efficient accurate reanalysis for structural optimization the combined approximations method developed recently is an efficient reanalysis method providing high quality results through the use of this approach the computed terms of a series expansion are used as basis vectors in a reduced basis expression by solving a reduced system of equations first and second order approximations were demonstrated in previous studies for small structures the efficiency and the accuracy of the method are improved and results are illustrated for larger structures by the utilization of a gram schmidt orthogonalization procedure new set of basis vectors is generated and normalized such that the reduced system of equations becomes uncoupled the advantage in using the latter vectors is that all expressions for evaluating the displacements are explicit functions of the design variables consequently additional vectors can be considered without modifying the calculations that have already been carried out in addition the uncoupled system is more well conditioned some considerations related to the efficiency of the solution process and the accuracy of the results are discussed and the effect of various parameters on the accuracy is studied numerical results are demonstrated for several medium and large scale structures it is shown that accurate and efficient approximations are achieved for very large changes in the design

simulation of a free boundary problem using boundary element method and restarted re analysis technique in this work we deal with the numerical approximation of a free boundary problem reformulated as an optimal shape design one the boundary element method is used for the approximation of this problem the iterative method used to solve the discrete problem requires the resolution of intermediate linear systems associated with the successive modification in the design process in many cases one of the main obstacles is the high computational cost involved in the solution of large scale problems to reduce the computational cost a restarted re analysis technique is introduced to solve these systems numerical examples including comparison results are presented to show the efficiency of the proposed approach

joint uncertainty propagation in linear structural dynamics using stochastic reduced basis methods uncertainties in the properties of joints produce uncertainties in the dynamic response of built up structures line joints such as glued or continuously welded joints have spatially distributed uncertainty and can be modeled by a discretized random field techniques such as monte carlo simulation can be applied to estimate the output statistics but computational cost can be prohibitive this paper addresses how uncertainties in joints might be included straightforwardly in a finite element model with particular reference to approaches based on fixed interface craig bampton component mode synthesis and a stochastic reduced basis method with two variants these methods are used to determine the output statistics of a structure unlike perturbation based methods good accuracy can be achieved even when the coefficients of variation of the input random variables are not small undamped as well as proportionally damped components are considered efficient implementations are proposed based on an exact matrix identity that leads to a significantly lower computational cost if the number of joint degrees of freedom is sufficiently small compared with the structure s overall number of degrees of freedom a numerical example is presented the proposed formulation is an efficient and effective implementation of a stochastic reduced basis projection scheme it is seen that the method can be up to orders of magnitude faster than direct monte carlo simulation while providing results of comparable accuracy furthermore the proposed implementation is more efficient when fewer joints are affected by uncertainty

convergence and stability analyses for some vector extrapolation methods on the presence of defective iteration matrices abstract in two previous papers 10 11 convergence and stability results for the following vector extrapolation methods were presented minimal polynomial extrapolation reduced rank extrapolation modified minimal polynomial extrapolation and topological epsilon algorithm the analyses were carried out for vector sequences that include those arising from iterative methods for linear systems of equations having diagonalizable iteration matrices in this paper the analyses of 10 11 are extended to vector sequences that include those arising from iterative methods for linear systems having defective iteration matrices the results are illustrated with numerical examples the analyses above naturally suggest some old and some new extensions of the well known power method enabling one to obtain estimates for several dominant eigenvalues of a general matrix

qualitative decision theory from savage s axioms to nonmonotonic reasoning this paper investigates to what extent a purely symbolic approach to decision making under uncertainty is possible in the scope of artificial intelligence contrary to classical approaches to decision theory we try to rank acts without resorting to any numerical representation of utility or uncertainty and without using any scale on which both uncertainty and preference could be mapped our approach is a variant of savage s where the setting is finite and the strict preference on acts is a partial order it is shown that although many axioms of savage theory are preserved and despite the intuitive appeal of the ordinal method for constructing a preference over acts the approach is inconsistent with a probabilistic representation of uncertainty the latter leads to the kind of paradoxes encountered in the theory of voting it is shown that the assumption of ordinal invariance enforces a qualitative decision procedure that presupposes a comparative possibility representation of uncertainty originally due to lewis and usual in nonmonotonic reasoning our axiomatic investigation thus provides decision theoretic foundations to the preferential inference of lehmann and colleagues however the obtained decision rules are sometimes either not very decisive or may lead to overconfident decisions although their basic principles look sound this paper points out some limitations of purely ordinal approaches to savage like decision making under uncertainty in perfect analogy with similar difficulties in voting theory

vector sequence transformations methodology and applications to linear systems in this paper a methodology for the construction of various vector sequence transformations is formulated leading to a unified presentation of the subject and to new results the connections to the general interpolation problem and to projections are discussed various particular cases are examined in more details applications to the solution of systems of linear equations will end the paper and in particular their relation with lanczos method will be studied some numerical examples will be given

fast meshless reanalysis using combined approximations preconditioned conjugate gradient and taylor series multiple design iterations often require repeated stress analyses to be performed as the design is modified slightly a method is presented that combines the meshless stress analysis method with a reanalysis technique to avoid repeating the time consuming steps of remeshing and solving for small design changes an iterative reanalysis method based on the preconditioned conjugate gradient method is introduced and compared to the linear taylor series simple iteration and combined approximations reanalysis methods the asymptotic running time is presented for each reanalysis method and accuracy is compared for two example problems a cantilever beam and a hole in plate results show the taylor series to have the fastest run time followed in order by simple iteration preconditioned conjugate gradient and combined approximations for the two example problems accuracy of the simple iteration method is poor for design changes greater than 5 taylor series accuracy depends greatly on the choice of the design variable the example problem and the method for computing the sensitivity the combined approximations and preconditioned conjugate gradient methods both demonstrate less than 10 error up to a 100 change in height for the cantilever beam and 30 change in radius for the hole in plate example

exact and accurate solutions in the approximate reanalysis of structures combined approximations ca is an efe cient method for reanalysis of structures where binomial series terms are used as basis vectors in reduced basis approximations in previous studies high quality approximations have been achieved for large changes in the design but the reasons for the high accuracy were not fully understood in this work some typical cases where exact and accurate solutions are achieved by the method are presented and discussed exact solutions are obtained when a basis vector is a linear combination of the previous vectors such solutions are obtained also for low rank modie cations to structures or scaling of the initial stiffness matrix in general the ca method provides approximate solutions but the results presented explain the high accuracy achieved with only a small number of basis vectors accurate solutions are achieved in many cases where the basis vectors come close to being linearly dependent such solutions are achieved also for changes in a small number of elements or when the angle between the two vectors representing the initial design and modie ed design is small numerical examples of various changes in cross sections of elements and in the layout of the structure show that accurate results are achieved even in cases where the series of basis vectors diverges i introduction m ultiplerepeatedanalysesareneeded invariousdesign and optimization problems in general the structural response cannot be expressed explicitly in terms of the structure properties and structural analysis involves the solution of a set ofsimultaneous equations reanalysis methods are intended to efe ciently analyze structures modie ed due to changes in the design approximate reanalysis methods have been used extensively in structural optimization to reduce the number of exact analyses and the overall computational cost during the solution process the combined approximations ca method developed recently is considered in this paper the method combines several concepts and methods such as reduced basis series approximations matrix factorization and gram schmidt orthonormalization these and other methods are used to achieve effective solution procedures the effectivenessofthemethodinvariousoptimizationproblemshasbeen demonstrated in previous studies 1i5 initially the ca method was used only for linear reanalysis models recently the method has been used successfully also in eigenvalue 6 and nonlinear analysis 7 problems applications of the method in a large variety ofproblems are discussed elsewhere 8i11 high quality approximations of the structural response for large changes in the design have been achieved in previous studies but the reasons for the high accuracy were not fully understood in this paper some typical cases where exact and accurate solutions are achieved by the camethod are presented anddiscussed in general the ca method provides exact solutions but the results presented in the paper explain the high accuracy achieved with only a small number of basis vectors the solution procedure isbriee y described in sec ii three typical cases where exact solutions are achieved by the ca method are introduced and discussed in sec iii exact solutions are obtained when a basis vector is a linear combination of the previous vectors such solutions are obtained also for lowrank modie cations to structures or scaling of the initial stiffness matrix various cases of accurate solutions are discussed in sec iv convergence properties of the series of basis vectors and the series of the ca terms are presented and criteria intended to evaluate

stochastic reduced basis methods stochastic reduced basis methods for solving large scale linear random algebraic systems of equations such as those obtained by discretizing linear stochastic partial differential equations in space time and the random dimension are introduced the fundamental idea employed is to represent the system response using a linear combination of stochastic basis vectors with undetermined deterministic coefficients or random functions we present a theoretical justification for employing basis vectors spanning the preconditioned stochastic krylov subspace to approximate the response process subsequently variants of the bubnov galerkin scheme are employed to compute the undetermined coefficients which allow explicit expressions for the response quantities to be derived we also examine some theoretical properties of the projection scheme and procedures for computing the response statistics numerical studies are presented for static and dynamic analysis of stochastic structural systems we demonstrate that significant improvements over the neumann expansion scheme as well as other relevant techniques in the literature can be achieved

acceleration of convergence of vector sequences a general approach to the construction of convergence acceleration methods for vector sequences is proposed using this approach one can generate some known methods such as the minimal polynomial extrapolation the reduced rank extrapolation and the topological epsilon algorithm and also some new ones some of the new methods are easier to implement than the known methods and are observed to have similar numerical properties the convergence analysis of these new methods is carried out and it is shown that they are especially suitable for accelerating the convergence of vector sequences that are obtained when one solves linear systems of equations iteratively a stability analysis is also given and numerical examples are provided the convergence and stability properties of the topological epsilon algorithm are likewise given

lexicographic probabilities and choice under uncertainty conventional bayesian theory of choice under uncertainty subjective expected utility theory fails to satisfy the properties of admissibility and existence of well defined conditional probabilities weakly dominated acts may be chosen and the usual definition of conditional probabilities applies only to nonnull events this paper develops a non archimedean variant of subjective expected utility where decisionmakers have lexicographic beliefs this generalization can be made to satisfy admissibility and yield well defined conditional probabilities and at the same time allow for null events copyright 1991 by the econometric society

research note a representation theorem for minmax regret policies decision making under uncertainty is one of the central tasks of artificial agents due to their simplicity and ease of specification qualitative decision tools are popular in artificial intelligence brafman and tennenholtz r i brafman m tennenholtz an axiomatic treatment of three qualitative decision criteria j acm 47 3 2000 452 482 model an agent s uncertain knowledge as her local state which consists of states of the world that she deems possible a policy determines for each local state a total preorder of the set of actions which represents the agent s preference over these actions it is known that a policy is maximin representable if and only if it is closed under unions and satisfies a certain acyclicity condition in this paper we show that the above conditions although necessary are insufficient for minmax regret and competitive ratio policies a complete characterization of these policies is obtained by introducing the best equally strictness

topology optimization with mixed finite elements on regular grids abstract recently new families of mixed finite elements have been proposed to address the analysis of linear elastic bodies on regular grids adopting a limited number of degrees of freedom per element a two dimensional mixed discretization is implemented to formulate an alternative topology optimization problem where stresses play the role of main variables and both compressible and incompressible materials can be dealt with the structural compliance is computed through the evaluation of the complementary energy whereas the enforcement of stress constraints is straightforward numerical simulations investigate the features of the proposed approach comparisons with a conventional displacement based scheme are provided for compressible materials stress constrained solutions for structures made of incompressible media are introduced

vector extrapolation methods with applications to solution of large systems of equations and to pagerank computations an important problem that arises in different areas of science and engineering is that of computing the limits of sequences of vectors x n where x n c n with n very large such sequences arise for example in the solution of systems of linear or nonlinear equations by fixed point iterative methods and lim n x n are simply the required solutions in most cases of interest however these sequences converge to their limits extremely slowly one practical way to make the sequences x n converge more quickly is to apply to them vector extrapolation methods in this work we review two polynomial type vector extrapolation methods that have proved to be very efficient convergence accelerators namely the minimal polynomial extrapolation mpe and the reduced rank extrapolation rre we discuss the derivation of these methods describe the most accurate and stable algorithms for their implementation along with the effective modes of usage in solving systems of equations nonlinear as well as linear and present their convergence and stability theory we also discuss their close connection with the method of arnoldi and with gmres two well known krylov subspace methods for linear systems we show that they can be used very effectively to obtain the dominant eigenvectors of large sparse matrices when the corresponding eigenvalues are known and provide the relevant theory as well one such problem is that of computing the pagerank of the google matrix which we discuss in detail in addition we show that a recent extrapolation method of kamvar et al that was proposed for computing the pagerank is very closely related to mpe we present a generalization of the method of kamvar et al along with a very economical algorithm for this generalization we also provide the missing convergence theory for it

efficient finite difference design sensitivities the problem considered in this study is to evaluate efficiently displacement derivatives using global finite differences given the displacements for an initial design the displacements for various modified designs are evaluated by the recently developed combined approximations method calculations of finite difference sensitivity coefficients are demonstrated for static problems and eigenproblems the presented solution procedure is easy to implement efficient and can be used to calculate derivatives for various designs where the exact displacements are not known some numerical examples show that the accuracy of the results is similar to the accuracy obtained by finite difference calculations based on exact analysis

the implementation of a vector valued rational approximate method in structural reanalysis problems an efficient implementation of a vector valued rational approximation in structural reanalysis problems is presented the implementation is based on combining the power series expansion with a rational approximation the main objectives are 1 to preserve the ease of implementation of the local approximation and 2 to improve significantly the quality of the results such that the method can be used in problems with very large changes in the design variables including geometrical changes and elimination of members the method is suitable for different types of structures such as trusses frames grillages etc the computational cost is significantly reduced numerical examples have shown that excellent results can be achieved for very large changes in cross sections and in structural geometry

new approximation method for stress constraints in structural synthesis a new approximation method for dealing with stress constraints in structural synthesis is presented in previous methods it has been common to create an approximation of the actual constraints with respect to the design variables and then use this with optimization to produce a new candidate design in the present method the finite element nodal forces are instead approximated and these are used to create an explicit but often nonlinear approximation to the original problem the principal motivation is to create the best approximation possible in order to reduce the number of detailed finite element analyses needed to reach the optimum the method is shown to be quite simple while providing significant efficiency gains in the overall optimization task also the method produces such high quality approximations to the original problem that the need for move limits during the approximate optimization stage is greatly reduced examples are offered and compared with published results to demonstrate the efficiency and reliability of the proposed method it is concluded that there are considerable gains yet to be achieved through continued careful investigation of approximation techniques

the method of moving asymptotes a new method for structural optimization a new method for non linear programming in general and structural optimization in particular is presented in each step of the iterative process a strictly convex approximating subproblem is generated and solved the generation of these subproblems is controlled by so called moving asymptotes which may both stabilize and speed up the convergence of the general process

updating inverses in matrix analysis of structures we deal with the problem of updating inverses several methods which allow calculating the inverse of a matrix when one or several rows columns are changed or one or several rows and the same number of columns are added or removed are given they are based on a method for calculating inverses given by jubete and castillo which uses the concept of orthogonal sets and lead to a considerable saving in computational power the methods are ideal for being used in the design process of structures where stiffness matrices are sequentially modified by simply changing rows columns and adding or removing rows and columns as the result of modifying the geometric or structural characteristics of its pieces the structure s degrees of freedom and or the boundary conditions some examples of simple structures are given to illustrate the methodology finally a discussion about its practical application and some conclusions and recommendations are given 1998 john wiley sons ltd

on extensions of the power method for normal operators abstract in a recent work by sidi and bridger some old and some new extensions of the power method have been considered and some of these extensions have been shown to produce estimates of several dominant eigenvalues of an arbitrary square matrix in the present work we continue the analysis of two versions of one of these extensions called the mpe extensions as they are applied to normal matrices we show that the convergence rate of these methods for normal matrices is twice that for nonnormal matrices we also give precise asymptotic bounds on the errors of the estimates obtained for the eigenvalues further deflation type extensions of the power method for normal matrices are suggested and analyzed for their convergence all the results are stated and proved in the general setting of inner product spaces

structural optimization a new dual method using mixed variables a new and powerful mathematical programming method is described which is capable of solving a broad class of structural optimization problems the method employs mixed direct reciprocal design variables in order to get conservative first order approximations to the objective function and to the constraints by this approach the primary optimization problem is replaced with a sequence of explicit subproblems each subproblem being convex and separable it can be efficiently solved by using a dual formulation an attractive feature of the new method lies in its inherent tendency to generate a sequence of steadily improving feasible designs examples of application to real life aerospace structures are offered to demonstrate the power and generality of the approach presented

extrapolation methods for vector sequences this is an expository paper that describes and compares five methods for extrapolating to the limit or anti limit of a vector sequence without explicit knowledge of the sequence generator the methods are the minimal polynomial extrapolation mpe studied by cabay and jackson mesina and skelboe the reduced rank extrapolation rre of eddy which we show to be equivalent to mesina s version of mpe the vector and scalar versions of the epsilon algorithm vea sea introduced by wynn and extended by brezinski and gekeler and the topological epsilon algorithm tea of brezinski we cover the derivation and error analysis of iterated versions of the algorithms as applied to both linear and nonlinear problems and we show why these versions tend to converge quadratically we also present samples from extensive numerical testing that has led us to the following conclusions a tea in spite of its role as a theoretical link between the polynomial type and the epsilon type methods has no practical appl

moving morphable patches for three dimensional topology optimization with thickness control abstract thickness controllable topology optimization is presented for three dimensional problems using moving morphable patches geometric features of triangular patches were employed as design variables to enable the representation of shell like members and beam or bar members with a small number of design components the minimum thickness for mean compliance minimization problems can be controlled simply by setting the lower bound of thickness variables of the patches as the given minimum regarding the maximum thickness the patches with close to maximum thicknesses were controlled to be connected on their sides or perfectly overlapped for which a void mask is introduced on each patch avoiding partial overlapping through their faces thus the maximum thickness of a member was obtained as the maximum value of thickness variables of the patches consisting of the member therefore the maximum thickness of members can be controlled by the upper bound of thickness variables a constraint was imposed on the material volume of each patch to prevent partial overlapping or incomplete connection with other patches the effectiveness of the proposed formulation was verified by showing various examples with minimum maximum and uniform thickness controls

localization problem in one dimension mapping and escape a one dimensional schr odinger equation in a discontinuous quasiperiodic potential is reduced to a recursion relation for transfer matrices and then to one for traces of these matrices when the potential is periodic the bandwidth goes to zero as an algebraic function of the period with a critical index which depends upon the potential strength this critical index is also evaluated as the solution to an escape rate problem for the recursion relations

decision making on the sole basis of statistical likelihood this paper presents a new axiomatic decision theory for choice under uncertainty unlike bayesian decision theory where uncertainty is represented by a probability function in our theory uncertainty is given in the form of a likelihood function extracted from statistical evidence the likelihood principle in statistics stipulates that likelihood functions encode all relevant information obtainable from experimental data in particular we do not assume any knowledge of prior probabilities consequently a bayesian conversion of likelihoods to posterior probabilities is not possible in our setting we make an assumption that defines the likelihood of a set of hypotheses as the maximum likelihood over the elements of the set we justify an axiomatic system similar to that used by von neumann and morgenstern for choice under risk our main result is a representation theorem using the new concept of binary utility we also discuss how ambiguity attitudes are handled applied to the statistical inference problem our theory suggests a novel solution the results in this paper could be useful for probabilistic model selection

approximate reanalysis in topology optimization despite rapid improvements in computer performance there is still room for advances in computational efficiency for handling structural optimization applications due to the high computational cost involved in the optimization process in general the total computational cost of the optimization procedure is governed by the complexity of three aspects the model the analysis and the optimization 1 solving problems that consider high complexities in all three aspects is presently somewhat limited in problem size thus motivating the search for methods and procedures that require reduced computational resources but yield high quality results in this paper the implementation of an approximate reanalysis method in topology optimization is investigated we apply the so called nested approach where optimization is performed in the design variables only and where the equilibrium equations are treated as function calls the goal is to reduce the computation involved in repeated solutions of the equilibrium equations which for large problems will dominate the computational cost of the whole process the approximate reanalysis performed here is based on the combined approximations ca approach proposed by kirsch 2 for linear static reanalysis and later used successfully also in vibration dynamic and nonlinear reanalysis the main feature of ca is the integration of a local series expansion in a global reduced basis solution when using ca for repeated structural analysis one can substantially reduce the number of required factorizations of the stiffness matrix and thus removing a significant portion of the computational effort in this study ca has been implemented for topology optimization of linear structures and the accuracy of the solutions obtained has been benchmarked against solutions presented in the literature 3 and 4 the relative efficiency of the method has been evaluated by comparing with the case in which all analysis equations are solved by a direct method there is a clear trade off between the accuracy and the efficiency of the approximate procedure both are mainly influenced by two parameters the frequency of full matrix decompositions and the number of vectors generated for the reduced basis more frequent decompositions will result in smaller changes in stiffness and therefore a more accurate approximation but at the cost of matrix factorizations similarly using more basis vectors will give a better representation of the actual solution but will increase the computational effort for all the trial cases considered the optimal designs and the objective values obtained by the approximate procedure were practically

discrete adjoint sensitivity analysis for fluid flow topology optimization based on the generalized lattice boltzmann method abstract a discrete adjoint sensitivity analysis for fluid flow topology optimization based on the lattice boltzmann method lbm with multiple relaxation times mrt is developed the lattice boltzmann fluid solver is supplemented by a porosity model using a darcy force the continuous transition from fluid to solid facilitates a gradient based optimization process of the design topology of fluidic channels the adjoint lbm equation which is used to compute the gradient of the optimization objective with respect to the design variables is derived in moment space and found to be as simple as the original lbm the moment based spatial momentum derivatives used to express the discrete objective functional cost function have the advantage that the local stress tensor is a local quantity avoiding the numerical computation of gradients of the discrete velocity field this is particularly useful if dissipation is a design criterion as demonstrated in this paper the method is validated by a detailed comparison with results obtained by borrvall et al for stokes flow while their approach is only valid for stokes flow i e very low reynolds numbers our approach in its present form can in principle be applied for flows of different reynolds numbers just like the navier stokes equation based approaches this point is demonstrated with a bending pipe example for various reynolds numbers

development of iterative techniques and extrapolation methods for drazin inverse solution of consistent or inconsistent singular linear systems abstract consider the linear system of equations bx where b is an nxn singular matrix in an earlier work by the author it was shown that iterative techniques coupled with standard vector extrapolation methods can be used to obtain or approximate a solution of this system when it is consistent in the present work we expand on that approach to treat the case in which this system is in general inconsistent starting with richardson s iterative method we develop a family of new iterative techniques and vector extrapolation methods that enable us to obtain or approximate the drazin inverse solution of this system whether the index of b is 1 or greater than 1 we show that the drazin inverse solution can be constructed from a finite number of iterations this number being at most n 2 we also provide detailed convergence analyses of the new iterative techniques and vector extrapolation methods and give their precise rates of convergence

passive vibration suppression of flexible space structures via optimal geometric redesign acomputationalframework is presented for the design of large flexible space structures with nonperiodicgeometries to achieve passive vibration suppression the present system combines an approximationmodel management framework ammf developed for evolutionary optimization algorithms eas with reduced basis approximate dynamic reanalysis techniques a coevolutionary genetic search strategy is employed to ensure that design changes during the optimization iterations lead to low rank perturbations of the structural system matrices for which thereduced basis methods give high quality approximations the k means algorithm is employed for cluster analysis of the population of designs to determine design points at which exact analysis should be carried out the fitness of the designs in an ea generation is then approximated using reduced basis models constructed around the points where exact analysis is carried out results are presented for the optimal design of a two dimensional cantilevered space structure to achieve passive vibration suppression it is shown that significant vibration isolation of the order of 50 db over a 100 hz bandwidth can be achieved further it is demonstrated that the ammf can potentially arrive at a better design compared to conventional approaches when a constraint is imposed on the computational budget available for optimization

two axiomatic approaches to decision making using possibility theory this paper proposes a utility theory for decision making under uncertainty that is described by possibility theory we show that our approach is a natural generalization of the two axiomatic systems that correspond to pessimistic and optimistic decision criteria proposed by dubois et al the generalization is achieved by removing axioms that are supposed to reflect attitudes toward uncertainty namely pessimism and optimism in their place we adopt an axiom that imposes an order on a class of canonical lotteries that realize either in the best or in the worst prize we prove an expected utility theorem for the generalized axiomatic system based on the newly introduced concept of binary utility

a new type of transition between critical and extended states in one dimension the author studies a tight binding model psi n 1 psi n 1 lambda nvn psi n e psi n where vn is a fibonacci array of two potentials and lambda n f 12 n alpha for alpha 1 2 this model is asymptotically equivalent at large n to a continuous schrodinger equation with an electric field f and a quasiperiodic potential he finds that for this value of alpha almost all states are changed from critical to extended states as the field strength is increased however some states still remain critical and coexist with most extended states he also discusses the result for other values of alpha

optimal design in conductivity under locally constrained heat flux this paper addresses the relaxation of an optimal design problem in conductivity under a point wise constraint on the heat flux by using a variational approach developed by the authors in a previous work we obtained a complete relaxation involving the explicit computation of constrained quasiconvex envelopes this relaxed formulation turns out to be very simple in the remarkable compliance case for which numerical simulations are performed those simulations show that our approach and results are interesting from a theoretical point of view as well as from a practical perspective the emphasis of our work is placed on the local constraint on the heat flux which seems to be a new ingredient for this kind of optimal design problems

a reduction method for boundary element reanalysis abstract this paper is concerned with reanalysis for boundary element systems an efficient and accurate reduction method is proposed for reanalyzing such systems the new method has several merits in particular the reduced system has been uncoupled by a gram schmidt orthonormalization procedure also a computation inexpensive convergence criterion is proposed for the automatic determination of the number of basis vectors required to approximate the solution within a specified level of accuracy several example problems are illustrated to verify the accuracy and efficiency of the proposed reduction method

finding maps for belief networks is np hard given a probabilistic world model an important problem is to find the maximum a posteriori probability map instantiation of all the random variables given the evidence numerous researchers using such models employ some graph representation for the distributions such as a bayesian belief network this representation simplifies the complexity of specifying the distributions from exponential in n the number of variables in the model to linear in n in many interesting cases we show however that finding the map is np hard in the general case when these representations are used even if the size of the representation happens to be linear in n furthermore minor modifications to the proof show that the problem remains np hard for various restrictions of the topology of the graphs the same technique can be applied to the results of a related paper by cooper to further restrict belief network topology in the proof that probabilistic inference is np hard

qualitative decision theory with preference relations and comparative uncertainty an axiomatic approach this paper investigates a purely qualitative approach to decision making under uncertainty since the pioneering work of savage most models of decision under uncertainty rely on a numerical representation where utility and uncertainty are commensurate giving up this tradition we relax this assumption and introduce an axiom of ordinal invariance requiring that the decision maker s preference between two acts only depends on the relative position of their consequences for each state within this qualitative framework we determine the only possible form of the corresponding decision rule then assuming the transitivity of the strict preference the underlying partial confidence relations are those at work in non monotonic inference and thus satisfy one of the main properties of possibility theory the satisfaction of additional postulates of unanimity and anonymity enforces the use of a necessity measure unique up to a monotonic transformation for encoding the relative likelihood of events

accurate displacement derivatives for structural optimization using approximate reanalysis a unified approach for accurate approximations of displacements and displacement derivatives with respect to design variables is presented the solution procedure is based on results of a single exact analysis at an initial design unlike common approximations of the structural response the approach presented is not based on calculation of derivatives rather approximations of displacements are used to evaluate displacement derivatives at various modified designs it is shown that similar computational procedures are employed for evaluating displacements first and second order derivatives of displacements the procedure presented is suitable for different types of design variables and structures numerical results show that accurate approximations of derivatives can be achieved with a small computational effort for designs obtained by very large changes in the initial structure

improved first order approximation of eigenvalues and eigenvectors a method based on reduced basis approximation concepts is presented for improved first order approximation of eigenvalues and eigenvectors of modified structural dynamic systems the terms of a local approximation based on taylor or matrix power series are used as basis vectors for approximating the perturbed eigenparameters for each eigenmode a reduced eigensystem is generated by using the baseline eigenvector and the first order approximation term as ritz vectors the solution of the reduced eigensystem leads to two possible estimates of each perturbed eigenvalue and eigenvector criteria for selection of the best approximation are presented the zero and first order rayleigh quotient approximation can be directly recovered as special cases of the present method results are presented for approximate dynamic reanalysis of a 25 bar planar truss structure it is shown that high quality approximation of the perturbed eigenparameters can be obtained for moderate perturbations in the stiffness and mass matrices for very large local perturbations of the structure including deletion of some structural members it is shown that the present method yields reasonable quality approximations

structural approximate reanalysis for topological modifications of finite element systems conclusions aperturbationmethodusingacorrectionintransformationispresented to improve the condensation solution the method proved to be effective and is recommended as a postprocessor of the condensation theoretically the perturbation solution should approach the exact eigenvalue from above in practice however truncation error in the linear equation causes the approximation to overshoot the exact solution inclusion of several of the lowest terms can provide excellent estimations for both the eigenvalue and mode shape changes one of the most dife cult problems is the rate of convergence in the series expansion the sequential terms in the ine nite series may indicate the convergence characteristics in an eigenvalue approximation some of the nonlinear terms may be included to get more accurate solutions rather than iterations with nonlinear perturbation equations integrated reduction methodssuch as the hybrid dynamic condensation are preferable

topology optimization in thermal fluid flow using the lattice boltzmann method this paper proposes a topology optimization method for thermal fluid flow problems using the lattice boltzmann method lbm the design sensitivities are derived based on the adjoint lattice boltzmann method albm whose basic idea is that the adjoint problem is first formulated using a continuous adjoint approach and the adjoint problem is then solved using the lbm in this paper the discrete velocity boltzmann equation in which only the particle velocities are discretized is introduced to the albm to deal with the various boundary conditions in the lbm the novel sensitivity analysis is applied in two flow channel topology optimization problems 1 a pressure drop minimization problem and 2 a heat exchange maximization problem several numerical examples are provided to confirm the utility of the proposed method

optimal structural design considering flexibility a topology optimization method based on the homogenization method the homogenization design method has been successfully applied to a variety of optimization problems such as the stiffness maximization problem and the eigen frequency maximization problem in this study a methodology to obtain the optimal structure design considering flexibility is developed as a new extension of the homogenization design method first flexibility is formulated using the mutual energy concept second a new multi objective function is proposed to obtain optimal solutions incorporating flexibility and stiffness next the topology optimization procedure is constructed using the homogenization method and sequential linear programming slp finally some examples are presented to confirm that the methodology presented here can provide flexible structures satisfying the problem specifications

decision theoretic foundations of qualitative possibility theory abstract this paper presents a justification of two qualitative counterparts of the expected utility criterion for decision under uncertainty which only require bounded linearly ordered valuation sets for expressing uncertainty and preferences this is carried out in the style of savage starting with a set of acts equipped with a complete preordering relation conditions on acts are given that imply a possibilistic representation of the decision maker uncertainty in this framework pessimistic i e uncertainty averse as well as optimistic attitudes can be explicitly captured the approach thus proposes an operationally testable description of possibility theory

explicit constraint approximation forms in structural optimization part 1 analyses and projections abstract an analytical study of several alternative forms of constraint approximation relevant to problems in structural design is presented limitations of the existing forms of the constraint approximations are stated and methods are outlined to improve them a new generalized form of constraint approximation is proposed for optimal design problems with and without design variable linking a power form of constraint approximation is derived for bending types of finite elements having nonlinear size stiffness relationships a detailed analysis to determine the relative effectiveness of the various forms is included a rating guideline is proposed to quantify the characteristics of chosen approximations or family of approximations on grounds of accuracy and of conservatism of remaining feasible

a mixed fem approach to stress constrained topology optimization we present an alternative topology optimization formulation capable of handling the presence of stress constraints in a straightforward fashion the main idea is to adopt a mixed finite element discretization scheme wherein not only displacements as usual but also stresses are the variables entering the formulation by doing so any stress constraint may be handled within the optimization procedure without resorting to post processing operation typical of displacement based techniques that may also cause a loss in accuracy in stress computation if no smoothing of the stress is performed two dual variational principles of hellinger reissner type are presented in continuous and discrete form that which included in a rather general topology optimization problem in the presence of stress constraints that is solved by the method of moving asymptotes int j numer meth engng 1984 24 3 359 373 extensive numerical simulations are performed and ongoing extensions outlined including the optimization of elastoplastic and incompressible media copyright 2007 john wiley sons ltd

combined approximations for efficient probalistic analysis of structures real life analysis and design problems involve uncertainties quantification of the uncertainties in a system s response is important and requires a probabilistic analysis of the system a main challenge in probabilistic analysis of large structural systems is the high computational effort due to the multiple repeated analyses involved the combined approximations ca method which combines the strengths of both local and global approximations can be used for efficient probabilistic analysis of structures the ca method is a combination of binomial series local approximations also called neumann expansion approximations and reduced basis global approximations an efficient method is presented for probabilistic analysis of structural systems using the ca method the effectiveness of this method is demonstrated on analysis of mistuned bladed disk assemblies and systems with progressive collapse using monte carlo simulation it is shown that the method can predict accurately the probability distribution function of the responses of these systems at a considerably lower cost than a method using finite element analysis in each cycle of monte carlo simulation

generalized galerkin method for modal testing of structure with pseudomaterials this paper presents a generalized galerkin method based on the dynamic flexibility matrix expansion technique the main objective is to develop an analysis to predict the modes and frequencies of a real structure when the design verification methods used to conduct on the ground tests can only be performed on a pseudomaterial structure it is critical to develop analytical methods that correctly predict the dynamic behavior of real structure in order to guarantee a successful design of complex structures oftentimes a full scale spacecraft modal test cannot be performed on the real model due to hazardous payloads it carries stable and relatively inexpensive materials are often used to replace these hazardous materials during the test the basic idea for analyzing these test modes of pseudomaterial structures is based on eigenvalue reanalysis techniques this method is relatively easy to understand and can be implemented into the existing method it is numerically accurate and efficient and can be applied to assist in large complex space structure designs

the computational complexity of probabilistic inference using bayesian belief networks research note abstract bayesian belief networks provide a natural efficient method for representing probabilistic dependencies among a set of variables for these reasons numerous researchers are exploring the use of belief networks as a knowledge representation in artificial intelligence algorithms have been developed previously for efficient probabilistic inference using special classes of belief networks more general classes of belief networks however have eluded efforts to develop efficient inference algorithms we show that probabilistic inference using belief networks is np hard therefore it seems unlikely that an exact algorithm can be developed to perform probabilistic inference efficiently over all classes of belief networks this result suggests that research should be directed away from the search for a general efficient probabilistic inference algorithm and toward the design of efficient special case average case and approximation algorithms

a general framework for explaining the results of a multi attribute preference model the automatic generation of an explanation of the prescription made by a multi attribute decision model is crucial in many applications such as recommender systems this task is complex since the quantitative models are not designed to be easily explainable the major limitation of the previous research is that there is no formal justification of the arguments that are selected in the explanation the goal of this paper is to define a general framework to justify which arguments shall be selected in the case where the decision model is based on weights assigned to the attributes due to the complexity of explaining a preference model based on utility theory several explanation reasonings are necessary to cover all cases ranging from situations where the prescription is trivial to situations where the prescription is much more tight the set of selected arguments is in this framework a non dominated element of a combinatorial structure in the sense of an order relation our general approach is instantiated precisely on three models the probabilistic expected utility model the qualitative pessimistic minmax model and the concordance rule which are all constructed from a weight vector

two dimensional poroelastic acoustical foam shape design for absorption coefficient maximization by topology optimization method optimal shape design of a two dimensional poroelastic acoustical foam is formulated as a topology optimization problem for a poroelastic acoustical system consisting of an air region and a poroelastic foam region two different physical regions are continuously changed in an iterative design process to automatically account for the moving interfaces between two regions we propose a new unified model to analyze the whole poroelastic acoustical foam system with one set of governing equations biot s equations are modified with a material property interpolation from a topology optimization method with the unified analysis model we carry out two dimensional optimal shape design of a poroelastic acoustical foam by a gradient based topology optimization setting the specific objective is the maximization of the absorption coefficient in low and middle ranges of frequencies with different amounts of a poroelastic material the performances of the obtained shapes are compared with those of well known wedge s

anomaly and singular continuous spectrum in a one dimensional incommensurate system the authors study a tight binding model given by psi n 1 psi n 1 v cos 2 pi qn theta psi n e psi n where q is a liouville number it is demonstrated that all eigenstates are critical with singular continuous spectra for all values of v these critical states appear to be composed of connected extended states they also find a band centre anomaly the resistance of the band centre displays coupled oscillations and is much larger than that of other states

a method for modal reanalysis of topological modifications of structures a method for structural modal reanalysis for three cases of topological modifications the number of degrees of freedom dofs is unchanged decreased and increased is presented in this method the newly added dofs are linked to the original dofs of the modified structure by means of the dynamic reduction so as to obtain the condensed equation the methods for forming the stiffness and mass increments k and m resulting from the three cases of topological modifications of structures are discussed the extended kirsch method is used to improve the accuracy of the starting solutions of the initial structure and then the eigenvectors of newly added dofs resulting from topological modification can be recovered at last the rayleigh ritz analysis is used to evaluate the eigenvalues and eigenvectors for the modified structure three numerical examples are given to illustrate the applications of the present approach the results show that the proposed method is effective for structural modal reanalysis of three cases of the topological modifications and it is easy to implement on a computer by comparing with previous method it can be seen that the present method can give good approximate eigenvalues and eigenvectors even if the topological modifications are very large copyright 2005 john wiley sons ltd

reduced basis approximations of structural displacements for optimaldesign a new solution procedure for improved approximate reanalyses of structures using results of a single precise analysis is presented the proposed procedure is based on combining the computed terms of a series expansion used as high quality basis vectors with coefficients of a reduced basis expression the latter coefficients can readily be determined for each trial design by various criteria the results are measured by the errors in satisfying the analysis equations and are compared in terms of the quality of the approximations the proposed approach is suitable for various types of design variables and can be used with a general finite element model a general reanalysis procedure is introduced and the physical significance of first order approximations is demonstrated several numerical examples illustrate the effectiveness of the solution process it is shown that high quality approximations of displacements can be obtained with a small computational effort for very large changes in the design variables

singular continuous spectrum for a class of almost periodic jacobi matrices we consider operators parametrized by a o on 2 with matrix ojy i o i fl o y with an cos 2ttcw 6 if ce is a liouville number and 2 we prove that for a e 0 the operator s spectral measures are all singular continuous we consider the operator on l2 z depending upon three parameters x a 0 1 x a 0 u n u n 1 u n 1 x cos 2iran 6 u n in this note we will sketch the proof of the following result whose detailed proof will appear elsewhere 3 theorem 1 fix a an irrational number obeying

new adaptive technique of kirsch method for structural reanalysis the combined approximations method proposed by kirsch is an efficient reanalysis method providing high quality results to integrate the kirsch method into a structural optimization process this paper presents a new adaptive kirsch method to determine the minimum number of basis vectors using the k condition number consequently a closer relationship between the kirsch method and structural optimization is bridged moreover the effectiveness of the kirsch method is improved for application in optimal design problems the presented numerical results prove that the adaptive kirsch method is significantly more efficient than the kirsch method because of the advantage of adaptively determining the minimum number of basis vectors to satisfy the predefined reanalysis error

efficient non linear reanalysis of skeletal structures using combined approximations non linear reanalysis of large scale structures usually involves much computational effort because the set of non linear equations must be solved repeatedly during the solution process various approximations that are often used for linear reanalysis are not sufficiently accurate for non linear problems in this study solution procedures based on the combined approximations approach are developed and compared in terms of efficiency and accuracy various path independent non linear analysis and reanalysis problems are considered including material non linearity geometric non linearity and buckling analysis numerical examples demonstrate the effectiveness of the procedures presented it is shown that in various cases accurate results can be achieved efficiently copyright 2007 john wiley sons ltd

accelerated engineering design optimization using successive matrix inversion method in a design optimization procedure many repeated system analyses are conducted to evaluate certain performances of successively modified structural designs to alleviate the high computational cost of structural reanalysis an augmented preconditioner is introduced by using the successive matrix inversion smi method the smi method as an exact matrix solver is successively applied to an iterative procedure to accelerate the solution convergence by improving the numerical condition of the reanalysis system in this work a new iterative technique the binomial series iterative bsi method is developed from the binomial series expansion by using the same concept as smi as a combined iterative ci method smi is incorporated in the procedure of bsi the ci method combined with smi shows sufficient efficiency and robustness through a stable iterative behaviour due to simple and straightforward computations in the iterative procedure published in 2005 by john wiley sons ltd

quantitative and constructive aspects of the generalized koenig s and de montessus s theorems for pade approximants abstract the generalized koenig s theorem and de montessus s theorem are two classical results concerning the convergence of the rows of the pade table for meromorphic functions employing a technique that was recently developed for the analysis of vector extrapolation methods refined versions of these theorems are proved in the present work specifically complete expansions for the numerators and denominators of pade approximants are derived these expansions are then used to obtain 1 precise asymptotic rates of convergence of the poles of the pade approximants to the corresponding poles simple or multiple of the meromorphic function in question and 2 the precise asymptotic behavior of the error in the relevant pade approximants one important feature of the asymptotic results derived in this work is that these are expressed in terms of a very small number of parameters approximations of optimal accuracy to multiple poles and the principal parts of the corresponding laurent expansions are also constructed in addition the convergence problem for the case in which the only singularities on the circle of meromorphy are poles is solved completely through the solution of a nonlinear integer programming problem

extrapolation vs projection methods for linear systems of equations it is shown that the four vector extrapolation methods minimal polynomial extrapolation reduced rank extrapolation modified minimal polynomial extrapolation and topological epsilon algorithm when applied to linearly generated vector sequences are krylov subspace methods and are equivalent to some well known conjugate gradient type methods a unified recursive method that includes the conjugate gradient conjugate residual and generalized conjugate gradient methods is developed finally the error analyses for these methods are unified and some known and some new error bounds for them are given

general topology optimization method with continuous and discrete orientation design using isoparametric projection a general topology optimization method which is capable of simultaneous design of density and orientation of anisotropic material is proposed by introducing orientation design variables in addition to the density design variable in this work the cartesian components of the orientation vector are utilized as the orientation design variables the proposed method supports continuous orientation design which is out of the scope of discrete material optimization approaches as well as design using discrete angle sets the advantage of this approach is that vector element representation is less likely to fail into local optima because it depends less on designs of former steps especially compared with using the angle as a design variable continuous fiber angle optimization by providing a flexible path from one angle to another with relaxation of orientation design space an additional advantage is that it is compatible with various projection or filtering methods such as sensitivity filters and density filters because it is free from unphysical bound or discontinuity such as the one at theta 2 pi and theta 0 seen with direct angle representation one complication of cartesian component representation is the point wise quadratic bound of the design variables that is each pair of element values has to reside in a given circular bound to overcome this issue we propose an isoparametric projection method which transforms box bounds into circular bounds by a coordinate transformation with isoparametric shape functions without having the singular point that is seen at the origin with polar coordinate representation a new topology optimization method is built by taking advantage of the aforementioned features and modern topology optimization techniques several numerical examples are provided to demonstrate its capability copyright c 2014 john wiley sons ltd

efficient sensitivity analysis for structural optimization abstract efficient sensitivity analysis based on high quality approximations of displacements is presented the improved approximations are achieved by combining the efficiency of local approximations series expansion and the quality of global approximations the reduced basis method three approximate sensitivity analysis methods are developed and compared the direct method the adjoint variable method and the finite difference method all the approximations are based on the results of a single exact analysis of the initial design and they can be used with a general finite element system the methods are easy to implement and suitable for different types of design variables and structures it is shown that high quality approximations of derivatives can be achieved with a relatively small computational effort for very large changes in the design variables

robust topology optimization of structures with imperfect geometry based on geometric nonlinear analysis abstract topology optimization often leads to structures consisting of slender elements which are particularly sensitive to geometric imperfections such imperfections might affect the structural stability and induce large displacement effects in these slender structures this paper therefore presents a robust approach to topology optimization which accounts for geometric imperfections and their potentially detrimental influence on the structural stability geometric nonlinear effects are incorporated in the optimization by means of a total lagrangian finite element formulation in the minimization of end compliance geometric imperfections are modeled as a vector valued random field in the design domain the resulting uncertain performance of the design is taken into account by minimizing a weighted sum of the mean and standard deviation of the compliance in the robust optimization problem these stochastic moments are typically estimated by means of sampling methods such as monte carlo simulation however these methods require multiple independent nonlinear finite element analyses in each design iteration of the optimization algorithm an efficient solution algorithm which uses adjoint differentiation in a second order perturbation method is therefore developed to estimate the stochastic moments during the optimization two applications with structures that exhibit different types of structural instabilities are examined in both cases it is demonstrated by means of an extensive monte carlo simulation that the deterministic design is very sensitive to imperfections while the design obtained by means of the proposed method is much more robust

approximate vibration reanalysis of structures thecombinedapproximationsmethodisdevelopedforvibrationreanalysisofstructures inthesolution process the terms of local series approximations are used as basis vectors in global reduced basis approximations the solution steps are straightforward and the method can be readily used with a general e nite element system the computational effort needed by the method is usually much smaller than the effort needed for complete vibration analysis the efe ciency of the calculations and the accuracy of the results can be controlled by the amount of information considered efe cient solutions are obtained by low order approximations and accurate results can be achievedbyconsideringhigher orderterms numericalexamplesshowthataccurateresultsareachievedefe ciently for very large changes in the design nomenclature b matrix dee ned by eq 21 c matrix dee ned by eq 16 e modulus of elasticity i moment of inertia i identity matrix k stiffness matrix kr reduced stiffness matrix l length m mass matrix mr reduced mass matrix r right hand side vector r displacement vector rb matrix of basis vectors s number of basis vectors u upper triangular matrix y vector of coefe cients coefe cient dee ned by eq 35 angle between vectors 1k change in the stiffness matrix 1m change in the mass matrix kronecker delta eigenvalue circular frequency

equivalence between the combined approximations technique and krylov subspace methods the objective of this note is to examine the equivalence between the ca technique and krylov subspace methods it is shown that the ca technique is a preconditioned krylov subspace method based on this connection it is briefly outlined why the ca technique will converge to the exact solution when the number of basis vectors is increased the ramification of the present research on the practical issue of integrating static reanalysis techniques with structural optimization procedures is also discussed

exact and efficient isogeometric reanalysis of accurate shape and boundary modifications abstract in the traditional design through analysis pipeline geometric models and modifications are approximately represented and transformed with computational models besides after each modification the latest design often needs to be completely analyzed again leading to reanalysis these procedures produce many errors and are extremely time consuming therefore in this paper we propose a novel and an exact and efficient isogeometric reanalysis methodology of accurate shape and boundary modifications that improves the totality of integration of design and analysis greatly geometric models and shape modifications are exactly represented and transformed and the corresponding computational models will change simultaneously when the geometric models are modified thereby reducing error and time in model representation and transformation furthermore we extend and propose the isogeometric based exact reanalysis method termed indirect factorization updating ifu with the combination of isogeometric based reanalysis the method can efficiently obtain the exact solution of the modified structure without solving the complete set of modified equations of the new structure it is also applicable to all techniques for representing the cad geometry model and complex problems several examples illustrate and verify the accuracy and efficiency of this proposed method and furthermore the larger the scale of the problem the more advantageous the end result will be

accelerating numerical simulations of strain adaptive bone remodeling predictions abstract bone modeling and remodeling have been extensively studied in many fields of research the process of adaptive bone remodeling can be described mathematically and simulated in a computer model integrated with the finite element method fem the fem can determine the long term behavior of bone and the impact on bone biomechanics produced by prosthetic models as whole bone remodeling simulations are time consuming the aim of this paper is to combine fe analyses with numerical extrapolation techniques to accelerate bone remodeling simulations two vector extrapolation methods reduce ranked extrapolation rre and minimal polynomial extrapolation mpe are used to reduce the simulation time these extrapolation techniques are illustrated by numerical examples of 2 d and 3 d models based on a strain adaptive bone remodeling theory

an axiomatic treatment of three qualitative decision criteria the need for computationally efficient decision making techniques together with the desire to simplify the processes of knowledge acquisition and agent specification have led various researchers in artificial intelligence to examine qualitative decision tools however the adequacy of such tools is not clear this paper investigates the foundations of maximin minmax regret and competitive ratio three central qualitative decision criteria by characterizing those behaviors that could result from their use this characterizaton provides two important insights 1 under what conditions can we employ an agent model based on these basic qualitative decision criteria and 2 how rational are these decision procedures for the competitive ratio criterion in particular this latter issue is of central importance to our understanding of current work on on line algorithms our main result is a constructive representation theorem that uses two choice axioms to characterize maximin minmax regret and competitive ratio

accurate reanalysis of structures by a preconditioned conjugate gradient method a preconditioned conjugate gradient pcg method that is most suitable for reanalysis of structures is developed the method presented provides accurate results efficiently it is easy to implement and can be used in a wide range of applications including non linear analysis and eigenvalue problems it is shown that the pcg method presented and the combined approximations ca method developed recently provide theoretically identical results consequently available results from one method can be applied to the other method effective solution procedures developed for the ca method can be used for the pcg method and various criteria and error bounds developed for conjugate gradient methods can be used for the ca method numerical examples show that the condition number of the selected preconditioned matrix is much smaller than the condition number of the original matrix this property explains the fast convergence and accurate results achieved by the method copyright 2002 john wiley sons ltd

lexicographic probabilities and equilibrium refinements this paper develops a decision theoretic approach to normal form refinements of nash equilibrium and provides characterizations of normal form perfect equilibrium and proper equilibrium the approach relies on a theory of single person decision making that is a non archimedean version of subjective expected utility theory copyright 1991 by the econometric society

some results about vector extrapolation methods and related fixed point iterations abstract in this work we consider polynomial extrapolation methods for vector sequences we give a unified presentation of these methods and a new recursive algorithm for the implementation of the modified minimal polynomial extrapolation mmpe method properties operation counts and storage requirements of the algorithm will be given the second part of the work is devoted to the application of these methods for solving systems of nonlinear equations a sufficient condition for quadratic convergence is given

fuzzy sets as a basis for a theory of possibility the theory of possibility described in this paper is related to the theory of fuzzy sets by defining the concept of a possibility distribution as a fuzzy restriction which acts as an elastic constraint on the values that may be assigned to a variable more specifically if f is a fuzzy subset of a universe of discourse u u which is characterized by its membership function f then a proposition of the form x is f where x is a variable taking values in u induces a possibility distribution tx which equates the possibility of x taking the value u to f u the compatibility of u with f in this way x becomes a fuzzy variable which is associated with the possibility distribution tx in much the same way as a random variable is associated with a probability distribution in general a variable may be associated both with a possibility distribution and a probability distribution with the weak connection between the two expressed as the possibility probability consistency principle a thesis advanced in this paper is that the imprecision that is intrinsic in natural languages is in the main possibilistic rather than probabilistic in nature thus by employing the concept of a possibility distribution a proposition p in a natural language may be translated into a procedure which computes the probability distribution of a set of attributes which are implied by p several types of conditional translation rules are discussed and in particular a translation rule for propositions of the form x is f is possible where is a number in the interval 0 1 is formulated and illustrated by examples

shape and topology optimization of compliant mechanisms using a parameterization level set method in this paper a parameterization level set method is presented to simultaneously perform shape and topology optimization of compliant mechanisms the structural shape boundary is implicitly embedded into a higher dimensional scalar function as its zero level set resultantly establishing the level set model by applying the compactly supported radial basis function with favorable smoothness and accuracy to interpolate the level set function the temporal and spatial hamilton jacobi equation from the conventional level set method is then discretized into a series of algebraic equations accordingly the original shape and topology optimization is now fully transformed into a parameterization problem namely size optimization with the expansion coefficients of interpolants as a limited number of design variables design of compliant mechanisms is mathematically formulated as a general optimization problem with a nonconvex objective function and two additionally specified constraints the structural shape boundary is then advanced as a process of renewing the level set function by iteratively finding the expansion coefficients of the size optimization with a sequential convex programming method it is highlighted that the present method can not only inherit the merits of the implicit boundary representation but also avoid some unfavorable features of the conventional discrete level set method such as the cfl condition restriction the re initialization procedure and the velocity extension algorithm finally an extensively investigated example is presented to demonstrate the benefits and advantages of the present method especially its capability of creating new holes inside the design domain

preference structures the problem of the consistency of qualitative judgements about the difference of attractiveness between alternatives is studied our proposal deals with smooth t conorms to be used for aggregation of elementary judgements

convergence and stability properties of minimal polynomial and reduced rank extrapolation algorithms the minimal polynomial and reduced rank extrapolation algorithms are two acceleration of convergence methods far sequences of vectors in a recent survey these methods were tested and compared with the scalar vector and topological epsilon algorithms and were observed to be more efficient than the latter it was also observed that the two methods have similar convergence properties the purpose of the present work is to analyze the convergence and stability properties of these methods and to show that they are bona fide acceleration methods when applied to a class of vector sequences that includes those sequences obtained from systems of linear equations by using matrix iterative methods

topology optimization by a neighbourhood search method based on efficient sensitivity calculations this paper deals with topology optimization of discretized load carrying continuum structures where the design of the structure is represented by binary design variables indicating material or voi

solution of integral equations using generalised inverse function valued pade approximants i abstract neumann series solutions for the linear integral equation x 1 1 0 1 x y y d y converge for small values of we use generalised inverse function valued pade approximants to accelerate the convergence of the neumann series and to estimate the singular value of these estimates are found to compare very favourably with those from the fredholm determinant method and the pade approximant method

on the equivalence of optimality criterion and sequential approximate optimization methods in the classical topology layout problem we study the classical topology optimization problem in which minimum compliance is sought subject to linear constraints using a dual statement we propose two separable and strictly convex subproblems for use in sequential approximate optimization sao algorithms respectively the subproblems use reciprocal and exponential intermediate variables in approximating the non linear compliance objective function any number of linear constraints or linearly approximated constraints are provided for the relationships between the primal variables and the dual variables are found in analytical form for the special case when only a single linear constraint on volume is present we note that application of the ever popular optimality criterion oc method to the topology optimization problem combined with arbitrary values for the heuristic numerical damping factor proposed by bendsoe results in an updating scheme for the design variables that is identical to the application of a rudimentary dual sao algorithm in which the subproblems are based on exponential intermediate variables what is more we show that the popular choice for the damping factor 0 5 is identical to the use of sao with reciprocal intervening variables finally computational experiments reveal that subproblems based on exponential intervening variables result in improved efficiency and accuracy when compared to sao subproblems based on reciprocal intermediate variables and hence the heuristic topology oc method hitherto used this is attributed to the fact that a different exponent is computed for each design variable in the two point exponential approximation we have used using gradient information at the previously visited point copyright 2007 john wiley sons ltd

efficient implementation of minimal polynomial and reduced rank extrapolation methods abstract the minimal polynomial extrapolation mpe and reduced rank extrapolation rre are two very effective techniques that have been used in accelerating the convergence of vector sequences such as those that are obtained from iterative solution of linear and nonlinear systems of equations their definitions involve some linear least squares problems and this causes difficulties in their numerical implementation in this work timewise efficient and numerically stable implementations for mpe and rre are developed a computer program written in fortran 77 is also appended and applied to some model problems among them a hypersonic flow problem involving chemical reactions

structural reanalysis for general layout modifications a procedure for reanalysis of structures subjected to various layout modifications is presented the procedure is based on exact analysis of the initial design it is suitable for all types of layout changes including the general case in which some members and joints are added other members and joints are deleted and some joint coordinates are modified in the particular and challenging case of addition of joints where the number of degrees of freedom is increased a simple reanalysis of a modified initial design is first carried out further changes are then applied to the latter design it is shown that for changes in a limited number of members of a truss structure an exact solution is readily achieved for changes in numerous members of a general structure an approximate solution can be efficiently obtained high quality approximations are demonstrated for various types of layout modifications