing medical images comparative experimental results show that the proposed method outperforms other state of the art methods from the literature

comparison of two linearization schemes for the nonlinear bending problem of a beam pinned at both ends the nonlinear bending problem of a constant cross section simply supported beam pinned at both ends and subject to a uniformly distributed load q x is analyzed in detail the numerical integration of the two point boundary value problem bvp derived for the nonlinear timoshenko beam is tackled through two different linearization schemes the multi step transversal linearization mtrl and the multi step tangential linearization mtnl proposed by viswanath and roy 2007 the fundamentals of these linearization techniques are to replace the nonlinear part of the governing odes through a set of conditionally linearized ode systems at the nodal grid points along the neutral axis ensuring the intersection between the solution manifolds transversally in the mtrl and tangentially in the mtnl in this paper the solution values are determined at grid points by means of a centered finite differences method with multipoint linear constraints keller 1969 and a simple iterative strategy the analytical solution for this kind of bending problem including the extensional effects can be worked out by integration of the governing two point bvp equations monleon et al 2008 finally the comparison of analytical and numerical results shows the better ability of mtnl with the proposed iterative strategy to reproduce the theoretical behavior of the beam for each load step because the restraint of equating derivatives in mtnl leads to further closeness between solution paths of the governing odes and the linearized ones in comparison with mtrl this result is opposed to the conclusion reached in viswanath and roy 2007 where the relative errors produced by mtrl are said to be smaller than the mtnl ones for the simply supported beam and the tip loaded cantilever beam problems

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

an orthogonal array based particle swarm optimizer with nonlinear time varying evolution particle swarm optimization pso is a population based heuristic optimization technique it has been developed to be a prominent evolution algorithm due to its simplicity of implementation and ability to quickly converge to a reasonable solution however it has also been reported that the algorithm has a tendency to get stuck in a near optimal solution in multi dimensional spaces to overcome the stagnation in searching a globally optimal solution a pso method with nonlinear time varying evolution pso ntve is proposed to approach the optimal solution closely when determining the parameters in the proposed method matrix experiments with an orthogonal array are utilized in which a minimal number of experiments would have an effect that approximates the full factorial experiments to demonstrate the performance of the proposed pso ntve method five well known benchmarks are used for illustration the results will show the feasibility and validity of the proposed method and its superiority over several previous pso algorithms

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

bounds on packings of spheres in the grassmann manifold we derive the gilbert varshamov and hamming bounds for packings of spheres codes in the grassmann manifolds over r and c asymptotic expressions are obtained for the geodesic metric and projection frobenius chordal metric on the manifold

matched subspace detectors we formulate a general class of problems for detecting subspace signals in subspace interference and broadband noise we derive the generalized likelihood ratio glr for each problem in the class we then establish the invariances for the glr and argue that these are the natural invariances for the problem in each case the glr is a maximal invariant statistic and the distribution of the maximal invariant statistic is monotone this means that the glr test glrt is the uniformly most powerful invariant detector we illustrate the utility of this finding by solving a number of problems for detecting subspace signals in subspace interference and broadband noise in each case we give the distribution for the detector and compute performance curves

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

partitioned formulation of internal and gravity waves interacting with flexible structures abstract this paper presents a partitioned modeling of internal and gravity fluid waves that interact with flexible structures the governing interaction model consists of three completely partitioned entities fluid model structural model and interface model that acts as an internal constraint on the fluid structure interface boundary thus the proposed partitioned multi physics modeling can employ two completely modular fluid and structure software modules plus an interface solver hence amenable to partitioned solution algorithms the interface discretization can exploit the nonmatching interface algorithm previously developed via the method of localized lagrange multipliers also noted is that the present fluid model can make use of widely available finite element software for standard poisson type problems

modified quantum behaved particle swarm optimization for parameters estimation of generalized nonlinear multi regressions model based on choquet integral with outliers in this paper a generalized nonlinear multi regression model based on choquet integral nmrci is proposed and applied for estimation of non additive systems that include outliers under inherent interaction among inputs the parameters estimation for the proposed model is also performed via a modified algorithm based on particle swarm optimization with quantum behavior qpso named mqpso from the proposed model the high breakdown regression estimator a least trimmed squares lts is applied to eliminate the influence caused by these observations that contain outliers besides elitist crossover of genetic algorithm ga and adaptive decay of simulated annealing sa are used for conquering premature and controlling search policy respectively hence the proposed mqpso algorithm which combines the mechanisms of ga sa and lts within the qpso algorithm can deal with the proposed model with outliers from simulation results the proposed mqpso readily corrects the deviation caused by outliers without losing precisions and swiftly achieves convergences on estimating the parameters of the proposed generalized nmrci model for the non additive systems with outliers

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

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

a mixed tetrahedral element with nodal rotations for large displacement analysis of inelastic structures summary a novel mixed four node tetrahedral finite element equipped with nodal rotational degrees of freedom is presented its formulation is based on a hu washizu type functional suitable to the treatment of material nonlinearities rotation and skew symmetric stress fields are assumed as independent variables the latter entering the functional to impose rotational compatibility and suppress spurious modes exploiting the choice of equal interpolation for strain and symmetric stress fields a robust element state determination procedure requiring no element level iteration is proposed the mixed element stability is assessed by means of an original and effective numerical test the extension of the present formulation to geometric nonlinear problems is achieved through a polar decomposition based corotational framework after validation in both material and geometric nonlinear context the element performances are investigated in demanding simulations involving complex shape memory alloy structures supported by the comparison with available linear and quadratic tetrahedrons and hexahedrons the numerical results prove accuracy robustness and effectiveness of the proposed formulation copyright 2016 john wiley sons ltd

on best fit corotated frames for 3d continuum finite elements summary we discuss a strategy to construct corotated frames for three dimensional continuum finite elements by minimizing deformations within the frame we find that irrespective of the type of element and the number of nodes using a quaternion parametrization of rotations this minimization is naturally stated as computing the smallest eigenvalue of a 4 4 matrix the simplicity of this smallest eigenvalue plays a crucial role when linearizing the kinematics ensuant quaternion algebra although lengthy results in remarkably simple formulas for projections that arise in the linearized kinematics the exact stiffness matrix does not require computation of the second derivative of the rotation function and is also given by a simple formula as a result the implementation of this corotational formulation becomes particularly straightforward furthermore in contrast to other results in the literature the stiffness matrix for elements with translational dofs is symmetric for illustration this corotational formulation is applied to a solid shell finite element and numerical results are presented copyright 2014 john wiley sons ltd received 25 april 2013 revised 15 october 2013 accepted 10 december 2013

decoupled linear estimation of affine geometric deformations and nonlinear intensity transformations of images we consider the problem of registering two observations on an arbitrary object where the two are related by a geometric affine transformation of their coordinate systems and by a nonlinear mapping of their intensities more generally the framework is that of jointly estimating the geometric and radiometric deformations relating two observations on the same object we show that the original high dimensional nonlinear and nonconvex search problem of simultaneously recovering the geometric and radiometric deformations can be represented by an equivalent sequence of two linear systems a solution of this sequence yields an exact explicit and efficient solution to the joint estimation problem

an excursion into large rotations the present discourse develops an enlarged exploration of the matrix formulation of finite rotations in space initiated in 1 it is shown how a consistent but subtle matrix calculus inevitably leads to a number of elegant expressions for the transformation or rotation matrix t appertaining to a rotation about an arbitrary axis also analysed is the case of multiple rotations about fixed or follower axes particular attention is paid to an explicit derivation of a single compound rotation vector equivalent to two consecutive arbitrary rotations this theme is discussed in some detail for a number of cases semitangential rotations for which commutativity holds first proposed in 2 3 are also considered furthermore an elementary geometrical analysis of large rotations is also given finally we deduce in an appendix using a judicious reformulation of quarternions the compound pseudovector representing the combined effect of n rotations in the author s opinion the present approach appears preferable to a pure vectorial scheme and even more so to an indicial formulation and is computationally more convenient

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

aeroelastic design optimization for laminar and turbulent flows abstract the design of flexible structures undergoing aeroelastic deformations is a challenging task in particular if the prediction of the fluid loads and the evaluation of the aerodynamic performance criteria require accounting for laminar and turbulent effects this paper presents a general optimization methodology for fluid structure interaction problems based on turbulent flow models the structure is modeled via a geometrically nonlinear finite element method the flow field is computed by solving a finite volume approximation of the navier stokes equations on moving grids augmented by turbulence models the global design sensitivity equations are presented and solution methods for computing the numerically consistent and approximated design sensitivities are introduced the accuracy of the sensitivity analysis methods are studied by numerical examples for three dimensional problems the potential of the overall optimization methodology is illustrated by the shape and thickness optimization of a realistic wing the numerical examples suggest that the derivatives of the turbulence variables can be neglected in the sensitivity analysis without noticeable errors comparing the optimization results for euler and navier stokes flow models shows the importance of accounting for viscous laminar and turbulent effects for fine tuning the design and obtaining reliable optimization results

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

meshfree co rotational formulation for two dimensional continua in this paper a meshfree co rotational formulation for two dimensional continua is proposed in a co rotational formulation the motion of a body is separated into rigid motion and strain producing deformation traditionally this has been done in the setting of finite elements for beams and shell type elements in the present work every node in a meshfree discretized domain has its own co rotating coordinate system three key ingredients are established in order to apply the co rotational formulation i the relationship between global and local variables ii the angle of rotation of a typical co rotating coordinate system and iii a variationally consistent tangent stiffness matrix an algorithm for the co rotational formulation based on load control is provided maximum entropy basis functions are used to discretize the domain and stabilized nodal integration is implemented to construct the global system of equations numerical examples are presented to demonstrate the validity of the meshfree co rotational formulation copyright 2009 john wiley sons ltd

a genetic algorithm approach to find the best regression econometric model among the candidates although statistical modeling is a common task in different fields of science it is still difficult to estimate the best model that can accurately describe inherent characteristics of a system for which historical or experimental data are available since we may classify estimating techniques as optimizations we can model this problem as an optimization problem and solve it by a new heuristic algorithm like neural networks genetic algorithms and tabu search or by classic ones such as regression and econometric models in this paper we propose a new type of genetic algorithm to find the best regression model among all suggested and evaluate its performances by an economical case study

the construction of free free flexibility matrices for multilevel structural analysis abstract this article considers a generalization of the classical structural flexibility matrix it expands on previous papers by taking a deeper look at computational considerations at the substructure level direct or indirect computation of flexibilities as influence coefficients has traditionally required pre removal of rigid body modes by imposing appropriate support conditions mimicking experimental arrangements with the method presented here the flexibility of an individual element or substructure is directly obtained as a particular generalized inverse of the free free stiffness matrix this generalized inverse preserves the stiffness spectrum the definition is element independent and only involves access to the stiffness generated by a standard finite element program and the separate construction of an orthonormal rigid body mode basis the free free flexibility has proven useful in special application areas of finite element structural analysis notably massively parallel processing model reduction and damage localization it can be computed by solving sets of linear equations and does not require processing an eigenproblem or performing a singular value decomposition if substructures contain thousands of d o f exploitation of the stiffness sparseness is important for that case this paper presents a computation procedure based on an exact penalty method and a projected rank regularized inverse stiffness with diagonal entries inserted by the sparse factorization process these entries can be physically interpreted as penalty springs this procedure takes advantage of the stiffness sparseness while forming the full free free flexibility or a boundary subset and is backed by an in depth null space analysis for robustness

a study of optimal membrane triangles with drilling freedoms abstract this article compares derivation methods for constructing optimal membrane triangles with corner drilling freedoms the term optimal is used in the sense of exact inplane pure bending response of rectangular mesh units of arbitrary aspect ratio following a comparative summary of element formulation approaches the construction of an optimal three node triangle using the andes formulation is presented the construction is based upon techniques developed by 1991 in student term projects but taking advantage of the more general framework of templates developed since the optimal element that fits the andes template is shown to be unique if energy orthogonality constraints are enforced two other formulations are examined and compared with the optimal model retrofitting the conventional linear strain triangle element by midpoint migrating and congruential transformations is shown unable to produce an optimal element while rank deficiency is inevitable use of the quadratic strain field of the 1988 allman triangle or linear filtered versions thereof is also unable to reproduce the optimal element moreover these elements exhibit serious aspect ratio lock these predictions are verified on benchmark examples

a simplified co rotational method for quadrilateral shell elements in geometrically nonlinear analysis summary this paper presents a simplified co rotational formulation for quadrilateral shell elements inheriting the merit of element independence from the traditional co rotational approach in literature with the objective of application to nonlinear analysis of civil engineering structures the authors further simply the formulation of the geometrical stiffness using the small strain assumption which is valid in the co rotational approach with the warping effects considered as eccentricities compared with the traditional element independent co rotational method the projector is neglected both in the tangent stiffness matrix and the internal force vector for simplicity in formulation meanwhile a quadrilateral flat shell element allowing for drilling rotations is adopted and incorporated into this simplified co rotational algorithm for geometrically nonlinear analysis involved with large displacements and large rotations several benchmark problems are presented to confirm the efficiency and accuracy of the proposed method for practical applications

partitioned analysis of flexible multibody systems using filtered linear finite element deformational modes summary this work presents a partitioned finite element formulation for flexible multibody systems based on the floating frame ff approach under the assumption of small deformations but arbitrarily large rotations of the bodies in classical ff of reference methods deformational modes are normally computed by modal analysis in this approach free floating modes are eliminated from the linear model using projection techniques and substituted by a complete set of non linear finite rotations in this way all deformational modes are retained and no modal selection is needed the main difference between this work and a classical ff of reference formulation is an algebraic separation of pure deformational modes from rigid body motions the proposed methodology presents the following advantages first the position and orientation of the ff has no restriction and can be freely located in the body with identical results second the formulation uses only the linear finite element matrices of a classical vibration problem hence they can be easily obtained from linear fem packages third no selection of modes is needed all deformational modes are retained through the filtering process and finally thanks to the use of localized lagrangian multipliers llm a partitioned system is obtained that can be solved iteratively and in a distributed manner by available scalable solvers copyright 2014 john wiley sons ltd

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

component mode synthesis with constant mass and stiffness matrices applied to flexible multibody systems in flexible multibody systems component mode synthesis is used to reduce the size of system matrices of the single bodies from millions to a few hundred while maintaining the full coupling between body deformation and overall rigid body motion the combination of clamped eigenmodes and static deformation modes results in a dense and non diagonal structure of the system matrices which is computationally costly in the present paper the conventional concept of the floating frame of reference is transformed to a description based on absolute coordinates and a corotational linearization of the deformation the constant mass matrix and the corotated stiffness matrix need to be factorized only once for the whole simulation in a planar example component mode synthesis is applied to this absolute coordinate formulation by using twice as many deformation modes as usual while the solution of the overall system becomes less expensive due to efficient factorization the size of the system matrices needs to be increased considerably for each axis of rotation however the computational complexity for the factorization reduces from cubic to quadratic numerical examples are presented in order to demonstrate the difference between standard procedures and the methodology now proposed copyright 2007 john wiley sons ltd

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

a large rotation finite element analysis of 3d beams by incremental rotation vector and exact strain measure with all the desirable features abstract different strategies based on rotation vector and exact strain measure have been proposed over the years for analyzing flexible bodies undergoing arbitrary large rotations to avoid the singularity of the vector like parametrization the interpolation of the incremental rotation vector is the most popular approach in this context even if this leads to path dependence and numerical instability i e error accumulation it is also non objective although both objectivity and path independence are recovered with h and p refinement corotational approaches do not have these drawbacks even though the geometrically exact model is achieved by mesh refinement in this work we develop a novel strategy which uses the incremental nodal rotation vectors to define corotational nodal rotations which are then interpolated for the evaluation of the nonlinear strains this choice makes the approach singularity free allows for additive updates within each increment and preserves all the features of the theoretical problem for any mesh and interpolation rotational variables objectivity exact strain measure path independence and symmetric stiffness matrix for conservative loads this last property is a consequence of the direct differentiation of the relation between local and global rotations whose compact form also makes a simple and general definition of the internal forces and the tangent stiffness for any order of interpolation possible in addition we show how the common approach of interpolating incremental vectors can be made stable by a simple updating procedure based on local rotations carried out at the end of each increment in order to avoid cumulative errors geometrically exact 3d beams are considered as a demonstrative example an iterative strategy based on mixed integration points is used to solve the nonlinear discrete equations efficiently

variational formulation in the geometrically nonlinear thin elastic shell theory abstract the variational formulation for thin elastic shells undergoing large deflections is discussed no restrictions are imposed on the magnitude of the rotational part of the deformation gradient yet it is assumed that the strains remain small everywhere in the shell ten functional and associated variational principles are derived including the hu washizu the hellinger reissner the generalized complementary energy and the stationary potential energy principles the total lagrangian description tld is exclusively used