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

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

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

on maximal eigenfrequency separation in two material structures the 1d and 2d scalar cases abstract we present a method to maximize the separation of two adjacent eigenfrequencies in structures with two material components the method is based on finite element analysis and topology optimization in which an iterative algorithm is used to find the optimal distribution of the materials results are presented for eigenvalue problems based on the 1d and 2d scalar wave equations two different objectives are used in the optimization the difference between two adjacent eigenfrequencies and the ratio between the squared eigenfrequencies in the 1d case we use simple interpolation of material parameters but in the 2d case the use of a more involved interpolation is needed and results obtained with a new interpolation function are shown in the 2d case the objective is reformulated into a double bound formulation due to the complication from multiple eigenfrequencies it is shown that some general conclusions can be drawn that relate the material parameters to the obtainable objective values and the optimized designs

completely positive measures and feller semigroups on donne d abord une approche unifiee aux mesures completement positives qui jouent un role important dans la theorie des equations de volterra a travers le theoreme de bernstein puis on etudie la solution d une equation de transport liee par une mesure non negative qu elle definit a l equation qui caracterise les noyaux completement positifs on obtient une desorption complete des generateurs de semigroupes de feller induits par de telles mesures on donne une application aux equations de flux thermique lineaire dans des materiaux avec memoire

a multiscale strategy for structural optimization this paper presents a multiscale strategy dedicated to structural optimization the applications concern the study of geometric details such as holes surface profiles etc within the structures with frictional contacts the first characteristic of the method is that it uses a micro macro approach this approach is based on a domain decomposition into substructures and interfaces which involves the resolution of independent micro problems in each substructure and transfers macro information only through the interfaces the second characteristic is the use of a multiresolution strategy in order to reduce the computation cost for problems with evolving design parameters the last characteristic is the capability to model the geometry of details without remeshing thanks to two features the use of a local enrichment method and the use of level set functions to easily modify the boundary of the detail during the optimization process

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

identification of elastic properties of laminates based on experiment design abstract a numerical experimental method for identification of elastic properties of laminated composites from the experimental results is developed it is proposed to use the method of experiment design and the response surface approach to solve the identification inverse problems the response surface approximations are obtained by using the information on the behavior of a structure in the reference points of the experiment design the finite element modeling of the structure is performed only in the reference points therefore a significant reduction about 50 100 times in calculations of the identification functional can be achieved in comparison with the conventional methods of minimization the functional to be minimized describes the difference between the measured and numerically calculated eigenfrequencies of structure by minimizing the functional the identification parameters are obtained it was shown that identification functional is convex if the stiffness matrix linearly depends on unknown parameters the method is employed to identify the elastic properties of cross ply laminates from the measured eigenfrequencies of composite plates

a newly developed qp relaxation method for element connectivity parameterization to achieve stress based topology optimization for geometrically nonlinear structures the aim of this work is to present a novel computational approach to employ the stress based topology optimization method stom to minimize the volume subject to the locally defined stress constraints of a geometrically nonlinear structure in the framework of the element connectivity parameterization ecp method considering the locally defined stress constraints in topology optimization to is a classic and challenging engineering problem and successful optimization procedures have recently been developed using the density based to method for linear elastic structures however no study has yet considered the static failure constraint when using to for a geometrically nonlinear structure therefore the present study develops a novel computational approach for the stom for a geometrically nonlinear structure to successfully optimize a geometrically nonlinear structure the unstable element issue must be properly addressed in addition to the stress singularity issue the existence of a large number of constraints and the highly nonlinear behavior of the local stress constraints to effectively resolve these issues this research adopts the ecp method to interpolate and optimize the connectivities among solid finite elements furthermore we find that a stress singularity issue linked to the local optima issue arises in the ecp method that is different from that of the density based to by investigating the singularity behavior in detail we develop a new qp relaxation method that is suitable for the ecp method to demonstrate the improved capability of the proposed ecp method with the modified qp relaxation several two dimensional to problems are solved

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

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

higher order multi resolution topology optimization using the finite cell method this article presents a detailed study on the potential and limitations of performing higher order multi resolution topology optimization with the finite cell method to circumvent stiffness overestimation in high contrast topologies a length scale is applied on the solution using filter methods the relations between stiffness overestimation the analysis system and the applied length scale are examined while a high resolution topology is maintained the computational cost associated with nested topology optimization is reduced significantly compared with the use of first order finite elements this reduction is caused by exploiting the decoupling of density and analysis mesh and by condensing the higher order modes out of the stiffness matrix

response surface techniques for diffuser shape optimization the design of incompressible diffusers for maximum pressure recovery is used to demonstrate the utility of response surface approximations for design optimization of eow devices two examples involving two and eve design variables are treated with the diffuser wall shapes described by polynomials and b splines in both cases monotonicity conditions drastically reduce the design space in this irregularly shaped space a pool of designs is selected by a d optimality criterion and analyzed by a e nite volume computational euid dynamics cfd code quadratic polynomial response surfaces are then e tted to the pressure recovery coefe cients to improve the prediction accuracy uncertain regressor terms and possible outlier design points are excluded based on statistical tests a standard optimization algorithm is used to e nd the optimal diffuser design from the response surface approximations the optimum diffusers exhibit minimal e ow separation and yield similar wall shapes for the two parameterizations a main asset of the response surface optimization approach lies in the smoothing of noisy response functions therefore theissueofnumericalnoiseincfd results basedon theuseof two different analysis codes is addressed

generalized pointwise bias error bounds for response surface approximations this paper proposes a generalized pointwise bias error bounds estimation method for polynomial based response surface approximations when bias errors are substantial a relaxation parameter is introduced to account for inconsistencies between the data and the assumed true model the method is demonstrated with a polynomial example where the model is a quadratic polynomial while the true function is assumed to be cubic polynomial the effect of relaxation parameter is studied it is demonstrated that when bias errors dominate the bias error bounds characterize the actual error field better than the standard error the bias error bound estimates also help to identify regions in the design space where the accuracy of the response surface approximations is inadequate it is demonstrated that this information can be utilized for adaptive sampling in order to improve accuracy in such regions copyright 2005 john wiley sons ltd

collision integrals for attractive potentials motivated by previous discussions of particle interactions under the manev potential u r r e r2 we construct the collision integrals for attractive potentials u r satisfying the condition u r r2 e as r 0 with e 0 for e 0 we obtain a boltzmann type integral with a collision law allowing spiral interactions and nonunique correspondence between impact parameter and scattering angle for e 0 an additional smoluchowski type coagulation integral arises all these integrals are derived and possible applications are discussed

simulation designs for quadratic response surface models in the presence of model misspecification this article considers the selection of experimental designs for the estimation of second order response surface metamodels in a simulation environment rather than construct designs based on the premise that the postulated model exactly represents the simulated response as is the case in optimal design theory we assume that the estimation process may be biased by the presence of unfitted third order terms we therefore seek to specify experimental plans that address the bias due to possible model misspecification as well as traditional variance considerations the performance measure used for this fit protect scenario is box and draper s design criterion of average mean squared error of predicted response four important classes of response surface experimental plans are examined 1 central composite designs 2 box behnken plans 3 three level factorial experiments and 4 small central composite designs each design class is studied in conjunction with three pseudorandom number assignment str

graphical tools for assessing the sensitivity of response surface designs to model misspecification when comparing different designs for an experiment optimality criteria and other measures often depend on the correctness of the assumed model in this article we develop and illustrate an approach for comparing designs given the potential effect of bias due to an underspecified model we illustrate this approach using graphical summaries of the expected mean squared error emse that allow assessment of the robustness of designs to model misspecification for response surface designs in cuboidal regions the excellent performance of the central composite designs when the quadratic model is correct is tempered when bias is present the box behnken designs demonstrate superiority in the presence of missing cubic terms for a screening design scenario the amount of bias present leads to different conclusions as to which design is best

efficient designs with minimal aliasing for some experimenters a disadvantage of the standard optimal design approach is that it does not consider explicitly the aliasing of specified model terms with terms that are potentially important but are not included in the model for example when constructing an optimal design for a first order model aliasing of main effects and interactions is not considered this can lead to designs that are optimal for estimation of the primary effects of interest yet have undesirable aliasing structures in this article we construct exact designs that minimize the squared norm of the alias matrix subject to constraints on design efficiency we demonstrate use of the method for the construction of screening and response surface designs

response surface approximations for structural optimization response surface methodology can be used to construct global and midrange approximations to functions in structural optimization since structural optimization requires expensive function evaluations it is important to construct accurate function approximations so that rapid convergence may be achieved in this paper techniques to find the region of interest containing the optimal design and techniques for finding more accurate approximations are reviewed and investigated aspects considered are experimental design techniques the selection of the best regression equation intermediate response functions and the location and size of the region of interest standard examples in structural optimization are used to show that the accuracy is largely dependent on the choice of the approximating function with its associated subregion size while the selection of a larger number of points is not necessarily cost effective in a further attempt to improve efficiency different regression models were investigated the results indicate that the use of the two methods investigated does not significantly improve the results finding an accurate global approximation is challenging and sufficient accuracy could only be achieved in the example problems by considering a smaller region of the design space 1998 john wiley sons ltd

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

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

many body problem with quadratic and or inversely quadratic potentials in one and more dimensional spaces some retrospective remarks in the context of an ambient space with an arbitrary number d of dimensions the many body problem consisting of an arbitrary number n of particles confined by a common external harmonic potential realizing a container with soft walls and interacting among themselves and with the environment with arbitrary conservative repulsive forces scaling as the inverse cube of distances displays a peculiar behaviour its effective volume oscillates isochronously without damping we recently discovered this remarkable phenomenon valid in the context of both classical and quantum mechanics and discussed its implications in the context of statistical mechanics and thermodynamics but after publishing these findings we were informed that essentially analogous results had been previously obtained by lyndell bell and lyndell bell in the present paper motivated by the need we felt to acknowledge this fact we also offer some retrospective remarks on the n body problem with quadratic and or inversely quadratic potentials in one and more dimensional space

model robust two level designs using coordinate exchange algorithms and a maximin criterion we propose a candidate list free exchange algorithm that facilitates construction of exact model robust two level experiment designs in particular we investigate two model spaces previously considered in the literature the first assumes that all main effects and an unknown subset of two factor interactions are active but that the experimenter knows the number of active interactions the second assumes that an unknown subset of the main effects and all associated two factor interactions are active previous literature uses two criteria for design construction first maximize the number of estimable models then differentiate between designs equivalent in estimability by choosing the design with the highest average efficiency we adopt a similar strategy but 1 do not impose orthogonality or factor level balance constraints resulting in generally equal or larger numbers of estimable models and 2 use a flexible secondary criterion that maximizes the minimum efficiency we provide results fo

a sequential nonlinear interval number programming method for uncertain structures a sequential nonlinear interval number programming sninp method is suggested to deal with the uncertain optimization problems a general uncertain optimization model is investigated in which the objective function and constraints are both nonlinear and uncertain a nonlinear interval number programming ninp method is employed to transform the uncertain optimization problem into a deterministic two objective optimization problem then using the linear combination method and the constraint penalty function method a deterministic single objective and non constraint optimization problem is formulated in terms of a penalty function combining this ninp method with a modified approximation management framework amf an efficient sninp method is then constructed at each iterative step an approximation optimization problem is created based on the latin hypercube design lhd and the quadratic polynomial response surface approximation rsa and it can then be solved by the ninp method efficiently the trust region method is used to manage the sequence of the approximation optimization problems based on a reliability index an efficient method is suggested to calculate the actual penalty function and whereby the reliability index and based on it the current design space can be updated two numerical examples are presented to demonstrate the effectiveness of the present method

pitfalls of using a single criterion for selecting experimental designs for surrogate construction a good experimental design ed is essential to simultaneously reduce the effect of noise and bias errors however most eds cater to a single criterion and may lead to small gains in that criterion at the expense of large deteriorations in other criteria we use multiple criteria to assess the performance of different popular eds we demonstrate that these eds offer different trade offs and that use of a single criterion is indeed risky in addition we show that popular eds such as latin hypercube sampling lhs and d optimal designs often leave large regions of the design space unsampled even for moderate dimensions we discuss a few possible strategies to combine multiple criteria and illustrate them with examples we show that complementary criteria e g bias handling criterion for variance based designs and vice versa can be combined to improve the performance of eds we demonstrate improvements in the trade offs between noise and bias error by combining a model based criterion like the d optimality criterion and a geometry based criterion like lhs next we demonstrate that selecting an ed from three candidate eds using a suitable error based criterion helped eliminate potentially poor designs finally we show benefits from combining the multiple criteria based strategies that is generation of multiple eds using the d optimality and lhs criteria and selecting one design using a pointwise bias error criterion the encouraging results from the examples indicate that it may be worthwhile studying these strategies more rigorously and in more detail copyright 2007 john wiley sons ltd

one hundred years of the design of experiments on and off the pages of biometrika the earliest important papers on planned experiments in biometrika appeared within a year of each other in 1917 and 1918 roughly speaking one was concerned with design optimality and industrial experiments the other with agricultural trials and blocking we find this approximate division of the subject into two parts helpful in describing its development and growth as a result of the hostility between fisher and karl pearson much of the development of designs for agriculture in the 1920s and 1930s occurred off the pages of biometrika despite this we are able to trace a coherent history of the development of the subject from field trials and response surface methods to clinical trials and bayesian versions of design optimality

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

fast dynamic analysis of complicated beam type structure based on reduced super beam model in this study a new model reduction method based on the fine finite element model of complicated beam type structure is presented which can meet the needs of fast rough estimation of structural global dynamic performances in preliminary design based on the knowledge of deformation characteristics of beam type structures the plane cross section assumption and displacement interpolation function of the beam is introduced to construct a localized physical reduction base vector by dividing the structure into several parts the finite element method structural nodal degrees of freedom in each part are projected onto the nodal deflection and rotation degree of freedom of two master nodes at its two ends the part of the structure is reduced into a super beam element a free free reduced super beam model with fewer degrees of freedom than the original complicated one is obtained by assembling the super beam elements in series the accuracy of the reduced super beam model is further improved by modifying the

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

on subordinated holomorphic semigroups if e is a uniformly bounded c0 semigroup on a complex banach space x then a 0 a 1 generates a holomorphic semigroup on x and e is subordinated to e through the levy stable density function this was proved by yosida in 1960 by suitably deforming the contour in an inverse laplace transform representation using other methods we exhibit a large class of probability measures such that the subordinated semigroups are always holomorphic and obtain a necessary condition on the measure s laplace transform for that to be the case we then construct probability measures that do not have this property

existence and regularity for a class of integrodifferential equations of parabolic type the method we use rests on the inversion of the formal laplace transform of r and allows one to analyze the regularity of the solution u problem 1 1 has been studied by several authors using various methods see for instance l 18 211 the laplace transform approach presented here has been used in s 7 9 14 153 in our previous papers s 7 93 we have in fact analyzed a more general situation while here we take full 36 0022 247x 85 3 00

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

a mean squared error criterion for the design of experiments in estimating a response surface over a design region of interest mean squared error can arise both from sampling variance and bias introduced by model inadequacy the criterion adopted here for experimental design attempts to protect against bias resulting from a large class of deviations from the assumed model two algorithms are proposed for the construction of either approximate or exact designs and an example is given

a class of globally convergent optimization methods based on conservative convex separable approximations this paper deals with a certain class of optimization methods based on conservative convex separable approximations ccsa for solving inequality constrained nonlinear programming problems each generated iteration point is a feasible solution with lower objective value than the previous one and it is proved that the sequence of iteration points converges toward the set of karush kuhn tucker points a major advantage of ccsa methods is that they can be applied to problems with a very large number of variables say 104 105 even if the hessian matrices of the objective and constraint functions are dense

design sensitivity analysis for shape optimization based on the lie derivative abstract the paper presents a theoretical framework for the shape sensitivity analysis of systems governed by partial differential equations the proposed approach based on geometrical concepts borrowed from differential geometry shows that sensitivity of a performance function i e any function of the solution of the problem with respect to a given design variable can be represented mathematically as a lie derivative i e the derivative of that performance function along a flow representing the continuous shape modification of the geometrical model induced by the variation of the considered design variable theoretical formulae to express sensitivity analytically are demonstrated in detail in the paper and applied to a nonlinear magnetostatic and a linear elastic problem following both the direct and the adjoint approaches following the analytical approach one linear system of which only the right hand side needs be evaluated the system matrix being known already has to be solved for each of the design variables in the direct approach or for each performance functions in the adjoint approach a substantial gain in computation time is obtained this way compared to a finite difference evaluation of sensitivity which requires solving a second nonlinear system for each design variable this is the main motivation of the analytical approach there is some freedom in the definition of the auxiliary flow that represents the shape modification we present a method that makes benefit of this freedom to express sensitivity locally as a volume integral over a single layer of finite elements connected to both sides of the surfaces undergoing shape modification all sensitivity calculations are checked with a finite difference in order to validate the analytic approach convergence is analyzed in 2d and 3d with first and second order finite elements

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

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

a sufficient condition for the carasso kato theorem so that f y 1 p dy cxz in 0 2 then remark 2 of 1 p 298 implies that a 0 p t x 0 for t 0 x 0 therefore for c 0 the inverse laplace transform for 0 1 leads to 2 1 theorem 7 6a of 2 p 69 in addition we add the following correction a lines 5 1 from bottom on p 335 will be changed as follows it is called the subordinated semigroup define the operator x a by

pointwise bias error bounds and min max design for response surface approximations bounds on response surface approximation errors as a result of model inadequacy bias error are presented and a design of experiments minimizing the maximal bias error is proposed the bias error bounds are considered as a tool to identify locations in the design space where the accuracy of the approximation fitted on a given design of experiments might be poor two approaches to characterize the bias error assume that the functional form of the true model is known and seek at each point in design space worst case bounds on the absolute error the first approach is implemented before data generation this data independent error bound can easily be implemented in a search for a design of experiments that minimize the bias error bound as it requires very little computation the second approach is to be used posterior to the data generation and provides tightened error bound consistent with the data this data dependent error bound requires the solution of two linear programming problems at each point the data independent error bound for design of experiments of two variable examples is demonstrated randomly generated polynomials in two variables are then used to validate the data dependent bias error bound distribution although the two approaches are used in conjunction in the given examples the data independent error bound design of experiment is not a prerequisite for the application of the data dependent error bounds in search for the high bias error regions

model robust response surface designs scaling two level factorials summary response surface methods use simple graduating functions to study the relationship between an experimental response variable and a set of continuous explanatory variables in designing a response surface study an experimenter must decide how far apart to set the levels of each factor i e how to scale the design a good choice should be sensitive to the fact that the graduating function is only an approximation to the true response function a bayesian model is proposed that makes explicit assumptions about the inadequacy of an assumed model and a design criterion based on the model leads to reasonable choices of scale for two level factorial designs the choice of scale is found to be insensitive to the prior distributions in the model

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

analytic resolvent operators for integral equations in banach space on etudie l equation integrodifferentielle x t a 0 x t 0 t b t s x s ds f t t 0 x 0 x 0 ed a x et l equation integrale x t 0 t a t s x s ds f t dans un espace de banach x les operateurs a a 0 b t et a t sont des operateurs clos sur x a domaine dense

on subordination of holomorphic semigroups abstract we prove that for any bernstein function the operator a generates a bounded holomorphic c 0 semigroup e t a t 0 on a banach space whenever a does this answers a question posed by kishimoto and robinson moreover giving a positive answer to a question by berg boyadzhiev and de laubenfels we show that e t a t 0 is holomorphic in the holomorphy sector of e t a t 0 and if e t a t 0 is sectorially bounded in this sector then e t a t 0 has the same property we also obtain new sufficient conditions on in order that for every banach space x the semigroup e t a t 0 on x is holomorphic whenever e t a t 0 is a bounded c 0 semigroup on x these conditions improve and generalize well known results by carasso kato and fujita

on vlasov manev equations ii local existence and uniqueness we prove that the initial value problem associated with the vlasov manev system a vlasov equation in which a correction of type e r 2 is added to the newtonian or coulomb potential has a local in time classical and unique solution for sufficiently regular initial data

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

a novel multi objective optimization method based on an approximation model management technique in this paper a novel multi objective optimization method is suggested based on an approximation model management technique it is a sequential approximation method in which a multi objective optimization with approximation models subject to design variable move limits is iterated until convergence in each iteration step the approximation models are constructed by the response surface approximations with the samples which are obtained from the design of experiments and a pareto optimal set predicted by the approximations is identified through a multi objective genetic algorithm according to the prediction of the approximation models a move limits updating strategy is employed to determine the design variable move limits for the next iteration at the end of each iteration step some uniform distributed points chosen from the predictive pareto optimal frontier are verified by the high fidelity models and the obtained actual pareto optimal set is stored in an external archive the high efficiency of the present method is demonstrated by four different test functions and two engineering applications

stability and uniqueness for the spatially homogeneous boltzmann equation with long range interactions in this paper we prove some a priori stability estimates in weighted sobolev spaces for the spatially homogeneous boltzmann equation without angular cutoff covering all physical collision kernels these estimates are conditional on some regularity estimates on the solutions and therefore reduce the stability and uniqueness issue to one of proving suitable regularity bounds on the solutions we then prove such regularity bounds for a class of interactions including the so called non cutoff and non mollified hard potentials and moderately soft potentials in particular we obtain the first result of global existence and uniqueness for these long range interactions