free material design via semidefinite programming the multiload case with contact conditions free material design deals with the question of finding the stiffest structure with respect to one or more given loads which can be made when both the distribution of material and the material itself can freely vary the case of one single load has been discussed in several recent papers and an efficient numerical approach was presented in m kocvara m zibulevsky and j zow rairo model math anal numer 32 1998 pp 255 281 we attack here the multiload situation understood in the worst case sense which is of much more interest for applications but also significantly more challenging from both the theoretical and the numerical points of view after a series of transformation steps we reach a problem formulation for which we can prove existence of a solution a suitable discretization leads to a semidefinite programming problem for which modern polynomial time algorithms of interior point type are available a number of numerical examples demonstrates the efficiency of our approach

integral representation results for energies defined on stochastic lattices and application to nonlinear elasticity this article is devoted to the study of the asymptotic behavior of a class of energies defined on stochastic lattices under polynomial growth assumptions we prove that the energy functionals f varepsilon stored in the deformation of an varepsilon scaling of a stochastic lattice converge to a continuous energy functional when varepsilon goes to zero in particular the limiting energy functional is of integral type and deterministic if the lattice is ergodic we also generalize to systems and nonlinear settings well known results on stochastic homogenization of discrete elliptic equations as an application of the main result we prove the convergence of a discrete model for rubber towards the nonlinear theory of continuum mechanics we finally address some mechanical properties of the limiting models such as frame invariance isotropy and natural states

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

cutfem topology optimization of 3d laminar incompressible flow problems abstract this paper studies the characteristics and applicability of the cutfem approach of burman et al 2014 as the core of a robust topology optimization framework for 3d laminar incompressible flow and species transport problems at low reynolds numbers r e 200 cutfem is a methodology for discretizing partial differential equations on complex geometries by immersed boundary techniques in this study the geometry of the fluid domain is described by an explicit level set method where the parameters of a discretized level set function are defined as functions of the optimization variables the fluid behavior is modeled by the incompressible navier stokes equations species transport is modeled by an advection diffusion equation the governing equations are discretized in space by a generalized extended finite element method face oriented ghost penalty terms are added for stability reasons and to improve the conditioning of the system the boundary conditions are enforced weakly via nitsche s method the emergence of isolated volumes of fluid surrounded by solid during the optimization process leads to a singular analysis problem an auxiliary indicator field is modeled to identify these volumes and to impose a constraint on the average pressure numerical results for 3d steady state and transient problems demonstrate that the cutfem analyses are sufficiently accurate and the optimized designs agree well with results from prior studies solved in 2d or by density approaches

design parameterization for topology optimization by intersection of an implicit function abstract this paper introduces a new approach to topology optimization where the structural boundary is defined by the intersection of an implicit signed distance function and a cutting surface the cutting surface is discretized using finite element shape function polynomials and the nodal values become the design variables during optimization thus the design parameterization is separated from the analysis discretization which enables a reduction in the number of design variables compared with methods that use element wise variables the proposed method can obtain solutions with smooth boundaries and the parameterization allows solution by standard optimization methods several 2d and 3d examples are used to demonstrate the effectiveness of the method including minimization of compliance and complaint mechanism problems the results show that the method can obtain good solutions to well known problems with smooth clearly defined boundaries and that this can be achieved using significantly fewer design variables compared with element based methods

objective priors for the bivariate normal model summary objective bayesian inference for the multivariate normal distribution is illustrated using dieren t types of formal objective priors jereys invariant reference and matching dieren t modes of inference bayesian and frequentist and dieren t criteria involved in selecting optimal objective priors ease of computation frequentist performance marginalization paradoxes and decision theoretic evaluation in the course of the investigation of the bivariate normal model in berger and sun 2006 a variety of surprising results were found including the availability of objective priors that yield exact frequentist inferences for many functions of the bivariate normal parameters such as the correlation coecien t certain of these results are generalized to the multivariate normal situation the prior that most frequently yields exact frequentist inference is the righthaar prior which unfortunately is not unique two natural proposals are studied for dealing with this non uniqueness rst mixing over the right haar priors second choosing the empirical bayes right haar prior that which maximizes the marginal likelihood of the data quite surprisingly we show that neither of these possibilities yields a good solution this is disturbing and sobering it is yet another indication that improper priors do not behave as do proper priors and that it can be dangerous to apply understandings from the world of proper priors to the world of improper priors

evolutionary topology optimization using design space adjustment based on fixed grid design space optimization for topology based on fixed grid is proposed and its superiority to conventional topology optimization is shown in the conventional topology optimization the design domain is fixed it is however desirable to make the design domain evolve into a better one during optimization process by increasing or decreasing the number of design pixels or variables which we call design space optimization a breakthrough in obtaining sensitivities when design space expands has been made recently with necessary mathematical background but due to coupling effect and others sensitivity results have not been satisfactory three innovative implementations are developed in this paper firstly the proper characteristics of artificial material are defined the second one is to decouple neighbouring elements for exact design space sensitivities the previous design space optimization has been tedious because only one layer can be added so the third innovation is a new expansion strategy with multi layers based on design space sensitivities as a result the proposed evolutionary method can get an optimum much faster than ever before especially for large scale problems it is also conjectured that this gives higher probability of getting the global optimum as confirmed by numerical examples

topology optimization using regularized intermediate density control abstract we consider topology optimization of elastic continua the elasticity tensor is assumed to depend linearly on the design function density as in the variable thickness sheet problem in order to get black white design pictures the intermediate density values are controlled by an explicit constraint this constraint is regularized by including a compact and linear operator s to guarantee existence of solutions a proof of convergence of the finite element fe discretized optimization problem s solutions to exact ones is also given so the method is not prone to numerical anomalies such as mesh dependence or checkerboards the procedure is illustrated in some minimum compliance examples where s is chosen to be a classical convolution type operator the fe discretized optimization problems are solved by sequential convex approximations

a multi resolution method for 3d multi material topology optimization abstract this paper presents a multi resolution implementation in 3d for multi material topology optimization problem an alternating active phase algorithm where the problem at hand is divided into a series of the traditional material void phase topology optimization is employed for the multi material problem different levels of discretization are used for the displacement mesh design variable mesh and density mesh which provides higher resolution designs for the solutions a projection scheme is employed to compute the element densities from design variables and control the length scale of the material density simple block coordinate descent method similar to the gauss seidel technique is used to solve the subproblems several 3d numerical examples are presented to demonstrate the ease and the effectiveness of the proposed implementation incorporating the multi resolution method into the multi material approach robust designs with improved resolution can be achieved for real life problems with complex geometries

asymptotic expansions of lattice green s functions we derive asymptotic expansions for the green functions associated with coercive difference equations on general lattices these expansions lead to rigorous methods for approximating the lattice green functions by polyharmonic rational functions

large scale topology optimization using preconditioned krylov subspace methods with recycling summary the computational bottleneck of topology optimization is the solution of a large number of linear systems arising in the finite element analysis we propose fast iterative solvers for large threedimensional topology optimization problems to address this problem since the linear systems in the sequence of optimization steps change slowly from one step to the next we can significantly reduce the number of iterations and the runtime of the linear solver by recycling selected search spaces from previous linear systems in addition we introduce a minres minimum residual method version with recycling and a short term recurrence to make recycling more efficient for symmetric problems furthermore we discuss preconditioning to ensure fast convergence we show that a proper rescaling of the linear systems reduces the huge condition numbers that typically occur in topology optimization to roughly those arising for a problem with constant density we demonstrate the effectiveness of our solvers by solving a topology optimization problem with more than a million unknowns on a fast pc

parallel methods for optimality criteria based topology optimization abstract topology optimization problems require the repeated solution of finite element problems that are often extremely ill conditioned due to highly heterogeneous material distributions this makes the use of iterative linear solvers inefficient unless appropriate preconditioning is used even then the solution time for topology optimization problems is typically very high these problems are addressed by considering the use of non overlapping domain decomposition based parallel methods for the solution of topology optimization problems the parallel algorithms presented here are based on the solid isotropic material with penalization simp formulation of the topology optimization problem and use the optimality criteria method for iterative optimization we consider three parallel linear solvers to solve the equilibrium problem at each step of the iterative optimization procedure these include two preconditioned conjugate gradient pcg methods one using a diagonal preconditioner and one using an incomplete lu factorization preconditioner with a drop tolerance a third substructuring solver that employs a hybrid of direct and iterative pcg techniques is also studied this solver is found to be the most effective of the three solvers studied both in terms of parallel efficiency and in terms of its ability to mitigate the effects of ill conditioning in addition to examining parallel linear solvers we consider the parallelization of the iterative optimality criteria method to tackle checkerboarding and mesh dependence we propose a multi pass filtering technique that limits the number of ghost elements that need to be exchanged across interprocessor boundaries

algebraic algorithms for the analysis of mechanical trusses infinite periodic lattices can be used as models for analyzing and understanding various properties of mechanical truss constructions with periodic structures for infinite lattices the problems of connectivity and stability are nontrivial from the mathematical point of view and have not been addressed adequately in the literature in this paper we will present a set of algebraic algorithms which are based on ideal theory to solve such problems to understand the notion of complicated three dimensional lattices readers need to be able to see the figures in color

multidisciplinary free material optimization we present a mathematical framework for the so called multidisciplinary free material optimization mdfmo problems a branch of structural optimization in which the full material tensor is considered as a design variable we extend the original problem statement by a class of generic constraints depending either on the design or on the state variables among the examples are local stress or displacement constraints we show the existence of optimal solutions for this generalized free material optimization fmo problem and discuss convergent approximation schemes based on the finite element method

a multi resolution approach for multi material topology optimization based on isogeometric analysis abstract a novel multi resolution scheme to perform the multi material topology optimization in the framework of isogeometric analysis iga is proposed to create high resolution optimized designs with a lower computational cost a new variable parameter space is supplemented to define design density variables and represent the optimal material distribution utilizing the bivariate b spline basis functions these functions are simply obtained by k refinement strategy in the iga the non uniform rational b spline nurbs basis functions are employed to exactly describe geometric domains and approximate unknown solutions in finite element analysis fea as well an alternating active phase algorithm associated with the block gauss seidel method is employed to convert a multiphase topology optimization problem under multiple volume fraction constraints into many binary phase topology optimization sub problems with only one volume fraction constraint accordingly the number of design variables depends only on one active phase in each of those sub problems regardless of the number of material phases and is significantly decreased in comparison with the original problem the optimality criteria oc method is used as an optimizer to update solutions for such sub problems the effectiveness and robustness of the proposed method are verified via testing various benchmark examples

sufficient optimality conditions hold for almost all nonlinear semidefinite programs we derive a new genericity result for nonlinear semidefinite programming nlsdp namely almost all linear perturbations of a given nlsdp are shown to be nondegenerate here nondegeneracy for nlsdp refers to the transversality constraint qualification strict complementarity and second order sufficient condition due to the presence of the second order sufficient condition our result is a nontrivial extension of the corresponding results for linear semidefinite programs sdp from alizadeh et al math program 77 2 ser b 111 128 1997 the proof of the genericity result makes use of forsgren s derivation of optimality conditions for nlsdp in forsgren math program 88 1 ser a 105 128 2000 due to the latter approach the positive semidefiniteness of a symmetric matrix g x depending continuously on x is locally equivalent to the fact that a certain schur complement s x of g x is positive semidefinite this yields a reduced nlsdp by considering the new semidefinite constraint s x succeq 0 s x 0 instead of g x succeq 0 g x 0 while deriving optimality conditions for the reduced nlsdp the well known and often mentioned h term in the second order sufficient condition vanishes this allows us to access the proof of the genericity result for nlsdp

a finite element analysis of optimal variable thickness sheets a quasi mixed finite element fe method for maximum stiffness of variable thickness sheets is analyzed the displacement is approximated with nine node lagrange quadrilateral elements and the thickness is approximated as elementwise constant one is guaranteed that the fe displacement solutions will converge in hh but in an example it is shown that in general one cannot expect any subsequence of the fe thickness solutions to converge in any l p omega norm however under a regularity and biaxiality assumption on the optimal stress field uniqueness of the optimal thickness function as well as convergence in l p omega 1 leq p infty of fe thickness solutions are proven

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

filters in topology optimization in this article a modified filtered version of the minimum compliance topology optimization problem is studied the direct dependence of the material properties on its pointwise density is replaced by a regularization of the density field by the mean of a convolution operator in this setting it is possible to establish the existence of solutions moreover convergence of an approximation by means of finite elements can be obtained this is illustrated through some numerical experiments the filtering technique is also shown to cope with two important numerical problems in topology optimization checkerboards and mesh dependent designs copyright 2001 john wiley sons ltd

from molecular models to continuum mechanics we present here a limiting process allowing us to write some continuum mechanics models as a natural asymptotic of molecular models the approach is based on the hypothesis that the macroscopic displacement is equal to the microscopic one we carry out the corresponding calculations in the case of two body energies including higher order terms and also in the case of thomas fermi type models

wave propagation in equivalent continuums representing truss lattice materials abstract stiffness scales linearly with density in stretch dominated lattice meta materials offering the possibility of very light yet very stiff structures current additive manufacturing techniques can assemble structures from lattice materials but the design of such structures will require accurate efficient simulation methods equivalent continuum models have several advantages over discrete truss models of stretch dominated lattices including computational efficiency and ease of model construction however the development an equivalent model suitable for representing the dynamic response of a periodic truss in the small deformation regime is complicated by microinertial effects this paper derives a dynamic equivalent continuum model for periodic truss structures suitable for representing long wavelength wave propagation and verifies it against the full bloch wave theory and detailed finite element simulations the model must incorporate microinertial effects to accurately reproduce long wavelength characteristics of the response such as anisotropic elastic soundspeeds the formulation presented here also improves upon previous work by preserving equilibrium at truss joints for simple lattices and by improving numerical stability by eliminating vertices in the effective yield surface

performance measures for optimal constrained beamformers in this paper the closed form expression is derived which relates the output signal to interference plus noise ratio to the minimum mean square error of constrained beamformers for narrowband and wideband signal environments

on the probability of observing misleading statistical evidence abstract the law of likelihood explains how to interpret statistical data as evidence specifically it gives to the discipline of statistics a precise and objective measure of the strength of statistical evidence supporting one probability distribution vis a vis another that measure is the likelihood ratio but evidence even when properly interpreted can be misleading observations can truly constitute strong evidence supporting one distribution when the other is true what makes statistical evidence valuable to science is that this cannot occur very often here we examine two bounds on the probability of observing strong misleading evidence one is a universal bound applicable to every pair of probability distributions the other bound much smaller applies to all pairs of distributions within fixed dimensional parametric models in large samples the second bound comes from examining how the probability of strong misleading evidence varies as a function of the alternative value of the parameter we

multiplicity adjustments in testing for bioequivalence bioequivalence of two drugs is usually demonstrated by rejecting two one sided null hypotheses using the two one sided tests for pharmacokinetic parameters area under the concentration time curve auc and maximum concentration cmax by virtue of the intersection union test there is no need for multiplicity adjustment in testing the two one sided null hypotheses within each parameter however the decision rule for bioequivalence often requires equivalence to be achieved simultaneously on both parameters that contain four one sided null hypotheses together without adjusting for multiplicity the family wise error rate fwer could fail to be controlled at the nominal type i error rate the multiplicity issue for bioequivalence in this regard is scarcely discussed in the literature to address this issue we propose two approaches including a closed test procedure that controls fwer for the simultaneous auc and cmax bioequivalence and requires no adjustment of the type i error and an alpha adaptive sequential testing aast that controls fwer by pre specifying the significance level on auc 1 and obtaining it for cmax 2 adaptively after testing of auc while both methods control fwer the closed test requires testing of eight intersection null hypotheses each at and aast is at times accomplished through a slight deduction in 1 and no deduction in 2 relative to the latter considers equivalence reached in auc a higher importance than that in cmax illustrated with published data the two approaches although operate differently can lead to the same substantive conclusion and are better than a traditional method like bonferroni adjustment copyright 2014 john wiley sons ltd

a simple fast adaptive algorithm for broad band null steering arrays a simple algorithm for adaptively steering the broadband null in a two element power inversion array which uses a tapped delay line filter as the processing element is presented and investigated by performing a simple signal transformation the algorithm constrains some of the filter weights so that a variable length delay line is approximated in the maximally flat sense by using the least mean square lms algorithm to adjust the weights controlling the length and gain of the delay line a broadband null is then adaptively formed to track and reject the broadband jammer as studied analytically and by using simulation results the convergence behavior of the algorithm is fast and depends only on the tolerable level of misadjustment noise its implementation complexity is comparable to that of using the lms algorithm directly

singularity sets of constant principal strain deformations abstract we show that if f is a mapping with constant principal strains cps mapping of a planar domain of the form d s where d is itself a domain and s is a closed subset of d with linear measure 0 then f has an extension to a cps mapping of d s where s s has no accumulation points in d the proof uses properties of cps mappings attributable to the nonlinear hyperbolic nature of the underlying system of partial differential equations as well as results about their behavior in neighborhoods of isolated singularities previously established by the author

parametric robust inferences for correlated ordinal data the aim of this article is to provide asymptotically valid likelihood inferences about regression parameters for correlated ordinal response variables the legitimacy of this novel approach requires no knowledge of the underlying joint distributions so long as their second moments exist the efficacy of the proposed parametric approach is demonstrated via simulations and the analyses of two real data sets

a fast null steering algorithm for linearly constrained adaptive arrays a fast null steering algorithm for adaptive arrays with a look direction constraint is investigated in this algorithm the least mean square lms algorithm is used to adaptively adjust the positions of the array response zeros one after another in a time multiplexed manner to track unknown jammers to ensure that the look direction response and the other zeros remain unchanged when a particular null is being updated the element signals are suitably transformed before the lms updating despite this signal transformation the new algorithm has almost the same implementation complexity as when the lms algorithm is employed directly as only one zero is being adaptively updated at any instant however with each null being independently steered the convergence behavior of the new algorithm is significantly faster and is almost independent of the external noise environment

adaptive beam forming using a cascade configuration a new technique for adaptive beam forming based on the davies cascade array configuration 11 is presented first of all it is shown that an n element linear array can be reconfigured as a number of subarrays of two elements each this two element array is capable of steering one null in an arbitrary direction while maintaining a desired gain in some other prespecified look direction to adaptively perform this function at any cascade stage the inverse of a 2 2 correlation matrix of the signal vector at a subarray is computed and substituted in the expression for the constrained optimum weight vector similar processing is performed at subsequent stages of the cascade configuration at each stage of adaptation a noise source contributing maximum power at that stage is nulled out simulation studies carried out verify the validity of this approach and demonstrate the fast convergence property of the proposed technique

adaptive zero tracking complemented by lms weight update for guaranteed convergence a low complexity zero tracking algorithm with fast and guaranteed convergence behavior is proposed and investigated the algorithm implements a zero tracking algorithm and a least mean square lms weight update algorithm in parallel with the former adjusting the zeros of the array in a time multiplexed manner to achieve fast asymptotic and tracking behavior while the latter improves the initial transient behavior of the algorithm and guarantees its convergence to the global optimum by comparing their output powers the relative performances of the two component algorithms are monitored and re initialization of one algorithm by the other may occur periodically this gives the algorithm both fast and guaranteed convergence behavior even though the zeros are directly available and the implementation complexity is only two times that for the conventional lms algorithm

performance analysis of a wavelet based generalized sidelobe canceller in this paper we carry out a detailed performance analysis of the recently addressed wavelet based generalized sidelobe canceller gsc which employs a set of p regular m band wavelet filters in the design of the blocking matrix involved we begin our analysis by developing a closed form expression of the output signal to interference plus noise ratio sinr of partially adaptive beamformers with the gsc as the underlying structure under a one jammer or multiple jammer environment this new expression is shown to encompass several previous works as special cases we then examine the relationship between the choices of the parameters p and m in the wavelet based gsc and the corresponding output sinr based on this expression some guidelines for the choices of these parameters can thus be induced to achieve superior performance simulation results are also furnished to justify these suggestions

exact artificial boundary conditions for continuum and discrete elasticity for the continuum and discrete elastic equations we derive exact artificial boundary conditions abcs often referred to as transparent boundary conditions that can be applied at a planar interface below which there are no forces solution of the elasticity equations can then be performed using this interface as an artificial boundary often with greatly reduced computational effort but without loss of accuracy a general solvability requirement is presented for the existence of an artificial boundary operator for discrete systems such as discrete elasticity on an unbounded semi infinite domain the solvability requirement is validated by introducing a sum of exponentials ansatz for the solution below the artificial boundary we also derive a new expression for the total energy for the system involving only the region above the artificial boundary numerical examples are provided to confirm and illustrate the accuracy and effectiveness of the results

a sequential convex semidefinite programming algorithm with an application to multiple load free material optimization a new method for the efficient solution of a class of convex semidefinite programming sdp problems is introduced the method extends the sequential convex programming scp concept to optimization problems with matrix variables the basic idea of the new method is to approximate the original optimization problem by a sequence of subproblems in which nonlinear functions defined in matrix variables are approximated by block separable convex functions the subproblems are semidefinite programs with a favorable structure which can be efficiently solved by existing sdp software the new method is shown to be globally convergent the article is concluded by a series of numerical experiments with free material optimization problems demonstrating the effectiveness of the generalized scp approach

inference of bioequivalence for log normal distributed data with unspecified variances two drugs are bioequivalent if the ratio of a pharmacokinetic pk parameter of two products falls within equivalence margins the distribution of pk parameters is often assumed to be log normal therefore bioequivalence be is usually assessed on the difference of logarithmically transformed pk parameters in the presence of unspecified variances test procedures such as two one sided tests tost use sample estimates for those variances bayesian models integrate them out in the posterior distribution these methods limit our knowledge on the extent that inference about be is affected by the variability of pk parameters in this paper we propose a likelihood approach that retains the unspecified variances in the model and partitions the entire likelihood function into two components f statistic function for variances and t statistic function for demonstrated with published real life data the proposed method not only produces results that are same as tost and comparable with bayesian method but also helps identify ranges of variances which could make the determination of be more achievable our findings manifest the advantages of the proposed method in making inference about the extent that be is affected by the unspecified variances which cannot be accomplished either by tost or bayesian method

parallelized structural topology optimization for eigenvalue problems a parallel topology optimization method is proposed to deal with large scale structural eigenvalue related design problems while existing parallel methods have been employed mainly for finite element analysis the present work deals with the entire parallel process of analysis and topology optimization using a parallel processing technique in the framework of the physical domain decomposition method the sensitivity analysis and design variable update are performed independently in each subdomain with minimum data communication among subdomains a successive estimation strategy over design iterations is proposed to expedite the design optimization process the preconditioned conjugate gradient method and the subspace iteration method are used as parallel solvers several numerical examples are considered to show the scalability and effectiveness of the present parallel approach in handling large scale design problems

free material optimization with fundamental eigenfrequency constraints the goal of this paper is to formulate and solve free material optimization problems with constraints on the smallest eigenfrequency of the optimal structure a natural formulation of this problem as a linear semidefinite program turns out to be numerically intractable as an alternative we propose a new approach which is based on a nonlinear semidefinite low rank approximation of the semidefinite dual we introduce an algorithm based on this approach and analyze its convergence properties the article is concluded by numerical experiments proving the effectiveness of the new approach

mechanics of materials with periodic truss or frame micro structures this paper describes the mechanics of materials with periodic skeletal micro structures in infinite domains the principal technical results consist of certain korn type inequalities that provide upper and lower bounds for the linear elastic strain energy in the material using these inequalities existence and uniqueness results for the equations of linear elastic equilibrium are derived and some asymptotic properties of the solutions are described particular attention is paid to the question of when a lattice structure can accurately be modeled as a pin jointed truss and when a rigid node frame model must be employed a practical technique for how to distinguish between the two types of material is given and the distinct differences in their mechanical behavior are described

large scale topology optimization in 3d using parallel computing we consider large scale topology optimization of elastic continua in 3d using the regularized intermediate density control introduced in 1 the nested approach is used i e equilibrium is solved at each iteration to get a high quality resolution of realistic designs in 3d problems involving several hundreds of thousand finite elements are solved in order to deal with problems of this size parallel computing is used in combination with domain decomposition the equilibrium equations are solved by a preconditioned conjugate gradient algorithm and the optimization part is solved using sequential convex programming several numerical results obtained from computations performed on a cray parallel computer are presented

hencky prandtl nets and constrained michell trusses abstract we study minimum weight trusses or truss like continua subject to technological constraints which limit the member forces in the optimal design the principal strains are constant over part of the domain and the principal stresses over another part leading to a combination of a michell truss and a slip line net we begin with a variational treatment of the unconstrained michell problem indicating one possible numerical approach and also suggesting spaces of stress and displacement fields which will allow a proof of the existence of optimal trusses for very general boundary conditions

free material optimization via mathematical programming this paper deals with a central question of structural optimization which is formulated as the problem of finding the stiffest structure which can be made when both the distribution of material as well as the material itself can be freely varied we consider a general multi load formulation and include the possibility of unilateral contact the emphasis of the presentation is on numerical procedures for this type of problem and we show that the problems after discretization can be rewritten as mathematical programming problems of special form we propose iterative optimization algorithms based on penalty barrier methods and interior point methods and show a broad range of numerical examples that demonstrates the efficiency of our approach

on the performance of the generalized sidelobe canceller in coherent situations the convergence rate for the adaptive weights to reach the optimum value in an adaptive array system depends on the eigenvalue spread ratio of the autocovariance matrix how the eigenvalue spread ratio in a generalized sidelobe canceller gsc is affected by the various parameters is studied expressions for the output power of the gsc in coherent situations are derived and numerical results are included

a preconditioning technique for indefinite systems resulting from mixed approximations of elliptic problems this paper provides a preconditioned iterative technique for the solution of saddle point problems these problems typically arise in the numerical approximation of partial differential equations by lagrange multiplier techniques and or mixed methods the saddle point problem is reformulated as a symmetric positive definite system which is then solved by conjugate gradient iteration applications to the equations of elasticity and stokes are discussed and the results of numerical experiments are given

infinitesimally rigid polyhedra i statics of frameworks from the time of cauchy mathematicians have studied the motions of convex polyhedra with the faces held rigid while changes are allowed in the dihedral angles in the 1940s alexandrov proved that even with additional vertices along the natural edges and with an arbitrary triangulation of the natural faces on these vertices such polyhedra are infinitesimally rigid in this paper the dual and equivalent concept of static rigidity for frameworks is used to describe the behavior of bar and joint frameworks built around convex and other polyhedra the static techniques introduced provide a new simplified proof of alexandrov s theorem as well as an essential extension which characterizes the static properties of frameworks built with more general patterns on the faces including frameworks with vertices interior to the faces the static techniques are presented and employed in a pattern appropriate to the extension of an arbitrary statically rigid framework built around any polyhedron nonconvex toroidal etc the techniques are also applied to derive the static rigidity of tensegrity frameworks with cables and struts in place of bars and the static rigidity of frameworks projectively equivalent to known polyhedral frameworks finally as an exercise to give an additional perspective to the results in 3 space detailed analogues of alexandrov s theorem are presented for convex 4 polytopes built as bar and joint frameworks in 4 space

improving multiresolution topology optimization via multiple discretizations summary unlike the traditional topology optimization approach that uses the same discretization for finite element analysis and design optimization this paper proposes a framework for improving multiresolution topology optimization imtop via multiple distinct discretizations for 1 finite elements 2 design variables and 3 density this approach leads to high fidelity resolution with a relatively low computational cost in addition an adaptive multiresolution topology optimization amtop procedure is introduced which consists of selective adjustment and refinement of design variable and density fields various two dimensional and three dimensional numerical examples demonstrate that the proposed schemes can significantly reduce computational cost in comparison to the existing element based approach copyright 2012 john wiley sons ltd

network approximation in the limit of small interparticle distance of the effective properties of a high contrast random dispersed composite we consider a high contrast two phase composite such as a ceramic polymer composite or a fiberglass composite our objective is to determine the dependence of the effective conductivity or the effective dielectric constant or the effective shear modulus of the composite on the random locations of the inclusions ceramic particles or fibers when the concentration of the inclusions is high we consider a two dimensional model and show that the continuum problem can be approximated by a discrete random network graph we use variational techniques to provide rigorous mathematical justification for this approximation in particular we have shown asymptotic equivalence of the effective constant for the discrete and continuum models in the limit when the relative interparticle distance goes to zero we introduce the geometrical interparticle distance parameter using voronoi tessellation and emphasize the relevance of this parameter due to the fact that for irregular non periodic geometries it is not uniquely determined by the volume fraction of the inclusions we use the discrete network to compute numerically for this purpose we employ a computer program which generates a random distribution of disks on the plane using this distribution we obtain the corresponding discrete network furthermore the computer program provides the distribution of fluxes in the network which is based on keller s formula for two closely spaced disks we compute the dependence of on the volume fraction of the inclusions v for monodispersed composites and obtaine results which are consistent with the percolation theory predictions for polydispersed composites random inclusions of two different sizes the dependence is not simple and is determined by the relative volume fraction v r of large and small particles we found some special values of v r for which the effective coefficient is significantly decreased the computer program which is based on our network model is very efficient and it allows us to collect the statistical data for a large number of random configurations

topology optimization of non linear elastic structures and compliant mechanisms abstract a linear elastic response is assumed in most structural topology optimization problems while this assumption is valid for a wide variety of problems it is not valid for structures undergoing large displacements the elastic structural analysis used here accommodates geometric and material non linearities the material density field is filtered to enforce a length scale on the field variation and is penalized to remove less effective intermediate densities the filtering scheme is embedded in the structural analysis to resolve the non existent solution to the solid void topology problem in this way we know precisely what optimization problem is being solved the structural topology optimization formulation is also used to design compliant mechanisms

a polytree based adaptive polygonal finite element method for multi material topology optimization abstract this study presents a polytree based adaptive methodology for multi material topology optimization mmtop polytree data structure is introduced as a general recursive multi level mesh that is automatically refined in processing based on error analysis in order to resolve hanging nodes in element edges the wachspress coordinate is employed on a reference element before using a mapping scheme to obtain shape functions and their derivatives for any polygons a new definition of filter radius is also proposed to improve the efficiency of filters and optimized results the combination of polytree meshes and adaptive filters not only clarifies the interfaces between material phases including void phase but also decreases the computing time of the overall process in comparison to using the regular fine meshes several benchmark and practical problems are considered to show distinct features of the proposed method

an evolutionary topology optimization approach with variationally controlled growth abstract previous works of junker and hackl 2016 have presented a variational growth approach to topology optimization in which the problem of checkerboarding was suppressed by means of a discontinuous regularization scheme this approach did not require additional filter techniques and also optimization algorithms were not needed any more however growth approaches to topology optimization demand some limitations in order to avoid a global and simultaneous generation of mass the limitation has been achieved by a rather simple approach with restricted possibilities for controlling in this contribution we eliminate this drawback by introducing a lagrange multiplier to control the total mass within the model space for each iteration step this enables us to achieve directly controlled growth behavior and even find optimized structures for prescribed structure volumes furthermore a modified growth approach which we refer to as the lagrange shift approach results a numerically stable model that is easy to handle after the derivation of the approach we present numerical solutions for different boundary problems that demonstrate the potential of our model

statistical evidence for glm regression parameters a robust likelihood approach when a likelihood ratio is used to measure the strength of evidence for one hypothesis over another its reliability i e how often it produces misleading evidence depends on the specification of the working model when the working model happens to be the true or correct model the probability of observing strong misleading evidence is low and controllable but this is not necessarily the case when the working model is misspecified royall and tsou j r stat soc ser b 2003 65 391 404 show how to adjust working models to make them robust to misspecification likelihood ratios derived from their robust adjusted likelihood are just as reliable asymptotically as if the working model were correctly specified in the first place in this paper we apply and extend these ideas to the generalized linear model glm regression setting we provide several illustrations both from simulated data and real data concerning rates of parasitic infection in philippine adolescents show how the required adjustment factor can be obtained from standard statistical software and draw some connections between this approach and the sandwich estimator for robust standard errors of regression parameters this substantially broadens the availability and the viability of likelihood methods for measuring statistical evidence in regression settings copyright 2007 john wiley sons ltd

boundary algebraic equations for lattice problems boundary algebraic equations corresponding to dirichlet boundary value problems on lattices are introduced these equations are based on the lattice green s function from which discrete single and double layer potentials are derived structurally the boundary algebraic equations are similar to the boundary integral equations of classical potential theory numerical experiments indicate that boundary algebraic equations possess excellent spectral properties

multiresolution topology optimization using isogeometric analysis summary the paper introduces a novel multi resolution scheme to topology optimization in the framework of the isogeometric analysis iga a new variable parameter space is added to implement multi resolution topology optimization mtop based on the solid isotropic material with penalization simp approach design density variables defined in the variable space are used to approximate the element analysis density by the bivariate b spline basis functions which are easily obtained employing k refinement strategy in the iga while the non uniform rational b splines nurbs basis functions are employed to exactly describe geometric domains and approximate unknown solutions in finite element analysis by applying a refined sensitivity filter optimized designs include highly discrete solutions in terms of solid and void materials without utilizing any black and white projection filters the method of moving asymptotes mma is used to solve the optimization problem various benchmark test problems including plane stress compliant mechanism inverter and two dimensional heat conduction are examined to demonstrate the effectiveness and robustness of the present method this article is protected by copyright all rights reserved

the output sinr of the linearly constrained beamformer the authors derive expressions of the output signal to interference plus noise ratio sinr of the linearly constrained narrowband beamformer in noncoherent situations using a vector approach numerical results are included

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 new efficient convergence criterion for reducing computational expense in topology optimization reducible design variable method summary a new efficient convergence criterion named the reducible design variable method rdvm is proposed to save computational expense in topology optimization there are two types of computational costs one is to calculate the governing equations and the other is to update the design variables in conventional topology optimization the number of design variables is usually fixed during the optimization procedure thus the computational expense linearly increases with respect to the iteration number some design variables however quickly converge and some other design variables slowly converge the idea of the proposed method is to adaptively reduce the number of design variables on the basis of the history of each design variable during optimization using the rdvm those design variables that quickly converge are not considered as design variables for the next iterations this means that the number of design variables can be reduced to save the computational costs of updating design variables then the iteration will repeat until the number of design variables becomes 0 in addition the proposed method can lead to faster convergence of the optimization procedure which indeed is a more significant time saving it is also revealed that the rdvm gives identical optimal solutions as those by conventional methods we confirmed the numerical efficiency and solution effectiveness of the rdvm with respect to two types of optimization static linear elastic minimization and linear vibration problems with the first eigenvalue as the objective function for maximization copyright 2012 john wiley sons ltd

on material design by the optimal choice of young s modulus distribution abstract this paper concerns the problem of optimal distribution of young s modulus within an elastic and isotropic body with prescribed not necessarily uniform distribution of poisson s ratio the merit function is the total compliance corresponding to a given single load case the unit cost of the design is assumed as the trace of hooke s tensor which is proportional to young s modulus here the problem thus formulated is a constrained version of the isotropic material design problem in which both bulk and shear elastic moduli of isotropy are design variables in contrast to the latter approach the optimal material is either nonsingular or degenerates to a void the optimal distribution of young s modulus is determined by a solution to an auxiliary minimization problem with the integrand of linear growth the problem dual to the latter assumes the form similar to that known from the theory of michell trusses the proposed numerical approach focuses on solving the former auxiliary problem the case studies comprise selected optimal designs corresponding to the isotropic material optimization and young s modulus optimization developed in this paper the exemplary optimal solutions show that admitting negative values of poisson s ratio may contribute to a decrease of the total compliance thus leading to better designs

interpreting statistical evidence by using imperfect models robust adjusted likelihood functions summary the strength of statistical evidence is measured by the likelihood ratio two key performance properties of this measure are the probability of observing strong misleading evidence and the probability of observing weak evidence for the likelihood function associated with a parametric statistical model these probabilities have a simple large sample structure when the model is correct here we examine how that structure changes when the model fails this leads to criteria for determining whether a given likelihood function is robust continuing to perform satisfactorily when the model fails and to a simple technique for adjusting both likelihoods and profile likelihoods to make them robust we prove that the expected information in the robust adjusted likelihood cannot exceed the expected information in the likelihood function from a true model we note that the robust adjusted likelihood is asymptotically fully efficient when the working model is correct and we show that in some important examples this efficiency is retained even when the working model fails in such cases the bayes posterior probability distribution based on the adjusted likelihood is robust remaining correct asymptotically even when the model for the observable random variable does not include the true distribution finally we note a link to standard frequentist methodology in large samples the adjusted likelihood functions provide robust likelihood based confidence intervals

application of discontinuity layout optimization to plane plasticity problems a new and potentially widely applicable numerical analysis procedure for continuum mechanics problems is described the procedure is used here to determine the critical layout of discontinuities and associated upper bound limit load for plane plasticity problems potential discontinuities which interlink nodes laid out over the body under consideration are permitted to crossover one another giving a much wider search space than when such discontinuities are located only at the edges of finite elements of fixed topology highly efficient linear programming solvers can be employed when certain popular failure criteria are specified e g tresca or mohr coulomb in plane strain stress velocity singularities are automatically identified and visual interpretation of the output is straightforward the procedure coined discontinuity layout optimization dlo is related to that used to identify the optimum layout of bars in trusses with discontinuities e g slip lines in a translational failure mechanism corresponding to bars in an optimum truss hence a recently developed adaptive nodal connection strategy developed for truss layout optimization problems can advantageously be applied here the procedure is used to identify critical translational failure mechanisms for selected metal forming and soil mechanics problems close agreement with the exact analytical solutions is obtained

modelling topology optimization problems as linear mixed 0 1 programs this paper deals with topology optimization of discretized continuum structures it is shown that a large class of non linear 0 1 topology optimization problems including stress and displacement constrained minimum weight problems can equivalently be modelled as linear mixed 0 1 programs the modelling approach is applied to some test problems which are solved to global optimality