shape optimization of three dimensional continuum structures via force approximation techniques the existing need to develop methods whereby the shape design efficiency can be improved through the use of high quality approximation methods is addressed an efficient approximation method for stress constraints in three dimensional shape design problems is proposed based on expanding the nodal forces in taylor series with respect to shape variations the significance of this new method is shown through elementary beam theory calculations and via numerical computations using three dimensional solid finite elements numerical examples including the classical cantilever beam structure and realistic automotive parts like the engine connecting rod are designed for optimum shape using the proposed method the numerical results obtained from these methods are compared with other published results to assess the efficiency and the convergence rate of the proposed method it is concluded that by taking advantage of this high quality approximation the total number of finite element analyses required for structural shape optimization can be reduced significantly resulting in the same level of efficiency achieved previously in sizing problems

topology optimization using polytopes abstract meshing complex engineering domains is a challenging task arbitrary polyhedral meshes can provide the much needed flexibility in automated discretization of such domains the geometric property of polyhedral meshes such as its unstructured nature and the connectivity of faces between elements makes them specially attractive for topology optimization applications numerical anomalies in designs such as the single node connections and checkerboard pattern can be naturally circumvented with polyhedrons in the current work we solve the governing three dimensional elasticity state equation using the virtual element method vem approach the main characteristic difference between vem and standard finite element methods fem is that in vem the canonical basis functions are not constructed explicitly rather the stiffness matrix is computed directly utilizing a projection map which extracts the linear component of the deformation such a construction guarantees the satisfaction of the patch test used by engineers as an indicator of optimal convergence of numerical solutions under mesh refinement finally the computations reduce to the evaluation of matrices which contain purely geometric surface facet quantities the present work focuses on the first order vem in which the degrees of freedom are associated with the vertices the features of the current optimization approach are demonstrated using numerical examples for compliance minimization and compliant mechanism problems

sensitivity analysis with the modified heaviside function for the optimal layout design of multi component systems two kinds of design variables i e pseudo density variables associated with the framework structure and location design variables associated with connected components are involved in the layout design of multi component systems although sensitivities with respect to the first ones can easily be carried out as in topology optimization the semi analytical method sam is often used for sensitivity analysis with respect to the location design variables due to the geometric perturbation of the finite element mesh the latter can then be regarded as a geometric perturbation model gpm in this paper we propose a material perturbation model mpm using fixed finite element fe mesh for sensitivity analysis with respect to location design variables the material discontinuity across the boundary between each component and the framework structure is smoothed approximately by means of a modified heaviside function when a location design variable of a certain component is perturbed attached finite elements to the component boundary are assumed to undertake only a shift of material properties while the finite element mesh itself remains geometrically unchanged as a result analytical sensitivities with respect to location design variables are achieved as easily as for pseudo density variables the computing efficiency is thus improved because the velocity field for the mesh perturbation in the semi analytical scheme is no longer needed the mpm is illustrated by means of numerical tests especially the design optimization of 3d multi component systems

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

limit sets zero dynamics and internal models in the problem of nonlinear output regulation in this paper we lay the foundations for a nonequilibrium theory of nonlinear output regulation giving a more general nonequilibrium definition of the problem deriving necessary conditions and using these necessary conditions we present a set of sufficient conditions and a design methodology for the solution of the problem in question our analysis leads to a nonequilibrium enhancement of the internal model principle

a computational procedure for response statistics based optimization of stochastic non linear fe models abstract an approach for an efficient solution of response statistics based optimization problems of non linear fe systems under stochastic loading is presented a sequential approximate optimization approach where approximate stochastic analyses are used during portions of the optimization process is implemented in the proposed formulation in this approach analytical approximations of the performance functions in terms of the design variables are considered during the optimization process the analytical approximations are constructed by combining a mixed linearization approach with a stochastic response sensitivity analysis the state of the system is defined in terms of the statistical second moment characteristics of the structural response the stochastic loading and the response of the system are represented by an orthogonal series expansion of the corresponding covariance matrices in particular a truncated karhunen loeve k l expansion is applied the system of non linear equations is replaced by a statistical equivalent linear system the evaluation of the k l vectors is carried out by an efficient procedure that combines local linearization modal analysis and static response of higher structural modes an illustrative example is presented that shows the efficiency of the proposed methodology it considers a building finite element model enforced with non linear hysteretic devices and subject to a stochastic ground acceleration two types of problems are considered a minimum structural weight design problem and an optimal non linear device design problem

structural optimization using beam elements techniques for handling beam elements in structural optimization are investigated the complexities of evaluating the geometrical properties of a section stress recovery and design variable selection are successfully handled by the concept of an element library use of equivalent stress and separation of sensitivity variables and design variables program implementation is based on the use of an existing finite element analysis package and a numerical optimizer the quality of linearization of the behavior constraint functions is also investigated

an efficient approximation technique for frequency constraints in frame optimization an efficient approximation technique is presented for dealing with frequency constraints in frame optimization the method is based on a linear approximation of the eigenvalues with respect to the member section properties using this an approximate optimization problem is solved treating the physical dimensions of the beams as design variables when the eigenvalues are required the section properties are first calculated then using the approximation the eigenvalues are estimated and returned to the optimizer when the approximate optimum is found a detailed analysis is performed and the process is repeated examples are presented to demonstrate the method the method is simple yet treats the physical dimensions of the structure as design variables and allows for large move limits during the approximate optimization

the effects of linear and nonlinear characteristic parameters on the output frequency responses of nonlinear systems the associated output frequency response function in the present study a new concept known as the associated output frequency response function aofrf is introduced to facilitate the analysis of the effects of both linear and nonlinear characteristic parameters on the output frequency responses of nonlinear systems based on the aofrf concept the study has shown for the first time that the output frequency responses of a wide class of nonlinear systems that are described by the narx nonlinear auto regressive with exogenous input model can be represented by a polynomial function of both the system linear and nonlinear characteristic parameters of interests to the system analysis moreover an efficient algorithm is derived to determine the structure and coefficients of the aofrf based representation for system output frequency responses finally a case study is provided to demonstrate the effectiveness and advantages of the new aofrf based representation and the implication of the result to the analysis and design of nonlinear systems in the frequency domain

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

technical communique uniquely connecting frequency domain representations of given order polynomial wiener hammerstein systems the notion of frequency response functions has been generalized to nonlinear systems in several ways however a relation between different approaches has not yet been established in this paper frequency domain representations for nonlinear systems are uniquely connected for a class of nonlinear systems specifically by means of novel analytical results the generalized frequency response function gfrf and the higher order sinusoidal input describing function hosidf for polynomial wiener hammerstein systems are explicitly related assuming the linear dynamics are known necessary and sufficient conditions for this relation to exist and results on the uniqueness and equivalence of the hosidf and gfrf are provided finally this yields an efficient computational procedure for computing the gfrf from the hosidf and vice versa

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

basic properties and characterizations of incremental stability prioritizing flow time for a class of hybrid systems abstract this paper introduces incremental stability notions for a class of hybrid dynamical systems given in terms of differential equations and difference equations with state constraints the specific class of hybrid systems considered are those that do not have consecutive jumps nor zeno behavior the notion of incremental asymptotic stability is used to describe the behavior of the distance between every pair of solutions to the system having stable behavior incremental stability and approaching zero asymptotically incremental attractivity a version of this notion that is uniform in hybrid time with respect to initial conditions is also introduced these notions prioritize flow time and are illustrated in examples basic properties of the class of systems are considered and those implied by the new notions are revealed an equivalence characterization of the uniform notion is provided in terms of a k l function moreover sufficient and necessary conditions under which asymptotic stability implies the new incremental notions are provided we consider the case when the original hybrid system has an asymptotically stable compact set and also the case when an auxiliary hybrid system which has twice the dimension of the original system has a diagonal like set asymptotically stable

feasible methods for nonconvex nonsmooth problems with applications in green communications we propose a general feasible method for nonsmooth nonconvex constrained optimization problems the algorithm is based on the inexact solution of a sequence of strongly convex optimization subproblems followed by a step size procedure key features of the scheme are i it preserves feasibility of the iterates for nonconvex problems with nonconvex constraints ii it can handle nonsmooth problems and iii it naturally leads to parallel distributed implementations we illustrate the application of the method to an open problem in green communications whereby the energy consumption in mimo multiuser interference networks is minimized subject to nonconvex quality of service constraints

truncation order and its effect in a class of nonlinear systems fundamental results are established for truncation order and its effect in the volterra class of nonlinear systems these results provide a significant insight into the analytical relationships among truncation order truncation error and estimation error for the output spectra of nonlinear systems and also lead to the development of novel methods for choosing the truncation order and excitation magnitudes for accurate determination of nonlinear frequency response components these results should be important in the kernel estimation and frequency domain analysis of nonlinear systems on the basis of the volterra series structure and order selection of block oriented nonlinear systems with polynomial nonlinearity the results also provide a much improved version of the multi level excitation method for system analysis and identification

a mass constraint formulation for structural topology optimization with multiphase materials this work is focused on the topology optimization of lightweight structures consisting of multiphase materials instead of adopting the common idea of using volume constraint a new problem formulation with mass constraint is proposed meanwhile recursive multiphase materials interpolation rmmi and uniform multiphase materials interpolation ummi schemes are discussed and compared based on numerical tests and theoretical analysis it is indicated that the nonlinearity of the mass constraint introduced by rmmi brings numerical difficulties to attain the global optimum of the optimization problem on the contrary the ummi 2 scheme makes it possible to formulate the mass constraint in a linear form with separable design variables one such formulation favors very much the problem resolution by means of mathematical programming approaches especially the convex programming methods moreover numerical analysis indicates that fully uniform initial weighting is beneficial to seek the global optimum when ummi 2 scheme is used besides the relationship between the volume constraint and mass constraint is theoretically revealed the filtering technique is adapted to avoid the checkerboard pattern related to the problem with multiphase materials numerical examples show that the ummi 2 scheme with fully uniform initial weighting is reliable and efficient to deal with the structural topology optimization with multiphase materials and mass constraint meanwhile the mass constraint formulation is evidently more significant than the volume constraint formulation copyright 2011 john wiley sons ltd

interval algorithm for random number generation the problem of generating a random number with an arbitrary probability distribution by using a general biased m coin is studied an efficient and very simple algorithm based on the successive refinement of partitions of the unit interval 0 1 which we call the interval algorithm is proposed a fairly tight evaluation on the efficiency is given generalizations of the interval algorithm to the following cases are investigated 1 output sequence is independent and identically distributed i i d 2 output sequence is markov 3 input sequence is markov 4 input sequence and output sequence are both subject to arbitrary stochastic processes

multiple object identification coding in the case of ordinary identification coding a code is devised to identify a single object among n objects but in this paper we consider a coding problem to identify k objects at once among n objects in the both cases that k objects are ranked or not ranked by combining moulin koetter scheme with the varepsilon almost strongly universal class of hash functions used in kurosawa yoshida scheme an efficient and explicit coding scheme is proposed for k multiple object identification k moid coding furthermore it is shown that the k moid capacity c text k moid which is the maximum achievable coding rate in the k moid coding is equal to the ordinary channel capacity and the proposed scheme can attain c text k moid

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

convergent systems vs incremental stability two similar stability notions are considered one is the long established notion of convergent systems the other is the younger notion of incremental stability both notions require that any two solutions of a system converge to each other yet these stability concepts are different in the sense that none implies the other as is shown in this paper using two examples it is shown under what additional assumptions one property indeed implies the other furthermore this paper contains necessary and sufficient characterizations of both properties in terms of lyapunov functions

high quality approximation of eigenvalues in structural optimization a new function for approximating natural frequency constraints during structural optimization is presented the rayleigh quotient approximation rqa presented here icreases the quality of the approximate frequency constraint by approximating the modal strain and kinetic energies instead of the frequency eigenvalue itself

disturbance attenuation and h sub infinity control via measurement feedback in nonlinear systems a solution to the problem of disturbance attenuation via measurement feedback with internal stability is presented for an affine nonlinear system it is shown that the concept of disturbance attenuation in the sense of truncated l sub 2 norms can be given an interpretation in terms of the response to periodic inputs in the sense of rms amplitude even in the nonlinear setup in the case of state feedback a family of controllers is also provided the proofs of all these results are simple and provide deeper insight even in the analysis of the corresponding linear control problem

explicit construction of optimal constant weight codes for identification via channels the identification coding theorems of r ahlswede and g dueck 1981 have shown that for any nonzero probabilities of missed and false identification it is possible to transmit exp exp nr messages with n uses of a noisy channel where r is as close as desired to the shannon capacity of the channel that capability is achieved by the identification codes explicitly constructed with a three layer concatenated constant weight code used in conjunction with a channel transmission code of rate r

topology optimization of continuum structures with local stress constraints we introduce an extension of current technologies for topology optimization of continuum structures which allows for treating local stress criteria we first consider relevant stress criteria for porous composite materials initially by studying the stress states of the so called rank 2 layered materials then on the basis of the theoretical study of the rank 2 microstructures we propose an empirical model that extends the power penalized stiffness model also called simp for solid isotropic microstructure with penalization for inter mediate densities in a second part solution aspects of topology problems are considered to deal with the so called singularity phenomenon of stress constraints in topology design an constraint relaxation of the stress constraints is used we describe the mathematical programming approach that is used to solve the numerical optimization problems and show results for a number of example applications 1998 john wiley sons ltd

approximating the steady state periodic solutions of contractive systems we consider contractive systems whose trajectories evolve on a compact and convex state space it is well known that if the time varying vector field of the system is periodic then the system admits a unique globally asymptotically stable periodic solution obtaining explicit information on this periodic solution and its dependence on various parameters is important both theoretically and in numerous applications we develop an approach for approximating such a periodic trajectory using the periodic trajectory of a simpler system e g an lti system the approximation includes an error bound that is based on the input to state stability property of contractive systems we show that in some cases this error bound can be computed explicitly we also use the bound to derive a new theoretical result namely that a contractive system with an additive periodic input behaves like a low pass filter we demonstrate our results using several examples from systems biology

local stress constrained and slope constrained sand topology optimisation summary we study the alternative simultaneous analysis and design sand formulation of the local stress and slope constrained topology design problem it is demonstrated that a standard trust region lagrange newton sequential quadratic programming sqp type algorithm based in this case on strictly convex and separable approximate subproblems may converge to singular optima of the local stress constrained problem without having to resort to relaxation or perturbation techniques moreover due to the negation of the sensitivity analyses in sand the density and displacement variables are independent and the immense sparsity of the sand problem solutions to large scale problem instances may be obtained in a reasonable amount of computation time this article is protected by copyright all rights reserved

convergence properties for discrete time nonlinear systems three similar convergence notions are considered two of them are the long established notions of convergent dynamics and incremental stability the other is the more recent notion of contraction analysis all three convergence notions require that all solutions of a system converge to each other in this note we investigate the differences between these convergence properties for discrete time and time varying nonlinear systems by comparing the properties in pairs and using examples we also demonstrate a time varying smooth lyapunov function characterization for each of these convergence notions and with appropriate assumptions we provide several sufficient conditions to establish relationships between these properties in terms of lyapunov functions

mapping from parametric characteristics to generalized frequency response functions of non linear systems based on the parametric characteristic of the nth order generalized frequency response function gfrf for non linear systems described by a non linear differential equation nde model a mapping function from the parametric characteristics to the gfrfs is established by which the nth order gfrf can be directly written into a more straightforward and meaningful form in terms of the first order gfrf i e an n degree polynomial function of the first order gfrf the new expression has no recursive relationship between different order gfrfs and demonstrates some new properties of the gfrfs which can explicitly unveil the linear and non linear factors included in the gfrfs and reveal clearly the relationship between the nth order gfrf and its parametric characteristic as well as the relationship between the nth order gfrf and the first order gfrf the new results provide a novel and useful insight into the frequency domain analysis and design of non linear systems based on the gfrfs several examples are given to illustrate the theoretical results

constrained spectrum control a novel nonlinear model predictive control nmpc scheme is proposed in order to shape the harmonic response of constrained nonlinear systems the salient ingredient is the short time fourier transform stft of the system s output signal which is constrained in an nmpc problem leading to the novel formulation of so called spectrum constraints recursive feasibility and asymptotic stability of the proposed nmpc scheme with such spectrum constraints are guaranteed by means of an appropriate ellipsoidal terminal invariant set the efficacy of the proposed approach is demonstrated on a nonlinear vibration damping problem

alternative approximation concepts for space frame synthesis a structural synthesis methodology for the minimum mass design of 3 dimensionall frame truss structures under multiple static loading conditions and subject to limits on displacements rotations stresses local buckling and element cross sectional dimensions is presented a variety of approximation concept options are employed to yield near optimum designs after no more than 10 structural analyses available options include a formulation of the nonlinear mathematcal programming problem in either reciprocal section property rsp or cross sectional dimension csd space b two alternative approximate problem structures in each design space and c three distinct assumptions about element end force variations fixed element design element linking and temporary constraint deletion features are also included the solution of each approximate problem in either its primal or dual form is obtained using conmin a feasible directions program the frame truss synthesis methodology is implemented in the compass computer program and is used to solve a variety of problems these problems were chosen so that in addition to exercising the various approximation concepts options the results could be compared with previously published work

convergent dynamics a tribute to boris pavlovich demidovich we review and pay tribute to a result on convergent systems by the russian mathematician boris pavlovich demidovich in a sense demidovich s approach forms a prelude to a field which is now called incremental stability of dynamical systems developments on incremental stability are reviewed from a historical perspective

a novel characteristic parameter approach for analysis and design of linear components in nonlinear systems nonlinearity always brings difficulties to the analysis and design of practical systems this study shows that for a wide class of nonlinear systems described by nonlinear differential equations the nonlinear output spectrum can be expressed as a polynomial function with respect to linear model parameters based on the recently developed concepts of parametric characteristic analysis and nonlinear characteristic output spectrum ncos function the coefficients of the new ncos function are independent of the linear parameters of interest and can be directly determined with proposed procedures this reveals an explicit and analytical relationship between the output spectrum of a nonlinear system and its linear components and therefore provides a convenient tool for the analysis and design of nonlinear systems using only linear components or linear feedback control while simultaneously fully considering inherent nonlinear influence this result is a useful complement to the ncos function based analysis and design recently developed in the literature the effectiveness and usefulness of the results are demonstrated through an application to the analysis of an amplifier with a multi tone input for suppressing intermodulation distortion it is shown that the new results reveal a straightforward insight into the parametric optimization of the amplifier for suppression of intermodulation distortion

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

nonlinear influence in the frequency domain alternating series the nonlinear influence on system output spectrum is studied for a class of nonlinear systems which have volterra series expansion it is shown that under certain conditions the system output spectrum can be expressed in an alternating series with respect to some model parameters which define system nonlinearities the magnitude of the system output spectrum can therefore be suppressed by exploiting the properties of alternating series sufficient and necessary conditions in which the output spectrum can be cast into an alternating series are studied these results reveal a novel frequency domain insight into the nonlinear influence on a system and provide a new method for the analysis and design of nonlinear systems in the frequency domain examples are given to illustrate the results

frequency response functions for nonlinear convergent systems convergent systems constitute a practically important class of nonlinear systems that extends the class of asymptotically stable linear time invariant systems in this note we extend frequency response functions defined for linear systems to nonlinear convergent systems such nonlinear frequency response functions for convergent systems give rise to nonlinear bode plots which serve as a graphical tool for performance analysis of nonlinear convergent systems in the frequency domain the results are illustrated with an example

an efficient reliability based optimization scheme for uncertain linear systems subject to general gaussian excitation a very efficient methodology to carry out reliability based optimization of linear systems with random structural parameters and random excitation is presented the reliability based optimization problem is formulated as the minimization of an objective function for a specified reliability the probability that design conditions are satisfied within a given time interval is used as a measure of the system reliability approximation concepts are used to construct high quality approximations of dynamic responses in terms of the design variables and uncertain structural parameters during the design process the approximations are combined with an efficient simulation technique to generate explicit approximations of the reliability measures with respect to the design variables in particular an efficient importance sampling technique is used to estimate the failure probabilities the number of dynamic analyses as well as reliability estimations required during the optimization process are reduced dramatically several example problems are presented to illustrate the effectiveness and feasibility of the suggested approach

identification via channels the authors main finding is that any object among doubly exponentially many objects can be identified in blocklength n with arbitrarily small error probability via a discrete memoryless channel dmc if randomization can be used for the encoding procedure a novel doubly exponential coding theorem is presented which determines the optimal r that is the identification capacity of the dmc as a function of its transmission probability matrix this identification capacity is a well known quantity namely shannon s transmission capacity for the dmc

globally convergent optimization algorithm using conservative convex separable diagonal quadratic approximations we implement and test a globally convergent sequential approximate optimization algorithm based on convexified diagonal quadratic approximations the algorithm resides in the class of globally convergent optimization methods based on conservative convex separable approximations developed by svanberg at the start of each outer iteration the initial curvatures of the diagonal quadratic approximations are estimated using historic objective and or constraint function value information or by building the diagonal quadratic approximation to the reciprocal approximation at the current iterate during inner iterations these curvatures are increased if no feasible descent step can be made although this conditional enforcement of conservatism on the subproblems is a relaxation of the strict conservatism enforced by svanberg global convergence is still inherited from the conservative convex separable approximations framework developed by svanberg a numerical comparison with the globally convergent version of the method of moving asymptotes and the nonconservative variants of both our algorithm and method of moving asymptotes is made

moving asymptotes and active set strategy for constrained optimization design in magnetostatic problems in this paper we present an improvement of the optimization technique of the moving asymptotes applied to a class of magnetostatic design problem our approach includes among other aspects an active set strategy which turns possible to find feasible points during the iterative process we present some numerical results obtained on real life case studies where the functions are computed by a complex finite element routine

identification in the presence of feedback a discovery of new capacity formulas a study is made of the identification problem in the presence of a noiseless feedback channel and the second order capacity c sub f resp c sub f for deterministic resp randomized encoding strategies is determined several important phenomena are encountered 1 although feedback does not increase the transmission capacity of a discrete memoryless channel dmc it does increase the second order identification capacity 2 noise increases c sub f 3 the structure of the new capacity formulas is simpler than c e shannon s 1948 familiar formula this has the effect that proofs of converses become easier than in the authors previous work

lyapunov characterization of forced oscillations this paper develops a lyapunov approach to the analysis of input output characteristics for systems under the excitation of a class of oscillatory inputs apart from sinusoidal signals the class of oscillatory inputs include multi tone signals and periodic signals which can be described as the output of an autonomous system the lyapunov approach is developed for linear systems homogeneous systems differential inclusions and nonlinear systems differential inclusions respectively in particular it is established that the steady state gain can be arbitrarily closely characterized with lyapunov functions if the output response converges exponentially to the steady state other output measures that will be characterized include the peak of the transient response and the convergence rate tools based on linear matrix inequalities lmis are developed for the numerical analysis of linear differential inclusions ldis this paper s results can be readily applied to the evaluation of frequency responses of general nonlinear and uncertain systems by restricting the inputs to sinusoidal signals guided by the numerical result for a second order ldi an interesting phenomenon is observed that the peak of the frequency response can be strictly larger than the l 2 gain

a hybrid optimal synthesis method for truss structures considering shape material and sizing variables a generalized hybrid optimal synthesis method is developed for truss structures in which the design variables are the co ordinates of the panel points cross sectional areas and discrete material kinds of member elements the primary design problem is formulated in terms of the shape material and sizing variables and approximated to a sequence of convex and separable subproblems by using mixed direct reciprocal design variables each subproblem is solved by a dual method in which the continuous shape and sizing variables are optimized by a newton type algorithm and the discrete material and continuous sizing variables are improved by a discrete sensitivity analysis using the proposed method discrete material kinds shape and sizing variables can be systematically improved to obtain an optimum solution the rigourness reliability and efficiency of the method are demonstrated by applying it to the minimum cost design of trusses subjected to stress and displacement constraints

strongly universal hashing and identification codes via channels this article shows that spl epsiv almost strongly universal classes of hash functions can yield better explicit constructions of identification codes via channels id codes and identification plus transmission codes it codes than the previous explicit constructions of verdu and wei 1993

a unified parametric design approach to structural shape optimization this paper presents a general parametric design approach for 2 d shape optimization problems this approach has been achieved by integrating practical design methodologies into numerical procedures it is characterized by three features i automatic selection of a minimum number of shape design variables based on the cad geometric model ii integration of sequential convex programming algorithms to solve equality constrained optimization problems iii efficient sensitivity analysis by means of the improved semi analytical method it is shown that shape design variables can be either manually or systematically identified with the help of equality constraints describing the relationship between geometric entities numerical solutions are performed to demonstrate the applicability of the proposed approach a discussion of the results is also given

efficient approximation concepts using second order information the primary goal of this paper is to show how second derivative information can be used in an effective way in structural optimization problems the basic idea is to generate such an information at the expense of only one more virtual load case in the sensitivity analysis part of the finite element code to achieve this goal a primal dual approach is employed that can also be interpreted as a sequential quadratic programming method another objective is to relate the proposed method to the well known family of approximation concepts techniques where the primary optimization problem is transformed into a sequence of non linear explicit subproblems when restricted to diagonal second derivatives the new approach can be viewed as a recursive convex programming method similar to the convex linearization method conlin and to its recent generalization the method of moving asymptotes mma this new method has been successfully tested on simple problems that can be solved in closed form as well as on sizing optimization of trusses in all cases the method converges faster than conlin mma or other approximation techniques based on reciprocal variables

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

on convergence properties of piecewise affine systems in this paper convergence properties of piecewise affine pwa systems are studied in general a system is called convergent if all its solutions converge to some bounded globally asymptotically stable steady state solution the notions of exponential uniform and quadratic convergence are introduced and studied it is shown that for non linear systems with discontinuous right hand sides quadratic convergence i e convergence with a quadratic lyapunov function implies exponential convergence for pwa systems with continuous right hand sides it is shown that quadratic convergence is equivalent to the existence of a common quadratic lyapunov function for the linear parts of the system dynamics in every mode for discontinuous bimodal pwa systems it is proved that quadratic convergence is equivalent to the requirements that the system has some special structure and that certain passivity like condition is satisfied for a general multimodal pwa system these conditions become sufficient for quadratic convergence an example illustrating the application of the obtained results to a mechanical system with a one sided restoring characteristic which is equivalent to an electric circuit with a switching capacitor is provided the obtained results facilitate bifurcation analysis of pwa systems excited by periodic inputs substantiate numerical methods for computing the corresponding periodic responses and help in controller design for pwa systems

brief paper spectral analysis of block structured nonlinear systems and higher order sinusoidal input describing functions when analyzing and modeling dynamical systems in the frequency domain the effects of nonlinearities need to be taken into account this paper contributes to the analysis of the effects of nonlinearities in the frequency domain by supplying new analytical tools and results that allow spectral analysis of the output of a class of nonlinear systems a mapping from the parameters defining the nonlinear and lti dynamics to the output spectrum is derived which allows analytic description and analysis of the corresponding higher order sinusoidal input describing functions the theoretical results are illustrated by examples that show both the use and efficiency of the proposed algorithms

steady state analysis and regulation of discrete time nonlinear systems this paper presents results on steady state analysis and regulation for nonlinear discrete time systems subject to time varying excitations in the analysis part of the paper for convergent nonlinear systems which have uniquely defined steady state responses to excitations we provide a complete characterization of the steady state responses to excitations generated by an exosystem as a corollary we obtain a nonlinear frequency response function which extends the well known frf defined for linear systems to the class of nonlinear convergent systems in the control part of the paper we present a characterization of all controllers solving the global output regulation problem all these results are obtained using the machinery of convergent systems extended to the discrete time setting for piecewise affine systems general results are supplied with a constructive design procedure

a novel method of non probabilistic reliability based topology optimization corresponding to continuum structures with unknown but bounded uncertainties abstract a new non probabilistic reliability based topology optimization nrbto method for detailed design of continuum structures is proposed in this paper in which the unknown but bounded ubb uncertainties existing in material and external loads are considered simultaneously based on the interval set theoretic model traditional displacement constraint is transformed into the non probabilistic reliability format in which a novel measuring index namely the optimization feature distance is defined by a combination of the area ratio ideas thus the optimal layout issue is converted by the lightweight design problem with displacement reliability constraints moreover the interval parametric vertex approach and the adjoint vector method are also employed to obtain the sensitivity information between the reliability measurement and design variables by utilizing the method of moving asymptotes mma the optimization problem that is investigated can be solved iteratively two engineering examples are eventually presented to demonstrate the validity and effectiveness of the methodology that has been developed and numerical results show that considering the ubb uncertainty effects during the whole procedure of topology optimization may have a significant influence on the final structural configurations

framework for the buckling optimization of variable angle tow composite plates variable angle tow describes fibers in a composite lamina that have been steered curvilinearly in doing so substantially enlarged freedom for stiffness tailoring of composite laminates is enabled variable angle tow composite structures have been shown to have improved buckling and postbuckling load carrying capability when compared to straight fiber composites however their structural analysis and optimal design is more computationally expensive due to the exponential increase in number of variables associated with spatially varying planar fiber orientations in addition to stacking sequence considerations in this work an efficient two level optimization framework using lamination parameters as design variables has been enhanced and generalized to the design of variable angle tow plates new explicit stiffness matrices are found in terms of component material invariants and lamination parameters the convex hull property of b splines is exploited to ensure pointwise feasibility of lamination paramet

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

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

an approximation concepts approach to shape optimal design abstract in the past much of the work done in structural optimization consisted in resizing the members of fixed configuration models in that case a powerful design procedure has now emerged which is based on the coordinate use of explicit high quality approximations of the behavior constraints and dual methods of mathematical programming there is however a large class of problems for which the main degrees of freedom for the designer correspond to the shape of the structure itself the main objectives of this paper are to recall briefly a convenient geometric representation in which the boundaries of the structure are represented by bezier or b spline curves and then to discuss the choice of optimization algorithm it is shown that cost efficient methods for structural sizing may be advantageously extended to shape optimal design problems different approximation schemes are tested and a new general optimization algorithm is presented that combines mixed approximations and dual methods many large scale applications are treated to demonstrate the generality and the efficiency of the new formulation finally considerations are given about an integrated approach including cad computer codes and finite element optimization software

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