return to equilibrium and stability of dynamics semigroup dynamics case a study is presented of asymptotically normal dynamical semigroups for which there exists a faithful normal state satisfying the detailed balance condition such dynamics reveals a return to a stationary state if additionally a weak cluster property is assumed the generalized stability condition and generalized wave operators are introduced the theory is illustrated by models

stochastic inverse heat conduction using a spectral approach an adjoint based functional optimization technique in conjunction with the spectral stochastic finite element method is proposed for the solution of an inverse heat conduction problem in the presence of uncertainties in material data process conditions and measurement noise the ill posed stochastic inverse problem is restated as a conditionally well posed l 2 optimization problem the gradient of the objective function is obtained in a distributional sense by defining an appropriate stochastic adjoint field the l 2 optimization problem is solved using a conjugate gradient approach accuracy and effectiveness of the proposed approach is appraised with the solution of several stochastic inverse heat conduction problems

on semi analytical probabilistic finite element method for homogenization of the periodic fiber reinforced composites the main aim of this paper is a development of the semi analytical probabilistic version of the finite element method fem related to the homogenization problem this approach is based on the global version of the response function method and symbolic integral calculation of basic probabilistic moments of the homogenized tensor and is applied in conjunction with the effective modules method it originates from the generalized stochastic perturbation based fem where taylor expansion with random parameters is not necessary now and is simply replaced with the integration of the response functions the hybrid computational implementation of the system maple with homogenization oriented fem code mcceff is invented to provide probabilistic analysis of the homogenized elasticity tensor for the periodic fiber reinforced composites although numerical illustration deals with a homogenization of a composite with material properties defined as gaussian random variables other composite parameters as well as other probabilistic distributions may be taken into account the methodology is independent of the boundary value problem considered and may be useful for general numerical solutions using finite or boundary elements finite differences or volumes as well as for meshless numerical strategies copyright 2011 john wiley sons ltd

finite difference heterogeneous multi scale method for homogenization problems in this paper we propose a numerical method the finite difference heterogeneous multi scale method fd hmm for solving multi scale parabolic problems based on the framework introduced in commun math sci 1 1 87 the numerical method relies on the use of two different schemes for the original equation at different grid level which allows to give numerical results at a much lower cost than solving the original equations we describe the strategy for constructing such a method discuss generalization for cases with time dependency random correlated coefficients nonconservative form and implementation issues finally the new method is illustrated with several test examples

boundary effects in a phase field approach to topology optimization a phase field based topology optimization approach is considered for the maximum stiffness or minimum compliance problem the objective functional to be minimized consists in addition to the compliance a cost for gray solutions and a cost for interfaces between void and full material since the interfaces between void and full material are penalized via a volume integral in the original phase field formulation there is no penalty associated with interfaces along the external boundaries in the present contribution an additional term representing the cost of interfaces at external boundaries is added to the functional subject to minimization it is shown that the new boundary term enters the optimization as a robin boundary condition the method is implemented in a finite element setting and numerical simulations of typical structures are considered the results indicate that the optimal designs are influenced by the cost of interfaces to a large less

optimization of dispersive coefficients in the homogenization of the wave equation in periodic structures we study dispersive effects of wave propagation in periodic media which can be modelled by adding a fourth order term in the homogenized equation the corresponding fourth order dispersive tensor is called burnett tensor and we numerically optimize its values in order to minimize or maximize dispersion more precisely we consider the case of a two phase composite medium with an eightfold symmetry assumption of the periodicity cell in two space dimensions we obtain upper and lower bound for the dispersive properties along with optimal microgeometries

sound quality characteristics of refrigerator noise in real living environments with relation to psychoacoustical and autocorrelation function parameters psychoacoustical and autocorrelation function acf parameters were employed to describe the temporal fluctuations of refrigerator noise during starting transition into from the stationary phase and termination of operation the temporal fluctuations of refrigerator noise include a click at start up followed by a rapid increase in volume a change of pitch and termination of the operation subjective evaluations of the noise of 24 different refrigerators were conducted in a real living environment the relationship between objective measures and perceived noisiness was examined by multiple regression analysis sound quality indices were developed based on psychoacoustical and acf parameters the psychoacoustical parameters found to be important for evaluating noisiness in the stationary phase were loudness and roughness the relationship between noisiness and acf parameters shows that sound energy and its fluctuations are important for evaluating noisiness also refrigerator sounds that had a fluctuat

wavelet based numerical homogenization a numerical homogenization procedure for elliptic differential equations is presented it is based on wavelet decompositions of discrete operators in fine and coarse scale components followed by the elimination of the fine scale contributions if the operator is in divergence form this is preserved by the homogenization procedure for periodic problems results similar to classical effective coefficient theory are proved the procedure can be applied to problems that are not cell periodic

sensitivity of the macroscopic response of elastic microstructures to the insertion of inclusions this paper proposes an exact analytical formula for the topological sensitivity of the macroscopic response of elastic microstructures to the insertion of circular inclusions the macroscopic response is assumed to be predicted by a well established multi scale constitutive theory where the macroscopic strain and stress tensors are defined as volume averages of their microscopic counterpart fields over a representative volume element rve of material the proposed formula a symmetric fourth order tensor field over the rve domain is a topological derivative which measures how the macroscopic elasticity tensor changes when an infinitesimal circular elastic inclusion is introduced within the rve in the limits when the inclusion matrix phase contrast ratio tends to zero and infinity the sensitivities to the insertion of a hole and a rigid inclusion respectively are rigorously obtained the derivation relies on the topological asymptotic analysis of the predicted macroscopic elasticity and is presented in detail the derived fundamental formula is of interest to many areas of applied and computational mechanics to illustrate its potential applicability a simple finite element based example is presented where the topological derivative information is used to automatically generate a bi material microstructure to meet pre specified macroscopic properties

topology optimization of fluid structure interaction problems in poroelasticity abstract this paper presents a method for applying topology optimization to fluid structure interaction problems in saturated poroelastic media the method relies on a multiple scale method applied to periodic media the resulting model couples the stokes flow in the pores of the structure with the deformation of the elastic skeleton through a macroscopic darcy type flow law the method allows to impose pressure loads for static problems through a one way coupling while transient problems are fully coupled modeling the interaction between fluid and solid the material distribution is determined by topology optimization in order to optimize the performance of a shock absorber and test the pressure loading capabilities and optimization of an internally pressurized lid

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

stress based topology optimization of frame structures under geometric uncertainty abstract probabilistic topology optimization has gained significant research attention recently this interest stems from the realization that the achieved high performance designs resulted from deterministic topology optimization algorithms may become suboptimal under real world conditions that are often accompanied with uncertainties among sources of these uncertainties the ones that define structural characteristics such as geometry are numerically challenging to treat as they lead to stochastic structural stiffness to date research on developing efficient probabilistic topology optimization under stochastic stiffness is mainly focused on displacement based objectives however in the design of structures stress is also a primary design criterion that needs to be directly controlled for a robust stress based topology optimization methodology for frame structures under geometric uncertainty is proposed in this work assuming that such uncertainties are small relative to frame member lengths the proposed methodology uses stochastic perturbation method to propagate these uncertainties up to the response level which is expressed by the maximum of expected values of von mises stresses throughout the domain sensitivities of the response with respect to design variables are derived analytically which allows using efficient gradient based optimizers the proposed algorithm is examined with stress based design of three frame structures under geometric uncertainty changes in the topology of these new designs are discussed and they are shown to outperform deterministic designs when subjected to geometric uncertainties moreover predictions and the resulting designs from the proposed methodology are found to be in excellent agreement with monte carlo simulation results

topology optimization with implicit functions and regularization summary topology optimization is formulated in terms of the nodal variables that control an implicit function description of the shape the implicit function is constrained by upper and lower bounds so that only a band of nodal variables needs to be considered in each step of the optimization the weak form of the equilibrium equation is expressed as a heaviside function of the implicit function the heaviside function is regularized to permit the evaluation of sensitivities we show that the method is a dual of the bendshe kikuchi method the method is applied both to problems of optimizing single material and

tauberian theorems and stability of one parameter semigroups the main result is the following stability theorem let t t t tzo be a bounded co semigroup on a reflexive space x denote by a the generator of t and by a a the spectrum of a if a a n ir is countable and no eigenvalue of a lies on the imaginary axis then limt boo t t x o for all x e x

designing materials with prescribed elastic properties using polygonal cells an extension of the material design problem is presented in which the base cell that characterizes the material microgeometry is polygonal the setting is the familiar inverse homogenization problem as introduced by sigmund using basic concepts in periodic planar tiling it is shown that base cells of very general geometries can be analysed within the standard topology optimization setting with little additional effort in particular the periodic homogenization problem defined on polygonal base cells that tile the plane can be replaced and analysed more efficiently by an equivalent problem that uses simple parallelograms as base cells different material layouts can be obtained by varying just two parameters that affect the geometry of the parallelogram namely the ratio of the lengths of the sides and the internal angle this is an efficient way to organize the search of the design space for all possible single scale material arrangements and could result in solutions that may be unreachable using a square or rectangular base cell examples illustrate the results copyright 2003 john wiley sons ltd

design of multi layer materials using inverse homogenization and a level set method abstract this work is concerned with the micro architecture of multi layer material that globally exhibits desired mechanical properties for instance a negative apparent poisson s ratio we use inverse homogenization the level set method and the shape derivative in the sense of hadamard to identify material regions and track boundary changes within the context of the smoothed interface the level set method and the shape derivative obtained in the smoothed interface context allows to capture within the unit cell the optimal micro geometry we test the algorithm by computing several multi layer auxetic micro structures the multi layer approach has the added benefit that contact during movement of adjacent branches of the micro structure can be avoided in order to increase its capacity to withstand larger stresses

levy processes and fourier analysis on compact lie groups we study the fourier expansion of the distribution density of a levy process in a compact lie group based on the peter weyl theorem

measurement of regional environmental noise by use of a pc based system an application to the noise near airport g marconi in bologna abstract measurements of aircraft noise were made at the airport g marconi in bologna by using a measurement system for regional environmental noise the system is based on the model of the human auditory brain system which is based on the interplay of autocorrelators and an interaural cross correlator acting on the pressure signals arriving at the ear entrances and takes into account the specialization of left and right human cerebral hemispheres see reference 8 measurements were taken through dual microphones at ear entrances of a dummy head the aircraft noise was characterized with the following physical factors calculated from the autocorrelation function acf and interaural cross correlation function iacf for binaural signals from the acf analysis 1 energy represented at the origin of delay 0 2 effective duration of the envelope of the normalized acf e 3 the delay time of the first peak 1 and 4 its amplitude 1were extracted from the iacf analysis 5 iacc 6 interaural delay time at which the iacc is defined iacc and 7 width of the iacf at the iacc wiaccwere extracted the factor 0 can be represented as the geometrical mean of the energies at both ears a noise source may be identified by these factors as timbre

asymptotic behavior of markov semigroups on preduals of von neumann algebras we develop a new approach for investigation of asymptotic behavior of markov semigroup on preduals of von neumann algebras with using of our technique we establish several results about mean ergodicity statistical stability and constrictiviness of markov semigroups

a note on the singular linear system of the generalized finite element methods we characterize the kernel of the global stiffness matrix in the singular linear system of the generalized finite element methods gfem which uses the classical finite element fe shape functions and local approximation space of harmonic polynomials

optimizing the layout of discrete objects in structures and materials a projection based topology optimization approach abstract this paper uses topology optimization to optimize the layout of discrete objects such as fixed shape void stiffening or functional inclusions in structures and periodic materials the methodology follows a material distribution approach and the heaviside projection method hpm is manipulated to ensure that the designed objects are discrete of fixed size length scale and shape and satisfy minimum spacing requirements these restrictions are achieved implicitly through projection without additional constraints or heuristics the methodology is built in the spirit of free form topology optimization and thus discrete objects are shown to appear vanish or translate across the design domain during the design evolution the technique is demonstrated on problems governed by mechanical stiffness including the design of structures and material microstructures whose elastic stiffness is to be enhanced by optimizing the location of stiff circular inclusions

generalized p fem in homogenization summary a new finite element method for elliptic problems with locally periodic microstructure of length varepsilon 0 is developed and analyzed it is shown that the method converges as varepsilon rightarrow 0 to the solution of the homogenized problem with optimal order in varepsilon and exponentially in the number of degrees of freedom independent of varepsilon 0 the computational work of the method is bounded independently of varepsilon numerical experiments demonstrate the feasibility and confirm the theoretical results

acoustical properties of aircraft noise measured by temporal and spatial factors abstract acoustical properties of aircraft noise were investigated by means of temporal and spatial factors in sound fields based on the model of auditory brain system see reference 10 the model consists of the autocorrelation and crosscorrelation mechanisms for sound signals arriving at two ears and the specialization of human cerebral hemisphere there are four temporal factors extracted from the autocorrelation function acf 1 sound energy 0 2 effective duration of acf e 3 delay time of the first peak 1 and 4 its amplitude 1 from the interaural crosscorrelation function iacf three spatial factors are extracted as 1 magnitude of the interaural crosscorrelation iacc 2 interaural delay time at iacc iacc and 3 width of the maximum peak of the iacf wiacc it is found that the acoustical properties are well represented by the factors extracted from the acf and the iacf

topological derivative for multi scale linear elasticity models applied to the synthesis of microstructures this paper proposes an algorithm for the synthesis optimization of microstructures based on an exact formula for the topological derivative of the macroscopic elasticity tensor and a level set domain representation the macroscopic elasticity tensor is estimated by a standard multi scale constitutive theory where the strain and stress tensors are volume averages of their microscopic counterparts over a representative volume element the algorithm is of simple computational implementation in particular it does not require artificial algorithmic parameters or strategies this is in sharp contrast with existing microstructural optimization procedures and follows as a natural consequence of the use of the topological derivative concept this concept provides the correct mathematical framework to treat topology changes such as those characterizing microstuctural optimization problems the effectiveness of the proposed methodology is illustrated in a set of finite element based numerical examples copyright 2010 john wiley sons ltd

numerical methods for multiscale elliptic problems we present an overview of the recent development on numerical methods for elliptic problems with multiscale coefficients we carry out a thorough study of two representative techniques the heterogeneous multiscale method hmm and the multiscale finite element method msfem for problems with scale separation but without specific assumptions on the particular form of the coefficients analytical and numerical results show that hmm gives comparable accuracy as msfem with much less cost for problems without scale separation our numerical results suggest that hmm performs at least as well as msfem in terms of accuracy and cost even though in this case both methods may fail to converge since the cost of msfem is comparable to that of solving the full fine scale problem one might expect that it does not need scale separation and still retains some accuracy we show that this is not the case specifically we give an example showing that if there exists an intermediate scale comparable to h the size of the macroscale mesh then msfem commits a finite error even with overlapping

large strain phase field based multi material topology optimization summary a multi material topology optimization scheme is presented the formulation includes an arbitrary number of phases with different mechanical properties to ensure that the sum of the volume fractions is unity and in order to avoid negative phase fractions an obstacle potential function which introduces infinity penalty for negative densities is utilized the problem is formulated for nonlinear deformations and the objective of the optimization is the end displacement the boundary value problems associated with the optimization problem and the equilibrium equation are solved using the finite element method to illustrate the possibilities of the method it is applied to a simple boundary value problem where optimal designs using multiple phases are considered copyright 2015 john wiley sons ltd

topology optimisation of manufacturable microstructural details without length scale separation using a spectral coarse basis preconditioner abstract this paper applies topology optimisation to the design of structures with periodic and layered microstructural details without length scale separation i e considering the complete macroscopic structure and its response while resolving all microstructural details as compared to the often used homogenisation approach the approach takes boundary conditions into account and ensures connected and macroscopically optimised microstructures regardless of the difference in micro and macroscopic length scales this results in microstructures tailored for specific applications rather than specific properties manufacturability is further ensured by the use of robust topology optimisation dealing with the complete macroscopic structure and its response is computationally challenging as very fine discretisations are needed in order to resolve all microstructural details therefore this paper shows the benefits of applying a contrast independent spectral preconditioner based on the multiscale finite element method msfem to large structures with fully resolved microstructural details it is shown that a single preconditioner can be reused for many design iterations and used for several design realisations in turn leading to massive savings in computational cost the density based topology optimisation approach combined with a heaviside projection filter and a stochastic robust formulation is used on various problems with both periodic and layered microstructures the presented approach is shown to allow for the topology optimisation of very large problems in matlab specifically a problem with 26 million displacement degrees of freedom in 26 hours using a single computational thread

a computational scheme for linear and non linear composites with arbitrary phase contrast a numerical method making use of fast fourier transforms has been proposed in moulinec and suquet 1994 1998 to investigate the effective properties of linear and non linear composites this method is based on an iterative scheme the rate of convergence of which is proportional to the contrast between the phases composites with high contrast typically above 104 or infinite contrast those containing voids or rigid inclusions or highly non linear materials cannot be handled by the method this paper presents two modified schemes the first one is an accelerated scheme for composites with high contrast which extends to elasticity a scheme initially proposed in eyre and milton 1999 its rate of convergence varies as the square root of the contrast the second scheme adequate for composites with infinite contrast is based on an augmented lagrangian method the resulting saddle point problem involves three steps the first step consists of solving a linear elastic problem using the fast fourier transform method in the second step a non linear problem is solved at each individual point in the volume element the third step consists of updating the lagrange multiplier applications of this scheme to rigidly reinforced and to voided composites are shown copyright 2001 john wiley sons ltd

multiscale isogeometric topology optimization for lattice materials abstract this paper presents isogeometric topology optimization ito for periodic lattice materials where non uniform rational b spline nurbs basis functions of cad models are directly used in the finite element analysis to improve computational accuracy and efficiency two to schemes that use asymptotic homogenization ah for the calculation of the mechanical properties are proposed for lattice materials with uniform and graded relative density respectively to accelerate ito for graded lattice materials the mechanical properties are expressed as a function of the relative density of the unit cell a step that avoids their iterative calculations during ito three benchmark examples are presented to validate the proposed scheme with results that show tangible advantages such as reduced computational time and faster convergence of ito over conventional to

a fuzzy stochastic multiscale model for fiber composites a one dimensional study abstract we study mathematical and computational models for computing the deformation of fiber reinforced polymers due to external forces a thorough study requires an understanding of both micro structural effects and uncertainty variability in the manufacturing process such as uncertainty in the size and distribution of fibers and variability in material properties and fracture parameters we first show that the present uncertainties variabilities which are of both random and non random types cannot be accurately characterized by current stochastic multiscale models based on precise probability theory such as stationary random fields next we present a new hybrid fuzzy stochastic model which can more accurately describe uncertainties variabilities in fiber composites the new model which is referred to as a fuzzy stationary random field consists of a random field with fuzzy moments we then construct a global local multiscale algorithm in a fuzzy stochastic framework for efficiently computing output quantities of interest such as displacements and stresses in regions of relatively small size e g hot spots the algorithm utilizes the concept of representative volume elements and homogenization and constructs a global solution to compute a local approximation that captures the microscale features of the problem the results are based on and backed by real experimental data through a calibration validation approach

a multiscale hp fem for 2d photonic crystal bands a multiscale generalised hp finite element method msfem for time harmonic wave propagation in bands of locally periodic media of large but finite extent e g photonic crystal phc bands is presented the method distinguishes itself by its size robustness i e to achieve a prescribed error its computational effort does not depend on the number of periods the proposed method shows this property for general incident fields including plane waves incident at a certain angle to the infinite crystal surface and at frequencies in and outside of the bandgap of the phc the proposed msfem is based on a precomputed problem adapted multiscale basis this basis incorporates a set of complex bloch modes the eigenfunctions of the infinite phc which are modulated by macroscopic piecewise polynomials on a macroscopic fe mesh the multiscale basis is shown to be efficient for finite phc bands of any size provided that boundary effects are resolved with a simple macroscopic boundary layer mesh the msfem constructed by combing the multiscale basis inside the crystal with some exterior discretisation is a special case of the generalised finite element method g fem for the rapid evaluation of the matrix entries we introduce a size robust algorithm for integrals of quasi periodic micro functions and polynomial macro functions size robustness of the present msfem in both the number of basis functions and the computation time is verified in extensive numerical experiments

design of maximum permeability material structures this paper extends recent advances in the topology optimization of fluid flows to the design of periodic porous material microstructures operating in a characteristic base cell of the material the goal is to determine the layout of solid and fluid phases that will yield maximum permeability and prescribed flow symmetries in the bulk material darcy s law governs flow through the macroscopic material while stokes equations govern flow through the microscopic channels permeability is computed via numerical homogenization of the base cell using finite elements solutions to the proposed inverse homogenization design problem feature simply connected pore spaces that closely resemble minimal surfaces such as the triply periodic schwartz p minimal surface for 3 d isotropic maximum permeability materials

probabilistic entropy in homogenization of the periodic fiber reinforced composites with random elastic parameters summary the purpose of this elaboration is to develop an efficient method for a determination of the probabilistic entropy loss in the homogenization process of the periodic composites with random material characteristics a definition of this entropy convenient for the gaussian continuous distribution is adopted and implemented into the computer algebra system maple homogenization of the fiber reinforced composite with randomly defined young s moduli of the constituents is carried out in the fem and homogenization oriented code based on the four noded plane strain elements probabilistic procedure has triple character and is alternatively based on the monte carlo simulation on the generalized stochastic perturbation based analysis and on the recently developed semi analytical determination of homogenized tensor using the response function method because of this triple usage of the probabilistic methods it is possible to make a detailed comparison of all those techniques especially in view of the entropy variation during the homogenization this procedure may be linked with other homogenization techniques also for various constitutive models and or for the upper and lower bounds on the effective tensor components copyright 2012 john wiley sons ltd

spectral stochastic homogenization of divergence type pdes this paper presents a formulation and numerical analysis of the homogenization of stochastic pdes the framework of homogenization is adopted to describe an effective medium that is equivalent in some sense to a heterogeneous medium of interest the parameters of the resulting homogeneous medium are described as stochastic processes characterized by their polynomial chaos decomposition the formulation yields a chaos decomposition for the predicted behavior of the homogeneous medium that captures in addition to the effect of heterogeneity the effect of variability once this description has been computed various statistics of the solution can be efficiently evaluated

analysis of the heterogeneous multiscale method for elliptic homogenization problems the heterogeneous multiscale method hmm is applied to various parabolic problems with multiscale coefficients these problems can be either linear or nonlinear optimal estimates are proved for the error between the hmm solution and the homogenized solution

a particle partition of unity method part ii efficient cover construction and reliable integration in this paper we present a meshfree discretization technique based only on a set of irregularly spaced points x i in mathbb r d and the partition of unity approach in this sequel to m griebel and m a schweitzer siam j sci comput 22 2000 pp 853 890 we focus on the cover construction and its interplay with the integration problem arising in a galerkin discretization we present a hierarchical cover construction algorithm and a reliable decomposition quadrature scheme here we decompose the integration domains into disjoint cells on which we employ local sparse grid quadrature rules to improve computational efficiency the use of these two schemes already reduces the operation count for the assembly of the stiffness matrix significantly now the overall computational costs are dominated by the number of the integration cells we present a regularized version of the hierarchical cover construction algorithm which reduces the number of integration cells even further and subsequently improves the computational efficiency in fact the computational costs during the integration of the nonzeros of the stiffness matrix are comparable to that of a finite element method yet the presented method is completely independent of a mesh moreover our method is applicable to general domains and allows for the construction of approximations of any order and regularity

annoyance of noise stimuli in relation to the spatial factors extracted from the interaural cross correlation function abstract while considering auditory brain model for subjective responses effects of spatial factors extracted from the interaural cross correlation function iacf on annoyance of noise stimuli are examined the previously developed indices to measure sound pressure levels spl and frequency characteristics cannot fully explain the psychological effects of noise in the first experiment subjects judged their annoyance by changing fluctuations in the magnitude of interaural cross correlation function iacc and the spl in the second they judged their annoyance by changing fluctuations in the interaural time delay iacc and the spl results show that 1 annoyance increased by increasing the fluctuations of iacc as well as the spl 2 annoyance increased by increasing the fluctuations of iacc as well as the spl

topology optimization of plane structures using smoothed particle hydrodynamics method summary this paper presents an alternative topology optimization method based on an efficient meshless smoothed particle hydrodynamics sph algorithm to currently calculate the objective compliance the deficiencies in standard sph method are eliminated by introducing corrective smoothed particle method and total lagrangian formulation the compliance is established relative to a designed density variable at each sph particle which is updated by optimality criteria method topology optimization is realized by minimizing the compliance using a modified solid isotropic material with penalization approach some numerical examples of plane elastic structure are carried out and the results demonstrate the suitability and effectiveness of the proposed sph method in the topology optimization problem copyright 2016 john wiley sons ltd

classical properties of infinite quantum open systems long time asymptotic properties of a class of environmentally induced dynamical semigroups on arbitrary von neumann algebras are discussed such a semigroup selects observables called effective observables which are immune to the process of decoherence and so evolve in a reversible automorphic way in particular it is shown that effective observables of the quantum system in the thermodynamic limit subjected to a specific interaction with another quantum system obey classical dynamics

the loudness of complex noise in relation to the factors extracted from the auto correlation function abstract the loudness of complex signals which include bandpass noises with different center frequencies complex noise is examined while changing the effective duration of the autocorrelation function e based on a model of the human auditory brain system for subjective response to a sound field the center frequencies of each component of the complex noises were 2000 and 3000 hz so that the perceived pitch was centered on 1000 hz the bandwidth of each component was changed by using a 2068 db octave sharp filter to control the e of the source signal the scale values for the loudness of the complex noises were obtained using a paired comparison method the results showed that the loudness increases with the eof the source signal similar to that of the single noise component centered on 1000 hz the loudness of complex noises having equal sound pressure levels is not constant within the critical band 160 hz

eddy viscosity of cellular flows by upscaling the eddy viscosity is the tensor in the equation that governs the transport of the large scale modulational perturbations of small scale stationary flows as an approximation to eddy viscosity the effective tensor that arises in the limit as the ratio between the scales e 0 can be considered we are interested here in the accuracy of this approximation we present results of computational investigation of eddy viscosity when the small scale flows are cellular special periodic stationary flows with the stream function sin y1 sin y2 cos y1 cos y2 y x e 0 1 for small e we used a numerical upscaling method we designed this method so that it captures the modulational perturbations for any e with o e2 accuracy and independent of e complexity

optimal design of material properties and material distribution for multiple loading conditions an extension of recent work 1 on the simultaneous optimization of material and structure to address the design of structures under multiple loading conditions is presented material properties are represented in the most general form possible namely as elements of the unrestricted set of positive semi definite constitutive tensors of a linearly elastic continuum existence of solutions can be shown when the objective is a weighted average of compliances and a resource constraint measured as the 2 norm or the trace of the constitutive tensors is included the optimized material properties can be derived analytically the optimization of the layout of the material leads to a sizing problem of structural optimization involving a non linear non smooth elasticity analysis the computational solution of this problem is discussed and illustrated with examples

multiscale analytical sensitivity analysis for composite materials we describe a methodology aimed at determining the sensitivity of the global structural behaviour such deformation or vibration modes with respect to the local characteristics such as material constants of micro constituents an analytical gradient computation which involves the direct differentiation of the multiple scale strong forms with respect to the design parameters is developed comparison of the multiple scale sensitivity analysis masa to the central finite difference cfd approximation in terms of accuracy and computation efficiency is carried out we demonstrate the robustness of the masa approach compared to the cfd approximation which has been found to be highly sensitive to the choice of the step size whose optimal value is problem dependent copyright 2001 john wiley sons ltd

topology optimization using a reaction diffusion equation abstract this paper presents a structural topology optimization method based on a reaction diffusion equation in our approach the design sensitivity for the topology optimization is directly employed as the reaction term of the reaction diffusion equation the distribution of material properties in the design domain is interpolated as the density field which is the solution of the reaction diffusion equation so free generation of new holes is allowed without the use of the topological gradient method our proposed method is intuitive and its implementation is simple compared with optimization methods using the level set method or phase field model the evolution of the density field is based on the implicit finite element method as numerical examples compliance minimization problems of cantilever beams and force maximization problems of magnetic actuators are presented to demonstrate the method s effectiveness and utility

multiple spatial and temporal scales method for numerical simulation of non classical heat conduction problems one dimensional case abstract a multiple spatial and temporal scales method is studied to simulate numerically the phenomenon of non fourier heat conduction in periodic heterogeneous materials the model developed is based on the higher order homogenization theory with multiple spatial and temporal scales in one dimensional case the amplified spatial scale and the reduced temporal scale are introduced respectively to account for the fluctuations of non fourier heat conduction due to material heterogeneity and non local effect of the homogenized solution by separating the governing equations into various scales the different orders of homogenized non fourier heat conduction equations are obtained the reduced time dependence is thus eliminated and the fourth order governing differential equations are derived to avoid the necessity of c1 continuous finite element implementation a c0 continuous mixed finite element approximation scheme is put forward numerical results are shown to demonstrate the efficiency and validity of the proposed method

scale related topology optimization of cellular materials and structures the integrated optimization of lightweight cellular materials and structures are discussed in this paper by analysing the basic features of such a two scale problem it is shown that the optimal solution strongly depends upon the scale effect modelling of the periodic microstructure of material unit cell muc i e the so called representative volume element rve however with the asymptotic homogenization method used widely in actual topology optimization procedure effective material properties predicted can give rise to limit values depending upon only volume fractions of solid phases properties and spatial distribution of constituents in the microstructure regardless of scale effect from this consideration we propose the design element de concept being able to deal with conventional designs of materials and structures in a unified way by changing the scale and aspect ratio of the de scale related effects of materials and structures are well revealed and distinguished in the final results of optimal design patterns to illustrate the proposed approach numerical design problems of 2d layered structures with cellular core are investigated

isogeometric shape optimization of smoothed petal auxetic structures via computational periodic homogenization an important feature that drives the auxetic behaviour of the star shaped auxetic structures is the hinge functional connection at the vertex connections this feature poses a great challenge for manufacturing and may lead to significant stress concentrations to overcome these problems we introduced smoothed petal shaped auxetic structures where the hinges are replaced by smoothed connections to accommodate the curved features of the petal shaped auxetics a parametrisation modelling scheme using multiple nurbs patches is proposed next an integrated shape design frame work using isogeometric analysis is adopted to improve the structural performance to ensure a minimum thickness for each member a geometry sizing constraint is imposed via piece wise bounding polynomials this geometry sizing constraint in the context of isogeometric shape optimization is particularly interesting due to the non interpolatory nature of nurbs basis the effective poisson ratio is used directly as the objective function and an adjoint sensitivity analysis is carried out the optimized designs smoothed petal auxetic structures are shown to achieve low negative poisson s ratios while the difficulties of manufacturing the hinges are avoided for the case with six petals an in plane isotropy is achieved

patch dynamics with buffers for homogenization problems an important class of problems exhibits smooth behaviour on macroscopic space and time scales while only a microscopic evolution law is known for such time dependent multi scale problems an equation free framework has been proposed of which patch dynamics is an essential component patch dynamics is designed to perform numerical simulations of an unavailable macroscopic equation on macroscopic time and length scales it uses appropriately initialized simulations of the available microscopic model in a number of small boxes patches which cover only a fraction of the space time domain we show that it is possible to use arbitrary boundary conditions for these patches provided that suitably large buffer regions shield the boundary artefacts from the interior of the patches we analyze the accuracy of this scheme for a diffusion homogenization problem with periodic heterogeneity and illustrate the approach with a set of numerical examples which include a non linear reaction diffusion equation and the kuramoto sivashinsky equation

optimization of structure and material properties for solids composed of softening material an existing formulation for the prediction of the optimal material properties tensor for systems made of linear material is extended here to encompass design with nonlinear softening material the original model for the linear case was stated as a convex constrained nonlinear programming problem and this property is preserved in the extension the development is exemplified for the case of design for minimum global compliance an extremum problem formulation for elastostatics is incorporated into the design problem as a convenient way to model the structural analysis of general softening systems unlike the case for design with linear material in the nonlinear problem the form of the solution for optimal material properties and the associated stress fields as well evolve with increasing load computational results are presented for a two dimensional example problem in which a system is designed for different loads while parameters in the material model are held fixed

on the structure of covariant dynamical semigroups abstract dynamical semigroups in b h without the norm continuity assumption are investigated by introducing the notion of form generator giving the mathematical expression for the idea of markovian master equation it is shown that any form generator on b h admits a standard representation and the non uniqueness of this representation is described the equations for the components of the standard representation of a covariant form generator are deduced in terms of low order cohomology of the symmetry group in particular noncommutative levy khinchin type formulae for the shift covariant form generators are obtained relations with previous works on characterisation of the unbounded generator of a dynamical semigroup are discussed

sensitivity and randomness in homogenization of periodic fiber reinforced composites via the response function method the main issue this paper addresses is the derivation and implementation of a general homogenization method including the simultaneous determination of sensitivity gradients and probabilistic moments of the effective elasticity tensor this is possible with an application of the perturbation method based on taylor expansion and with the effective modules method the computational procedure is implemented using plane strain analysis carried out with the finite element method program mcceff and the symbolic computations system maple the sensitivity gradients and probabilistic moments are commonly determined on the basis of partial derivatives for the homogenized elasticity tensor calculated using the response function method with respect to some composite parameters they are subjected separately to a normalization procedure in deterministic analysis and the relevant algebraic combinations for the stochastic case this enriched homogenization procedure is tested on a periodic fiber reinforced two component composite where the material parameters are taken as design variables and then the input random quantities the results of computational analysis are compared against the results of the central finite difference approach in the case of sensitivity gradients determination as well as the direct monte carlo simulation approach this numerical methodology may be further applied not only in the context of the homogenization method but also to extend various discrete computational techniques such as boundary finite element and finite difference together with various meshless methods

a topology optimization method based on the level set method for the design of negative permeability dielectric metamaterials abstract this paper presents a level set based topology optimization method for the design of negative permeability dielectric metamaterials metamaterials are artificial materials that display extraordinary physical properties that are unavailable with natural materials the aim of the formulated optimization problem is to find optimized layouts of a dielectric material that achieve negative permeability the presence of grayscale areas in the optimized configurations critically affects the performance of metamaterials positively as well as negatively but configurations that contain grayscale areas are highly impractical from an engineering and manufacturing point of view therefore a topology optimization method that can obtain clear optimized configurations is desirable here a level set based topology optimization method incorporating a fictitious interface energy is applied to a negative permeability dielectric metamaterial design problem the optimization algorithm uses the finite element method fem for solving the equilibrium and adjoint equations and design problems are formulated for both two and three dimensional cases first the level set based topology optimization method is explained and the optimization problems for the design of metamaterials are then discussed several optimum design examples for the design of dielectric metamaterials that demonstrate negative effective permeability at prescribed frequencies are provided to confirm the utility and validity of the presented method

continuity and generators of dynamical semigroups for infinite bose systems abstract for a class of quasifree quantum dynamical semigroups on the algebra of the canonical commutation relations ccr we give sufficient conditions for these semigroups to extend to ultraweakly continuous semigroups of normal operators on the von neumann algebra associated with a representation of the ccr then the explicit form of the generators of the extended semigroups is calculated

numerical methods for elliptic partial differential equations with rapidly oscillating coefficients this paper presents two methods for the numerical solution of the classical homogenization problem of elliptic operators with periodically oscillating coefficients the numerical solution of such problems is difficult because of the presence of rapidly oscillating coefficients the first method based on the classical one which consists of the homogenized solution the first and second order correctors whereas the second one is based on the bloch wave approach further for the calculation of the homogenized coefficients and some auxiliary functions involved in this method we applied both methods and compared their accuracies the bloch approximation consists in determining an oscillating integral numerically the bloch method provides a better approximation to the exact solution than the classical first order corrector term in the smooth coefficients case moreover we provided taylor approximations for the bloch approximation function and implemented it numerically in order to show the efficiency of these methods exhaustive numerical examples in both one and two dimensional cases are presented

geometry the leading parameter for the poisson s ratio of bending dominated cellular solids control over the deformation behaviour that a cellular structure shows in response to imposed external forces is a requirement for the effective design of mechanical metamaterials in particular those with negative poisson s ratio this article sheds light on the old question of the relationship between geometric microstructure and mechanical response by comparison of the deformation properties of bar and joint frameworks with those of their realisation as a cellular solid made from linear elastic material for ordered planar tessellation models we find a classification in terms of the number of degrees of freedom of the framework model first in cases where the geometry uniquely prescribes a single deformation mode of the framework model the mechanical deformation and poisson s ratio of the linearly elastic cellular solid closely follow those of the unique deformation mode the result is a bending dominated deformation with negligible dependence of the effective poisson s ratio on the underlying material s poisson s ratio and small values of the effective young s modulus second in the case of rigid structures or when geometric degeneracy prevents the bending dominated deformation mode the effective poisson s ratio is material dependent and the young s modulus view the mathml sourcee cs large all analysed structures of this type have positive values of the poisson s ratio and large values of view the mathml sourcee cs third in the case where the framework has multiple deformation modes geometry alone does not suffice to determine the mechanical deformation these results clarify the relationship between mechanical properties of a linear elastic cellular solid and its corresponding bar and joint framework abstraction they also raise the question if in essence auxetic behaviour is restricted to the geometry guided class of bending dominated structures corresponding to unique mechanisms with inherently low values of the young s modulus

determination of the closure of the set of elasticity functionals we determine the closure for mosco convergence in l2 3 of the set of elasticity functionals we prove that this closure coincides with the set of all non negative lower semicontinuous quadratic functionals which are objective i e which vanish for rigid motions the result is still valid if we consider only the set of isotropic elasticity functionals which have a prescribed poisson coefficient this shows that a very large family of materials can be reached when homogenizing a composite material with highly contrasted rigidity coefficients

pitch of iterated rippled noise iterated rippled noise irn stimuli are generated by a cascade of delay d gain g and add networks the matched pitch of irn stimuli was determined as a function of the type of network used to generate irn stimuli the delay d 2 4 and 8 ms the number of iterations n 1 2 3 4 6 8 of the delay and add networks and whether the delayed noise was added g 1 to or subtracted g 1 from the undelayed noise the matched pitch of irn stimuli did not depend on the type of network when g 1 addition the matched pitch did not depend on the number of stages of iterations n and was always equal to the reciprocal of the delay 1 d when g 1 subtraction the match pitch depended on n when n 1 the matched pitch of irn stimuli was ambiguous having two pitches in the region of 1 d 10 when n 8 the match pitch was equal to 1 2d this change in the pitch occurred between n 2 and 6 the results are discussed in terms of spectral and temporal models of complex pitch processing a temporal model based on autocorrelation was able to provide quantitative predictions for the pitch of these irn stimuli however a spectral type of model can also account for the pitch of these irn stimuli

dynamics of geometrically exact sandwich beams 1 d plates computational aspects a galerkin projection of the complete equations of motion of geometrically exact sandwich beams applicable to 1 d plates is presented here the beam can take any arbitrary initial position in the 2 d space each layer of the beam can have different material constants with no restriction on the mass distribution and layer thickness further each layer can take on different length thus allowing the modeling of multilayer structures with ply drop offs finite rotation and shear deformation are accommodated for in each layer the deformed cross section of the beam is continuous piecewise linear the continuity of displacement across the interlayer boundaries is exactly enforced extensive numerical examples including sandwich beams with three identical layers sandwich structures with ply drop off free flying and spin up maneuver of sandwich beams are presented to illustrate the applicability and versatility of the proposed formulation

a stochastic computational method for evaluation of global and local behavior of random elastic media a stochastic computational method is developed to evaluate global effective properties and local probabilistic behavior of random elastic media the elasticity solution for random media is addressed with a method that combines a fast iterative numerical method with stochastic decomposition techniques stochastic homogenization problems are mathematically formulated with an ensemble average approximation scheme based on a concept of stochastic representative volume element srve probabilistic descriptors of local strain are generated based on convolution equations derived from the equilibrium equations of elasticity with the application of the galerkin formulation in probability space and the fourier transform of the convolution equations an efficient numerical scheme is implemented using an iterative algorithm that takes advantage of fast fourier transform two algorithms are provided for gaussian and non gaussian random media respectively with corresponding sufficient conditions for convergence derived finally numerical experiments are conducted for a gaussian and a non gaussian random medium respectively with verifications obtained from monte carlo simulation

ergodic properties of diffusion type quantum dynamical semigroups we develop a framework for investigation of asymptotic behavior of quantum markov semigroups on c algebras associated with noncommutative elliptic generators an exponential rate of convergence toward the projection onto the fixed point subalgebra has been established and in a particular case of the semigroup selecting rotationally invariant states of a three dimensional quantum system the time factor of such a convergence has been estimated

thermo mechanical analysis of periodic multiphase materials by a multiscale asymptotic homogenization approach a spatial and temporal multiscale asymptotic homogenization method used to simulate thermo dynamic wave propagation in periodic multiphase materials is systematically studied a general field governing equation of thermo dynamic wave propagation is expressed in a unified form with both inertia and velocity terms amplified spatial and reduced temporal scales are respectively introduced to account for spatial and temporal fluctuations and non local effects in the homogenized solution due to material heterogeneity and diverse time scales the model is derived from the higher order homogenization theory with multiple spatial and temporal scales it is also shown that the modified higher order terms bring in a non local dispersion effect of the microstructure of multiphase materials one dimensional non fourier heat conduction and dynamic problems under a thermal shock are computed to demonstrate the efficiency and validity of the developed procedure the results indicate the disadvantages of classical spatial homogenization

loudness of sharply 2068 db octave filtered noises in relation to the factors extracted from the autocorrelation function this study examines the loudness of bandpass noises with center frequencies of 250 500 and 1000hz while changing the autocorrelation function acf the bandwidth of the source signal was altered with a 2068 db octave sharp filter to control the acf of the source signal the scale values of loudness were obtained using a paired comparison method it is shown that the loudness of the bandpass noises inside the critical band is not constant the loudness of the pure tone is greater than that of sharply filtered noises the loudness of the bandpass noises increases with increasing effective duration of the acf e of the source signal

topology optimization of hierarchical lattice structures with substructuring abstract this work presents a generalized topology optimization approach for the design of hierarchical lattice structures with the development of an approximation of reduced substructure with penalization arsp model the structure is assumed to be composed of substructures with a common lattice geometry pattern unlike conventional homogenization based designs assuming the separation of scales this work considers two different yet connected scales each substructure is condensed first into a super element with a reduced degrees of freedom and is associated with a density design variable indicating the material volume fraction the density design variable is linked to a lattice geometry feature parameter a surrogate model is particularly built with the aid of proper orthogonal decomposition and diffuse approximation mapping the density to super element stiffness matrix the derivative of super element matrix with respect to the associated density can therefore be evaluated efficiently and explicitly the super element matrix is further augmented with a penalized density to control the structural complexity the optimality criteria method is used for the update of design variables numerical examples show that both the size and the lattice pattern of substructure have essential influences on the design indicating the necessity of performing connected hierarchical modeling and design

on n widths for elliptic problems abstract sharp bounds for the n width of solution sets of a class of elliptic partial differential equations are given particular attention is paid to equations with rough coefficients and singularly perturbed problems of elliptic elliptic type

optimal distribution of material properties for an elastic continuum with structure dependent body force abstract the simultaneous optimization of material properties and structural layout for an elastic continuum is formulated and analyzed the objective is to obtain the maximum structural stiffness for prescribed surface loads and displacements taking into account a body force that depends on the structural layout optimization with an account of self weight or centrifugal forces are examples of these type of problems arbitrary elasticity tensor fields are considered as the problems variable and necessary conditions satisfied by the solution are established the use of a spectral decomposition of the elasticity tensor is emphasized since it provides a simple geometrical interpretation typical examples which illustrate the effects of the structure dependent body force are analyzed it is found that a commonly used isoperimetric restriction known as the resource constraint is not necessarily active and that the optimal structure is locally stiffer in areas where the body force and the displacement field have opposite directions and locally weaker otherwise this interestingly leads to a non symmetrical distribution of material properties even for prismatic bodies under anti symmetric surface loads

a wavelet galerkin scheme for analysis of large scale problems on simple domains a wavelet galerkin scheme tailored to address the numerical solution of large scale boundary value problems defined on domains of simple geometry is presented the variation of parameters e g material properties within the domain is arbitrary but the method is specifically designed to solve problems where parameters vary in raster like fashion boundary conditions are imposed via lagrange multipliers using a fictitious domain approach a preconditioner specially designed for this problem is developed to guarantee that convergence of conjugate gradient algorithms is quick and insensitive to problem size the strategy is applied to the solution of steady state heat conduction problems in 2 d but it can be generalized without conceptual changes to 3 d problems and to problems in linear elasticity copyright 1999 john wiley sons ltd

diagnostic system based on the human auditory brain model for measuring environmental noise an application to railway noise abstract measurements of railway noise were conducted by use of a diagnostic system of regional environmental noise the system is based on the model of the human auditory brain system the model consists of the interplay of autocorrelators and an interaural crosscorrelator acting on the pressure signals arriving at the ear entrances and takes into account the specialization of left and right human cerebral hemispheres different kinds of railway noise were measured through binaural microphones of a dummy head to characterize the railway noise physical factors extracted from the autocorrelation functions acf and interaural crosscorrelation function iacf of binaural signals were used the factors extracted from acf were 1 energy represented at the origin of the delay 0 2 effective duration of the envelope of the normalized acf e 3 the delay time of the first peak 1 and 4 its amplitude o 1 the factors extracted from iacf were 5 iacc 6 interaural delay time at which the iacc is defined iacc and 7 width of the iacf at the iacc w iacc the factor 0 can be represented as a geometrical mean of energies at both ears as listening level ll

stable generalized finite element method sgfem abstract the generalized finite element method gfem is a partition of unity method pum where the trial space of standard finite element method fem is augmented with non polynomial shape functions with compact support these shape functions which are also known as the enrichments mimic the local behavior of the unknown solution of the underlying variational problem gfem has been successfully used to solve a variety of problems with complicated features and microstructure however the stiffness matrix of gfem is badly conditioned much worse compared to the standard fem and there could be a severe loss of accuracy in the computed solution of the associated linear system in this paper we address this issue and propose a modification of the gfem referred to as the stable gfem sgfem we show that sgfem retains the excellent convergence properties of gfem does not require a ramp function in the presence of blending elements and the conditioning of the associated stiffness matrix is not worse than that of the standard fem moreover sgfem is very robust with respect to the parameters of the enrichments we show these features of sgfem on several examples

materials with prescribed constitutive parameters an inverse homogenization problem abstract this paper deals with the construction of materials with arbitrary prescribed positive semi definite constitutive tensors the construction problem can be called an inverse problem of finding a material with given homogenized coefficients the inverse problem is formulated as a topology optimization problem i e finding the interior topology of a base cell such that cost is minimized and the constraints are defined by the prescribed constitutive parameters numerical values of the constitutive parameters of a given material are found using a numerical homogenization method expressed in terms of element mutual energies numerical results show that arbitrary materials including materials with poisson s ratio 1 0 and other extreme materials can be obtained by modelling the base cell as a truss structure furthermore a wide spectrum of materials can be constructed from base cells modelled as continuous discs of varying thickness only the two dimensional case is considered in this paper but formulation and numerical procedures can easily be extended to the three dimensional case

simulation of the multi scale convergence in computational homogenization approaches although the asymptotic homogenization is known to explicitly predict the thermo mechanical behaviors of an overall structure as well as the microstructures the current developments in engineering fields introduce some kinds of approximation about the microstructural geometry in order for the homogenization method for periodic media to apply for general heterogeneous ones the problems arising from mathematical modeling are examined in the framework of representative volume element rve analyses here the notion of homogenization convergence allows us to eliminate the geometrical periodicity requirement when the size of rve is sufficiently large then the numerical studies in this paper realize the multi scale nature of the convergence of overall material properties as the unit cell size is increased in addition to such dependency of the macroscopic field variables on the selected size of unit cells the convergence nature of microscopic stress values is also studied quantitatively via the computational homogenization method similar discussions are made for the elastoplastic mechanical responses in both macro and microscopic levels in these multi scale numerical analyses the specific effects of the microstructural morphology are reflected by using the digital image based dib finite element fe modeling technique which enables the construction of accurate microstructural models

concurrent topology optimization design of material and structure within fe2 nonlinear multiscale analysis framework abstract this paper revisits concurrent design of material and structure within fe2 nonlinear multiscale analysis framework for structural stiffness maximization at macroscopic scale design variables are defined at the both scales cellular material models are defined at microscopic scale in a pointwise manner for the considered macroscopic structure they are optimized to adapt the macroscopic structural physical response though linear models are assumed at both scales the macroscopic structural equilibrium is in general nonlinear due to the adaptation of cellular material microstructures for this reason an iterative resolution based on fe2 scheme is developed to address this nonlinearity discrete topology optimization algorithm bi directional evolutionary structural optimization beso is used at the both scales it is shown by means of numerical tests that fe2 scheme can well bridge the two scales and address the nonlinearity reasonable design solutions of the macroscopic structure and its corresponding cellular materials have been obtained by the developed concurrent design framework

a time domain description for the pitch strength of iterated rippled noise two versions of a cascaded add attenuate and delay circuit were used to generate iterated rippled noise irn stimuli irn stimuli produce a repetition pitch whose strength relative to the noise can be varied by changing the type of circuit the attenuation or the number of iterations in the circuit listeners were asked to discriminate between various pairs of irn stimuli which differed in the type of network used to generate the sounds or the number of iterations n 1 2 3 4 7 and 9 performance was determined for irn stimuli generated with delays of 2 4 and 8 ms and for four bandpass filter conditions 0 2000 250 2000 500 2000 and 750 2000 hz some irn stimuli were extremely difficult to discriminate despite relatively large spectral differences while other irn stimuli produced readily discriminable changes in perception despite small spectral differences these contrasting results are inconsistent with simple spectral explanations for the perception of irn stimuli an explanation based on the first peak of the autocorrelation function of irn stimuli is consistent with the results simulations of the processing performed by the peripheral auditory system i e interval histograms and correlograms produce results which are consistent with the involvement of these temporal processes in the perception of irn stimuli

composite material design of two dimensional structures using the homogenization design method summary composite materials of two dimensional structures are designed using the homogenization design method the composite material is made of two or three dierent material phases designing the composite material consists of nding a distribution of material phases that minimizes the mean compliance of the macrostructure subject to volume fraction constraints of the constituent phases within a unit cell of periodic microstructures at the start of the computational solution the material distribution of the microstructure is represented as a pure mixture of the constituent phases as the iteration procedure unfolds the component phases separate themselves out to form distinctive interfaces the eective material properties of the articially mixed materials are dened by the interpolation of the constituents the optimization problem is solved using the sequential linear programming method both the macrostructure and the microstructures are analysed using the nite element method in each iteration step several examples of optimal topology design of composite material are presented to demonstrate the validity of the present numerical algorithm copyright 2001 john wiley sons ltd