multiscale approach for optimal design in conductivity of composite materials this paper discusses the multiscale approach for optimal design in conductivity of composite materials the homogenization method and the multiscale asymptotic method are presented the associated numerical algorithms and the convergence analysis are provided finally numerical examples are carried out to confirm the validity of the algorithm

minimum length scale control in structural topology optimization based on the moving morphable components mmc approach abstract a novel approach which can control the minimum length scale in topology optimization in a straightforward and explicit way is proposed in the present paper this approach is constructed under the so called moving morphable components mmc based solution framework where optimized structural topology can be found by changing the shapes and layout of a set of trapezoid shaped structural components on a fixed finite element mesh the extended finite element method xfem is employed for structural response analysis and shape sensitivity information is obtained by carrying out numerical integration along the structural boundary a precision definition of the minimum length scale of a structure is also suggested based on the proposed solution framework compared with existing approaches the proposed approach can achieve minimum length scale control by simply setting lower bounds on a set of geometric design variables only a small number of purely geometric constraints imposed on the sizes of intersection regions should be considered explicitly in order to get a complete minimum length scale control numerical examples demonstrate the effectiveness of the proposed method

higher order weighted sobolev spaces on the real line for strongly degenerate weights application to variational problems in elasticity of beams abstract for one dimensional interval and integrable weight function w we define via completion a weighted sobolev space h w m p of arbitrary integer order m the weights in consideration may suffer strong degeneration so that in general functions u from h w m p do not have weak derivatives this contribution is focussed on studying the continuity properties of functions u at a chosen internal point x 0 to which we attribute a notion of criticality of order k and with respect to the weight w for non critical points x 0 we formulate a local embedding result that guarantees continuity of functions u or their derivatives conversely we employ duality theory to show that criticality of x 0 furnishes a smooth approximation of functions in h w m p admitting jump type discontinuities at x 0 the work concludes with demonstration of established results in the context of variational problem in elasticity theory of beams with degenerate width distribution

color level sets a multi phase method for structural topology optimization with multiple materials in this paper we address the problem of structural shape and topology optimization in a multi material domain a level set method is employed as an alternative approach to the popular homogenization based methods of rule of mixtures for multi material modeling a multi phase level set model is adapted for material and topology representation this model eliminates the need for a material interpolation or phase mixing scheme it only requires m level set functions to represent a structure of n 2m different material phases in a principle similar to combining colors from the three primary colors therefore this multi phase model may be referred to as a color level set representation which has its unique benefits it is flexible to handle complex topologies it substantially reduces the number of model functions when n 3 it automatically avoids the problem of overlap between material phases of a conventional partitioning approach we describe numerical techniques for efficient and robust implementation of the method by embedding a rectilinear grid in a fixed finite element mesh defined on a reference design domain this would separate the issues of accuracy in numerical calculations of the physical equation and in the level set model propagation a gradient projection method is described for incorporating multiple constraints in the problem finally the benefits and the advantages of the developed method are illustrated with several 2d examples of mean compliance minimization of multi material structures

an investigation concerning optimal design of solid elastic plates abstract we consider the problem of maximizing the integral stiffness of solid elastic plates described by thin plate theory assuming the material volume and plate domain to be given we use the plate thickness function as the design variable and take both maximum and minimum allowable thickness values into account on the basis of a convenient tensorial formulation of the problem where the governing equations are derived by variational analysis and constitute necessary conditions for stationarity we develop an efficient and quite general numerical algorithm by means of which a number of stationary solutions for rectangular and axisymmetric annular plates with various boundary conditions are obtained these numerical results enable us to investigate the optimization problem itself in terms of its major parameters particularly the maximum and minimum values specified for the plate thickness for problems associated with large ratios between these constraint values plate designs with significant integral stiffeners are obtained we find however that these designs are only local optima and that a global optimal plate thickness function does generally neither exist within the class of smooth functions nor within the class of smooth functions with a finite number of discontinuities in order to determine a global optimal solution associated with given thickness constraint values it is therefore necessary to change the optimal design formulation with implications for a number of similar two dimensional optimization problems our results offer valuable indications of the lines along which such changes should be performed

optimal design of elastic plates with a constraint on the slope of the thickness function abstract a constraint on the maximum absolute value of the slope of the thickness function is found to have a profound influence on the problem of optimal design of axisymmetric elastic plates by securing a unique regular solution it is also shown that except for the case of axisymmetric deformation the constraint is active everywhere and the optimal design is a plate subdivided into annular regions of constant slope equal to the maximum value permitted

on the use of consistent approximations for the optimal design of beams this paper presents a discretization strategy based on the concept of consistent approximations for certain optimal beam design problems where the beam is modeled using euler bernoulli beam theory it is shown that any accumulation point of the sequence of the stationary points of the family of resulting approximating problems is a stationary point of the original infinite dimensional problem the construction of approximating problems requires the development of a relaxation of constraints to ensure existence of solutions the numerical solution of the approximating problems by means of nonlinear programming algorithms that are not scale invariant must be preceded by a change of variables to guard against deterioration of performance the use of such approximating problems in conjunction with a diagonalization strategy is illustrated by a numerical example

linear precoding via conic optimization for fixed mimo receivers in this paper the problem of designing linear precoders for fixed multiple input multiple output mimo receivers is considered two different design criteria are considered in the first the transmitted power is minimized subject to signal to interference plus noise ratio sinr constraints in the second the worst case sinr is maximized subject to a power constraint it is shown that both problems can be solved using standard conic optimization packages in addition conditions are developed for the optimal precoder for both of these problems and two simple fixed point iterations are proposed to find the solutions that satisfy these conditions the relation to the well known uplink downlink duality in the context of joint transmit beamforming and power control is also explored the proposed precoder design is general and as a special case it solves the transmit rank one beamforming problem simulation results in a multiuser system show that the resulting precoders can significantly outperform existing linear precoders

investigating duality on stability conditions this paper is devoted to investigate the role played by duality in stability analysis of linear time invariant systems we seek for a dual statement of a recently developed method for generating stability conditions which combines lyapunov stability theory with finsler s lemma this method developed in the time domain is able to generate a set of primal equivalent stability tests involving extra multipliers the resulting tests have very attractive properties stability is characterized via linear matrix inequalities and we use optimization theory to obtain the duals the dual problems are given a frequency domain interpretation

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

a review of an optimal design problem for a plate of variable thickness we revisit a classic design problem for a plate of variable thickness under the model of kirchhoff our main contribution has two goals one is to provide a rather general existence result under a main assumption on the structure of the tensor of material constants the other focuses on providing a minimal number of additional design variables for a relaxation of the problem when that assumption on the tensor of elastic constants does not hold in both situations the cost functional can be pretty general

explicit feature control in structural topology optimization via level set method abstract the present paper aims to address a long standing and challenging problem in structural topology optimization explicit feature control of the optimal topology the basic idea is to resort to the level set solution framework and impose constraints on the extreme values of the signed distance level set function used for describing the topology of the structure numerical examples are also presented and discussed to illustrate the effectiveness of the proposed approach

the coc algorithm part ii topological geometrical and generalized shape optimization abstract after outlining analytical methods for layout optimization and illustrating them with examples the coc algorithm is applied to the simultaneous optimization of the topology and geometry of trusses with many thousand potential members the numerical results obtained are shown to be in close agreement up to twelve significant digits with analytical results finally the problem of generalized shape optimization finding the best boundary topology and shape is discussed

on some necessary conditions of optimality for a nonlocal variational principle the aim of this work is to deduce optimality conditions for a nonlocal variational principle in the one dimensional scalar case we consider the relaxation of the problem in terms of young measures this relaxation is a new problem where we perform variations to derive optimality conditions and those conditions yield explicit information about minimizers in the homogeneous case it also provides a method capable of finding minimizers for some specific problems

reinforced mindlin plates with extremal stiffness for a prescribed area fraction of stiffeners we characterize the set of stiffener reinforced mindlin plates with extremal overall stiffness the method rests upon the derivation of optimal bounds of the hashin shtrikman type our method is distinct from the usual hashin shtrikman approach we make use of the underlying variational structure behind the hashin shtrikman method to show that the use of a comparison material is redundant we do this by proceeding directly and express the equilibrium equations in terms of positive definite integral operators the positivity of the operators is used to obtain a new hilbert space variational principle for the effective stiffness the associated bounds are shown to be realized by effective rigidities associated with hierarchical laminar arrangements of stiffeners

least weight design of perforated elastic plates ii abstract the paper investigates implications of some recent mathematical developments in the fields of shape optimization and relaxation of variational problems considering the least weight design of perforated elastic plates in either flexure or plane stress for a prescribed compliance it is shown that at low rib densities microstructures consisting of a combination of first and second order infinitesimal ribs is superior to those consisting of purely first order infinitesimal ribs moreover it is indicated that thin ribs of infinite length thickness ratio do not contribute significantly to the stiffness in a direction normal to their plane on the basis of this conclusion a simple specific cost function is derived and then it is used in the design of circular uniformly loaded perforated plates with zero value of poisson s ratio as a basis for comparison several intuitively selected topographies are optimized for the case of simply supported plates and in part ii of this study a variational analysis is used to obtain the optimal solutions for plates with simply supported clamped or loaded edges

sliding regimes and anisotropy in optimal design of vibrating axisymmetric plates abstract this paper deals with optimal design of solid elastic axisymmetric plates performing free transverse vibrations it is the objective to determine the plate thickness distribution from the condition that the plate volume is minimized for a given value of the fundamental natural frequency or for a given higher order natural frequency that corresponds to a vibration mode with a prescribed number of nodal diameters it is found that the weierstrass necessary condition for optimality is generally not satisfied for a traditional formulation of this problem and that the optimal design is characterized by a sliding regime of control where the plate thickness exhibits an infinite number of discontinuities as a system of infinitely thin circumferential stiffeners are formed on the optimal axisymmetric plate this inherent anisotropy of the optimal design is taken into account in a regularization of the initial optimization problem by establishing the tensorial character of the plate bending rigidity and using the concentration of thin circumferential stiffeners as a new design variable control it is shown that the new formulation of the problem can be solved numerically and examples of optimal designs are presented in the paper

structural optimization of thin elastic plates the three dimensional approach the natural way to find the most compliant design of an elastic plate is to consider the three dimensional elastic structures which minimize the work of the loading term and pass to the limit when the thickness of the design region tends to zero in this paper we study the asymptotics of such a compliance problem imposing that the volume fraction remains fixed no additional topological constraint is assumed on the admissible configurations we determine the limit problem in different equivalent formulations and we provide a system of necessary and sufficient optimality conditions these results were announced in bouchitte et al c r acad sci paris ser i 345 713 718 2007 furthermore we investigate the vanishing volume fraction limit which turns out to be consistent with the results in bouchitte and fragala arch rat mech anal 184 257 284 2007 siam j control optim 46 1664 1682 2007 finally some explicit computation of optimal plates are given

applications of the method of partial inverses to convex programming decomposition a primal dual decomposition method is presented to solve the separable convex programming problem convergence to a solution and lagrange multiplier vector occurs from an arbitrary starting point the method is equivalent to the proximal point algorithm applied to a certain maximal monotone multifunction in the nonseparable case it specializes to a known method the proximal method of multipliers conditions are provided which guarantee linear convergence

on cal h _ infty filtering for discrete time takagi sugeno fuzzy systems in this paper we present a new design method for the h filtering of discrete time takagi sugeno ts fuzzy systems the parameters of the filter are assumed to be linearly dependent on the normalized fuzzy weighting functions by using an augmentation technique the design parameters are incorporated into a filtering error system in order to derive less conservative results and reduce the filtering error a new condition is established to ensure the h performance of the filtering error system by introducing more slack matrices the solution set of the filter parameters is extended by using a partitioning technique a design method for the h filter is proposed in terms of linear matrix inequalities lmis an example demonstrates the improvement of the proposed design method over an existing approach

topology design with optimized self adaptive materials significant performance improvements can be obtained if the topology of an elastic structure is allowed to vary in shape optimization problems we study the optimal shape design of a two dimensional elastic continuum for minimum compliance subject to a constraint on the total volume of material the macroscopic version of this problem is not well posed if no restrictions are placed on the structure topology relaxation of the optimization problem via quasiconvexification or homogenization methods is required the effect of relaxation is to introduce a perforated microstructure that must be optimized simultaneously with the macroscopic distribution of material

a banach lattice approach to convergent integrably bounded set valued martingales and their positive parts denote by cf x the set of all nonempty convex closed subsets of a separable banach space x let be a complete probability space and denote by l1 cf x the complete metric space of equivalence classes of a e equal integrably bounded cf x valued functions for any preassigned filtration i we describe the space of convergent integrably bounded cf x valued martingales in terms of the closure of i 1 l1 i cf x in l1 cf x in particular we provide a formula to calculate the join of two such martingales and the positive part of such a martingale our object is achieved by considering the more general setting of a near vector lattice s d endowed with a riesz metric d by means of radstrom s embedding theorem for such spaces a link is established between the space of convergent martingales in s and the space of convergent martingales in the radstrom completion r s of s this link provides information about the former space of martingales via known properties of measure free martingales in riesz normed vector lattices applicable to r s we also apply our general results to the spaces of convergent ck x valued martingales where ck x denotes the set of all nonempty convex compact subsets of x

d stability of polynomial matrices necessary and sufficient conditions are formulated for the zeros of an arbitrary polynomial matrix to belong to a given region d of the complex plane the conditions stem from a general optimization methodology mixing quadratic and semidefinite programming lfrs and rank one lmis they are expressed as an lmi feasibility problem that can be tackled with widespread powerful interior point methods most importantly the d stability conditions can be combined with other lmi conditions arising in robust stability analysis

an elementary proof that the biharmonic green function of an eccentric ellipse changes sign p r garabedian showed in 1951 that the green function for the biharmonic boundary value problem with vanishing dirichlet data changes sign in case the domain is a sufficiently eccentric ellipse this refuted a conjecture made by j hadamard in 1908 the proof of garabedian was based on kernel functions the present note gives an elementary proof

material cloud method for topology optimization material cloud method mcm a new approach for topology optimization is presented in mcm an optimal structure can be obtained by manipulating the sizes and positions of material clouds which are material patches with finite sizes and constant material densities the optimal distributions of material clouds can be obtained by mcm using fixed background finite element meshes in the numerical analysis procedure only active elements where more than one material cloud is contained are treated optimal material distribution can be element wise extracted from the distribution of material clouds with mcm an expansion reduction procedure of design domain can be naturally realized through movements of material clouds so that a true optimal solution can be found without any significant increase of computational costs it is also shown that a clear material distribution with narrow region of intermediate density can be obtained with relatively fast convergence several numerical examples are shown some of the results are compared with those of the traditional density distribution method ddm copyright 2005 john wiley sons ltd

eigenfrequency optimized 3d continua with possibility for cavities abstract eigenfrequency optimization for 3d continua is formulated and exemplified by the geometry and boundary conditions of a thick plate numerical finite element models are based on four node tetrahedra and results from subspace iterations give directly the basis for the continuum redesign the 3d modeling with a large number of elements has the possibility in optimal design to obtain as found not only holes but also cavities in the continuum sensitivity analysis is presented on the element level with simple physical interpretation of the involved terms this general result has general value for control of eigenfrequencies it is found that in the combination of partial differentiation with the chain rule of differentiation a specific notation is needed and a suggestion is presented the optimization method is based on a derived optimality criterion and as such the maximization problem change to a problem of determining a design with uniform values of this criterion nonlinear stiffness interpolation may be a physical reality a two parameter interpolation function is incorporated analytical also in the sensitivity analysis and the optimality criterion but without focusing on 1 0 optimal solutions two cases of boundary conditions two cases of total amount of material and cases of linear and nonlinear stiffness interpolation are studied

optimizing zero forcing precoders for mimo broadcast systems in this paper we develop optimization techniques for linear zero forcing zf multiple input multiple output mimo broadcast bc precoders a computationally efficient technique based on qr update algorithms for implementing this optimization is then proposed the application of the proposed zf precoders and decoders to systems with both large and small numbers of users is considered the proposed optimization technique is also shown to perform very well in conjunction with nonlinear tomlinson harashima precoding both coded and uncoded performances are considered

generalized channel inversion methods for multiuser mimo systems block diagonalization bd is a well known precoding method in multiuser multi input multi output mimo broadcast channels this scheme can be considered as a extension of the zero forcing zf channel inversion to the case where each receiver is equipped with multiple antennas one of the limitation of the bd is that the sum rate does not grow linearly with the number of users and transmit antennas at low and medium signal to noise ratio regime since the complete suppression of multi user interference is achieved at the expense of noise enhancement also it performs poorly under imperfect channel state information in this paper we propose a generalized minimum mean squared error mmse channel inversion algorithm for users with multiple antennas to overcome the drawbacks of the bd for multiuser mimo systems we first introduce a generalized zf channel inversion algorithm as a new approach of the conventional bd applying this idea to the mmse channel inversion for identifying orthonormal basis vectors of the precoder and employing the mmse criterion for finding its combining matrix the proposed scheme increases the signal to interference plus noise ratio at each user s receiver simulation results confirm that the proposed scheme exhibits a linear growth of the sum rate as opposed to the bd scheme for block fading channels with four transmit antennas the proposed scheme provides a 3 db gain over the conventional bd scheme at 1 frame error rate also we present a modified precoding method for systems with channel estimation errors and show that the proposed algorithm is robust to channel estimation errors

optimization of clamped plates with discontinuous thickness we consider a new variational method for a clamped plate model and related shape optimization problems our approach allows the study of plates with discontinuous thickness

regularized formulation for optimal design of axisymmetric plates abstract this paper presents a regularized mathematical formulation necessary conditions of optimality and solutions of problems of optimal design of solid elastic axisymmetric plates of prescribed total material volume single purpose design criteria of minimum static compliance maximum stiffness and maximum frequency of free transverse vibrations are considered the regularization which alleviates some anomalies and difficulties encountered earlier in plate optimization problems is based on a new compound plate model with two simultaneous design variables namely variable thickness of a solid part of the plate and variable concentration of a dense system of thin integral stiffeners attached to the solid plate part a numerical optimality criterion based method of solution is developed for the problem and several optimal designs are presented the results are compared with results obtained from optimal design formulations applied heretofore and substantiate the superiority of the new regularized formulation

generalised nonlinear l 2 l filtering of discrete time markov jump descriptor systems this paper is devoted to the l2 l filter design problem for nonlinear discrete time markov jump descriptor systems subject to partially unknown transition probabilities the partially unknown transition probabilities are modelled via the polytopic uncertainties the objective is to propose a generalised nonlinear full order filter design method such that the resulting filtering error system is regular casual and stochastically stable and a prescribed l2 l attenuation level is satisfied for the autonomous discrete time descriptor system subject to lipschitz nonlinear condition by introducing some slack matrix variables a mode dependent stability criterion is established it cannot only ensure the regularity casuality and stochastic stability of system but also guarantee the considered system has a unique solution based on this obtained criterion a sufficient condition in terms of linear matrix inequalities lmis is derived such that the resulting filtering error system is regular casual s

zero forcing methods for downlink spatial multiplexing in multiuser mimo channels the use of space division multiple access sdma in the downlink of a multiuser multiple input multiple output mimo wireless communications network can provide a substantial gain in system throughput the challenge in such multiuser systems is designing transmit vectors while considering the co channel interference of other users typical optimization problems of interest include the capacity problem maximizing the sum information rate subject to a power constraint or the power control problem minimizing transmitted power such that a certain quality of service metric for each user is met neither of these problems possess closed form solutions for the general multiuser mimo channel but the imposition of certain constraints can lead to closed form solutions this paper presents two such constrained solutions the first referred to as block diagonalization is a generalization of channel inversion when there are multiple antennas at each receiver it is easily adapted to optimize for either maximum transmission rate or minimum power and approaches the optimal solution at high snr the second known as successive optimization is an alternative method for solving the power minimization problem one user at a time and it yields superior results in some e g low snr situations both of these algorithms are limited to cases where the transmitter has more antennas than all receive antennas combined in order to accommodate more general scenarios we also propose a framework for coordinated transmitter receiver processing that generalizes the two algorithms to cases involving more receive than transmit antennas while the proposed algorithms are suboptimal they lead to simpler transmitter and receiver structures and allow for a reasonable tradeoff between performance and complexity

zero forcing precoding and generalized inverses we consider the problem of linear zero forcing precoding design and discuss its relation to the theory of generalized inverses in linear algebra special attention is given to a specific generalized inverse known as the pseudo inverse we begin with the standard design under the assumption of a total power constraint and prove that precoders based on the pseudo inverse are optimal among the generalized inverses in this setting then we proceed to examine individual per antenna power constraints in this case the pseudo inverse is not necessarily the optimal inverse in fact finding the optimal matrix is nontrivial and depends on the specific performance measure we address two common criteria fairness and throughput and show that the optimal generalized inverses may be found using standard convex optimization methods we demonstrate the improved performance offered by our approach using computer simulations

scale effects in the optimal design of a microstructured medium against buckling abstract certain classes of problems in optimal structural design lead naturally to the introduction of periodic microstructured media as the basis material for the construction of a mechanical element the unit cell size of these microstructures cannot be arbitrarily small as suggested by the pertaining optimization analyses up to date and has to be related to the structure s overall dimensions one physically important mechanism that provides such microstructure size limitations is elastic buckling an analytically tractable model of an infinite periodic rectangular planar frame with axially compressed beams is used to study the optimal buckling loads for any given design one can find a critical stress above which buckling instability occurs in addition one can also find the region in the design space for which the optimal critical mode is a global one i e its characteristic length is much larger than the unit cell size in this region of the design space one can safely use the homogenized material properties to describe the medium for they provide all the information needed to predict a global buckling instability in addition to the detailed parametric study for the model problem investigated here implications for the optimal design against buckling of more general structures are also briefly discussed

a duality approach in the optimization of beams and plates we introduce a class of nonlinear transformations called resizing rules which associate with optimal shape design problems certain equivalent distributed control problems while preserving the state of the system this puts into evidence the duality principle that the class of system states that can be achieved under a prescribed force via modifications of the structure shape of the system can be obtained as well via the modifications of the force action under a prescribed structure we apply such transformations to the optimization of beams and plates and in the simply supported or cantilevered cases the obtained control problems are even convex in all cases we establish existence theorems for optimal pairs by assuming only boundedness conditions moreover in the simply supported case we also prove the uniqueness of the global minimizer a general algorithm that iterates between the original transformed problems is introduced and studied the applications also include the case of variational inequalities

solving large scale sparse semidefinite programs for combinatorial optimization we present a dual scaling interior point algorithm and show how it exploits the structure and sparsity of some large scale problems we solve the positive semidefinite relaxation of combinatorial and quadratic optimization problems subject to boolean constraints we report the first computational results of interior point algorithms for approximating maximum cut semidefinite programs with dimension up to 3 000

on non smoothness in optimal design of solid elastic plates abstract in the present paper minimum compliance design problems of thin solid elastic plates are discussed we follow up indications provided by numerical results obtained in a recent paper 1 and propose a new plate model where a uniform plate is equipped with an infinite number of infinitely thin integral stiffeners on the basis of this new plate model numerical and analytical investigations of a new formulation of the minimum compliance design problem are carried out it is demonstrated that the new formulation is under certain conditions superior to the corresponding traditional formulation for determining a possible global optimal solution for solid plates since both the new formulation and the traditional formulation are based on classical thin plate theory the superiority of the new plate model over the corresponding smooth one directly implies that optimal thickness distributions for thin solid elastic plates are generally not smooth functions but functions with an infinite number of discontinuities

nonlinear structural design using multiscale topology optimization part i static formulation we present a hierarchical multiscale design framework that couples computational homogenization with topology optimization to design a composite structure s microstructure to optimize its nonlinear elastostatic behavior to generate a well posed macroscopic topology optimization problem we use relaxation which requires homogenization to relate the macroscopic homogenized response to its microstructure and because closed form expressions for homogenized properties generally do not exist for materials with nonlinear response we rely on computational homogenization to evaluate them to optimize the homogenized properties of the unit cell we again use topology optimization and to make this unit cell optimization problem well posed we use restriction and thereby obtain a minimum microstructural length scale the coupled nonlinear analyzes and optimization problems are computationally intensive tasks that we resolve with a scalable parallel framework based on a single program multiple data programming paradigm numerical implementation is discussed and examples are provided

homogenization based topology optimization for high resolution manufacturable micro structures summary this paper presents a projection method to obtain high resolution manufacturable structures from efficient and coarse scale homogenization based topology optimization results the presented approach bridges coarse and fine scale such that the complex periodic microstructures can be represented by a smooth and continuous lattice on the fine mesh a heuristic methodology allows control of the projected topology such that a minimum length scale on both solid and void features is ensured in the final result numerical examples show excellent behavior of the method where performances of the projected designs are almost equal to the homogenization based solutions a significant reduction in computational cost is observed compared to conventional topology optimization approaches

optimal design and relaxation of variational problems iii abstract this paper has attempted a synthesis of three subjects that have developed separately optimal design homogenization and relaxation in the calculus of variations the underlying theme is that of oscillations they occur with certain definite patterns in minimizing sequences for the variational problem the same patterns recur in nearly optimal designs and in the coefficients of the equation being homogenized each problem is resolved by determining the structure of those oscillations and above all their macroscopic averages it is those averages that solve the relaxed problem they also determine the optimal design and the solution of the homogenized equation we emphasize also the role of optimization the homogenized equations and composite materials of interest here come not from arbitrary mixtures but from those that are extremal since they correspond to minimizing sequences for the variational problem the effective properties of these composites attain the optimal bounds for given materials in fixed proportions

second order energies on thin structures variational theory and non local effects abstract for a given positive measure on r n we consider integral functionals of the kind f u r n f x u 2 u d u c 0 r n and we study their relaxation with respect to the l p topology p being the growth exponent of f to obtain the relaxed energy f we develop a suitable theory of second order intrinsic operators related to a cosserat vector field and to a curvature tensor our main theorem shows that the functional f is in general a non local one this unexpected feature occurs even in very simple examples when is the one dimensional hausdorff measure over a closed lipschitz curve in the plane

topological design for vibrating structures the topological optimization technique using micro scale voids with the homogenization method for stress analysis of perforated structures has been applied to solve stiffness maximization problem with success here the homogenization design technique is extended to design problems concerning vibrating structures an extended optimization algorithm is also derived to maximize a set of eigenvalues as well as to identify the topology design for specified eigenvalues to characterize forced vibration of a structure

stability results for discrete time linear systems with markovian jumping parameters stability results for discrete time linear systems subject to random jumps in the parameters are obtained first necessary and sufficient conditions for mean square stability mss including the case in which the system is driven by an independent wide sense stationary random sequence are derived it is shown that mss is equivalent to the spectral radius of an augmented matrix being less than one or to the existence of a solution of a certain lyapunov equation in addition it is shown that the lyapunov equation can be derived in four equivalent forms and as a by product each one gives risc to an easier to check sufficient condition these results give inter alia a unified and rather complete picture for mss of markovian jump linear systems next we derive sufficient conditions for almost sure stability of the noiseless ease finally we conclude by presenting an illustrative application to adaptive filtering where a mild condition for almost sure convergence is provided

existence for shape optimization problems in arbitrary dimension we discuss some existence results for optimal design problems governed by second order elliptic equations with the homogeneous neumann boundary conditions or with the interior transmission conditions we show that our continuity hypotheses for the unknown boundaries yield the compactness of the associated characteristic functions which in turn guarantees convergence of any minimizing sequences for the first problem in the second case weaker assumptions of measurability type are shown to be sufficient for the existence of the optimal material distribution we impose no restriction on the dimension of the underlying euclidean space

homogenization and optimal bounds in linear elasticity in their celebrated paper of 1963 hashin shtrikman 1 addressed the problem of determining optimal bounds for the bulk and shear moduli of a statistically isotropic elastic composite material with arbitrary isotropic phase geometry they derived a set of bounds for these moduli in the physically meaningful case of three dimensional elasticity in the case of a two phase composite let k 1 1 and k 2 2 respectively denote the bulk and shear moduli for the first and the second phase let k denote their analogues for the composite and let 0 stand for the volume fraction of the first phase in the composite under the ordering restriction that both

explicit three dimensional topology optimization via moving morphable void mmv approach abstract three dimensional 3d topology optimization problems always involve huge numbers of degrees of freedom dofs in finite element analysis fea and design variables in numerical optimization respectively this will inevitably lead to large computational efforts in the solution process in the present paper an efficient and explicit topology optimization approach which can reduce not only the number of design variables but also the number of degrees of freedom in fea is proposed based on the moving morphable voids mmvs solution framework this is achieved by introducing a set of geometry parameters e g control points of b spline surfaces to describe the boundary of a structure explicitly and removing the unnecessary dofs from the fe model at every step of numerical optimization numerical examples demonstrate that the proposed approach does can overcome the bottleneck problems associated with a 3d topology optimization problem in a straightforward way and enhance the solution efficiency significantly

a gradient based parameter free approach to shape optimization in shape optimization the independent node movement approach wherein finite element node coordinates are used directly as design variables allows the most freedom for shape change and avoids the time consuming parameterization preprocess however this approach lacks a length scale control that is necessary to ensure a well posed shape optimization problem and avoid numerical instability motivated by the success of filtering techniques that impose minimum length scales in topology optimization we propose a scheme with consistent filtering to introduce a length scale and thereby ensure smoothness in shape optimization while preserving the advantages of the independent node movement approach

integral representation of convex functionals on a space of measures abstract in duality pairs such as m b c 0 and w 1 p w 0 1 p a convex integral functional on the space of functions has a polar which admits an integral representation this representation is the sum of a first term involving the absolutely continuous component of the measure and of a second one which is a positively homogeneous function of the singular part the duality is useful in plasticity theory in the sobolev case the study of non parametric integrands is new a description of the sub differential is obtained

a new model for thin plates with rapidly varying thickness abstract we study the bending of a thin plate with rapidly varying thickness for example one with rib like stiffeners or perforated by small holes we obtain a fourth order equation for the midplanc displacement using an asymptotic analysis based on three dimensional linear elasticity the coefficients of this equation represent the constitutive law relating bending moments to midplane curvature they are explicitly determined by the plate geometry our analysis distinguishes between three different cases in which the thickness varies on a length scale longer than on the order of or shorter than the mean thickness

a proximal based decomposition method for convex minimization problems this paper presents a decomposition method for solving convex minimization problems at each iteration the algorithm computes two proximal steps in the dual variables and one proximal step in the primal variables we derive this algorithm from rockafellar s proximal method of multipliers which involves an augmented lagrangian with an additional quadratic proximal term the algorithm preserves the good features of the proximal method of multipliers with the additional advantage that it leads to a decoupling of the constraints and is thus suitable for parallel implementation we allow for computing approximately the proximal minimization steps and we prove that under mild assumptions on the problem s data the method is globally convergent and at a linear rate the method is compared with alternating direction type methods and applied to the particular case of minimizing a convex function over a finite intersection of closed convex sets

optimal rectangular plate and shallow shell topologies using thickness distribution or homogenization abstract topological optimization of plates as well as shallow cylindrical and curved spherical shells are attempted in the present study for all structures examined our objective is the minimization of the strain energy function under a volume constraint an optimum distribution of thickness or microstructural density is sought under the hypothesis that the design variables can only be assigned their extreme allowable bounds or values very near them so that material can be removed from low density areas and thus an optimum topology can be determined the structural response is computed via a finite element analysis the analytical formulation is based on a form of linear shallow shell theory with the effects of transverse shear deformation and bending extensional coupling included the method of feasible directions is used to perform the optimization task numerical examples for various boundary conditions showing similarities or differences of the two methods are presented and discussed for all structures examined it is found that the assumption of a repetitious microstructure based on homogenization theory resulted in stronger optima for clamped plates and shells both methods converged to nearly identical topologies an indication of possible global optimal layouts

linear transmit processing in mimo communications systems we examine and compare the different types of linear transmit processing for multiple input multiple output systems where we assume that the receive filter is independent of the transmit filter contrary to the joint optimization of transmit and receive filters we can identify three filter types similar to receive processing the transmit matched filter the transmit zero forcing filter and the transmit wiener filter we show that the transmit filters are based on similar optimizations as the respective receive filters with an additional constraint for the transmit power moreover the transmit wiener filter has similar convergence properties as the receive wiener filter i e it converges to the matched filter and the zero forcing filter for low and high signal to noise ratio respectively we give closed form solutions for all transmit filters and present the fundamental result that their mean square errors are equal to the errors of the respective receive filters if the information symbols and the additive noise are uncorrelated however our simulations reveal that the bit error ratio results of the transmit filters differ from the results for the respective receive filters

optimality conditions for mass design problems and applications to thin plates we derive necessary and sufficient optimality conditions for a quite large class of structural design problems which can be formulated as follows under a given load and a total volume constraint minimize a suitable notion of compliance among all admissible mass distributions represented by positive measures with prescribed integral mean as a special case we focus attention on the optimization of thin plates we detail the corresponding optimality conditions and we show how they can be handled in order to determine analytically some optimal plates