a level set method for shape and topology optimization of large displacement compliant mechanisms a parameterization level set method is presented for structural shape and topology optimization of compliant mechanisms involving large displacements a level set model is established mathematically as the hamilton jacobi equation to capture the motion of the free boundary of a continuum structure the structural design boundary is thus described implicitly as the zero level set of a level set scalar function of higher dimension the radial basis function with compact support is then applied to interpolate the level set function leading to a relaxation and separation of the temporal and spatial discretizations related to the original partial differential equation in doing so the more difficult shape and topology optimization problem is now fully parameterized into a relatively easier size optimization of generalized expansion coefficients as a result the optimization is changed into a numerical process of implementing a series of motions of the implicit level set function via an existing efficient convex programming method with the concept of the shape derivative the geometrical non linearity is included in the rigorous design sensitivity analysis to appropriately capture the large displacements of compliant mechanisms several numerical benchmark examples illustrate the effectiveness of the present level set method in particular its capability of generating new holes inside the material domain the proposed method not only retains the favorable features of the implicit free boundary representation but also overcomes several unfavorable numerical considerations relevant to the explicit scheme the reinitialization procedure and the velocity extension algorithm in the conventional level set method

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

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

uniform decision problems for automatic semigroups we consider various decision problems for automatic semigroups which involve the provision of an automatic structure as part of the problem instance with mild restrictions on the automatic structure which are necessary to make the problem well defined the uniform word problem for semigroups described by automatic structures is decidable under the same conditions we show that one can also decide whether the semigroup is completely simple or completely zero simple in the case that it is one can compute a rees matrix representation for the semigroup in the form of a rees matrix together with an automatic structure for its maximal subgroup on the other hand we show that it is undecidable in general whether a given element of a given automatic monoid has a right inverse

composites with symmetry and their extremal properties abstract we identify microstructures that extremize sums of strain energy densities for one energy we exhibit optimal laminar composites that are orthotropic with axes given by the eigenbasis of the homogeneous strain some partial results on the uniqueness of the optimal microstructures are obtained

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

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

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

fault tolerant edge bipancyclicity of faulty hypercubes under the conditional fault model it is well known that the n dimensional hypercube qn is one of the most versatile and efficient interconnection network architecture yet discovered for building massively parallel or distributed systems let f be the faulty set of qn and let fv fe be the numbers of faulty vertices and faulty edges in f respectively an edge e x y is said to be free if e x y are not in f and a cycle is said to be fault free if there is no faulty vertex or faulty edge on the cycle in this paper we prove that each free edge x y in qn for n 3 lies on a fault free cycle of any even length from 6 to 2 n 2 f v if f v f e 2 n 5 f e n 2 and both x and y are incident to at least two free edges this result confirms a conjecture reported in the literature

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

effective stiffnesses of transversely non homogeneous plates with unidirectional periodic structure abstract this paper presents a derivation and analysis of closed formulae for the membrane bending and reciprocal effective stiffnesses of elastic orthotropic and transversely asymmetric plates with microstructures periodic in one direction the derivation is based on the concept of imposing hencky type displacement constraints on the solutions to the caillerie kohn vogelius local homogenization problems reduction of the dimension of the problems by one makes it possible to solve the new approximate local problems exactly thus enabling one to find the relevant formulae in closed form ready for engineering applications as well as for optimization and sensitivity studies this paper generalizes the previous results of the author int j solids structures 29 309 326 1992 concerning the bending of transversely symmetric periodic plates

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

sensitivity analysis and optimization of vibration modes in continuum systems abstract the sensitivity analysis of objective functions including the eigenmodes of continuum systems governed by scalar helmholtz equations is carried out in continuum form in addition based on the sensitivity the mode shapes are specified through numerical optimization using the continuum sensitivity and adjoint equation the physical nature of them can be analyzed which helps to explain the nature of the target optimization problem moreover the continuum sensitivity and adjoint equation contribute to the quick numerical implementation of sensitivity analysis using software that can solve an arbitrary partial differential equation directly a scalar helmholtz equation in 1d or 2d domain is considered the sensitivity analysis is performed for the general objective function formulated as a function of the eigenmode in continuum form a minimization problem using the least squared error i e difference between the eigenvector and target mode shape is set as a sample objective function for both the first and second eigenmodes the sensitivity and the adjoint equation are derived for this objective function 1d and 2d numerical sensitivity analysis and optimization examples are studied to illustrate the validity of the derived sensitivity

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

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

fault tolerance of vertex pancyclicity in alternating group graphs abstract we study fault tolerance of vertex k pancyclicity of the alternating group graph ag n a graph g is vertex k pancyclic if for every vertex p g there is a cycle going through p of every length from k to g xue and liu z j xue s y liu an optimal result on fault tolerant cycle embedding in alternating group graphs inform proc lett 109 2009 1197 1201 put the conjecture that ag n is 2 n 7 fault tolerant vertex pancyclic which means that if the number of faults f 2 n 7 then ag n f is still vertex pancyclic chang and yang j m chang j s yang fault tolerant cycle embedding in alternating group graphs appl math comput 197 2008 760 767 showed that for the shortest cycles the fault tolerance of ag n is much lower they noted that with n 2 faults one can cut all 3 cycles going through a given vertex p it is easy to observe that the same set of faults cuts all 4 and 5 cycles going through p on the other hand they show that ag n is n 3 fault tolerant vertex 3 pancyclic in this paper we show that the cycles of length 6 are much more fault tolerant more precisely we show that ag n is 2 n 6 fault tolerant vertex 6 pancyclic this bound is optimal because every vertex p has 2 n 4 neighbors

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

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

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

thickness optimization of a multilayered structure on the coupling surface between a structure and an acoustic cavity this paper describes a new design method to optimize thickness distribution of a multilayered structure which is located on the coupling surface between a structure and an acoustic cavity the design method is based on the concept of the density approach in topology optimization incorporating a transfer matrix for a multilayered structure that includes a poroelastic media layer the one dimensional transfer matrix adopted here is an approximate representation addressing vibro acoustic effects inherent in a multilayered structure and balances calculation resources and desired accuracy applying the transfer matrix representation as boundary conditions on the coupling surface between a structure and an acoustic cavity the modified equilibrium equation of the vibro acoustic system is derived which is approximately but efficiently solved by the modal approach in this study the problem of minimizing the acoustic pressure within the cavity over the prescribed frequency range is formulated under the volume constraint of the poroelastic media layer the continuous approximation of thickness distribution is assumed and the thickness of the poroelastic media layer at each nodal point is chosen as design variables numerical results show that an acoustic response is significantly reduced by the optimal thickness distribution having a total weight equal to or less than that in the initial uniform thickness these demonstrate that the proposed method is effective to design the optimal thickness distribution of a multilayered structure

extensions and submonoids of automatic monoids in this paper submonoids and extensions of automatic and p automatic monoids are studied the concept of a p automatic monoid is a variant on the usual concept of an automatic monoid designed to allow a geometric characterization analogous to the group case in the case of right cancellative monoids the two concepts coincide here we study rational submonoids of p automatic monoids being able to show in many cases that p automaticity is inherited our sharpest results concern rational subgroups also closure properties are established for various notions of extensions of p automatic monoids including different types of products ideal extensions and rees matrix constructions

fault tolerant cycle embedding in alternating group graphs abstract cycle embedding is an important issue in evaluating the efficiency of interconnection networks and is also an extension of the theoretical research on hamiltonicity in this paper we study the fault tolerant hamiltonicity of alternating group graphs which were recently proposed as interconnection topologies for parallel and distributed systems a cycle of length l is said to be an l cycle let f be a set of faulty vertices in an n dimensional alternating group graph ag n and let m be the number of vertices in ag n f a previous result in j m chang j s yang y l wang y cheng panconnectivity fault tolerant hamiltonicity and hamiltonian connectivity in alternating group graphs networks 44 2004 302 310 showed that for n 4 ag n f is hamiltonian i e ag n f possesses a hamiltonian cycle if f n 2 and ag n f is hamiltonian connected i e every two vertices of ag n f are connected by a hamiltonian path if f n 3 in this paper we show the following results i ag n f is pancyclic i e ag n f contains an l cycle for each l with 3 l m if f n 2 ii ag n f is vertex pancyclic i e every vertex of ag n f is contained in an l cycle for each l with 3 l m if f n 3 and iii ag n f is edge 4 pancyclic i e every edge of ag n f is contained in an l cycle for each l with 4 l m if f n 4 the first result is an improvement over the previous one and the last two results are new characterization of fault tolerant pancyclicity on ag n all the results we achieved are the best possible in the sense that the number of faulty vertices cannot be increased

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

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

conditional fault tolerant edge bipancyclicity of hypercubes with faulty vertices and edges let f be a faulty set in an n dimensional hypercube q n such that in q n f each vertex is incident to at least two edges and let f v f e be the numbers of faulty vertices and faulty edges in f respectively in this paper we consider the fault tolerant edge bipancyclicity of hypercubes it is shown that each edge in q n f for n 3 lies on a fault free cycle of any even length from 6 to 2 n 2 f v if f v f e 2 n 5 this gives an answer for a problem proposed by yang et al 2016 33 consider hypercubes with mixed faulty edges and faulty vertices under conditional fault model improve the previous results about the fault tolerant edge bipancyclicity of hypercubes give an affirmative answer for a problem proposed by yang et al 2016

analysis and optimization of nonsmooth arches it is our aim to present a new treatment for some classical models of arches and for their optimization in particular our approach allows us to study nonsmooth arches while the standard assumptions from the literature require w 3 infty regularity for the parametric representation moreover by a duality type argument the deformation of the arches may be explicitly expressed by integral formulas this also provides a complete solution of the so called as examples for the shape optimization problems under study we mention the design of the middle curve of a clamped arch such that under a prescribed load the obtained deflection satisfies certain desired properties in all cases no smoothness is required for the design parameters

fault hamiltonicity and fault hamiltonian connectivity of the arrangement graphs the arrangement graph a sub n k is a generalization of the star graph there are some results concerning fault hamiltonicity and fault hamiltonian connectivity of the arrangement graph however these results are restricted in some particular cases and thus are less completed we improve these results and obtain a stronger and simpler statement let n k spl ges 2 and f spl sube v a sub n k spl cup e a sub n k we prove that a sub n k f is hamiltonian if f spl les k n k 2 and a sub n k f is hamiltonian connected if f spl les k n k 3 these results are optimal

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

a new formulation of the problem of optimum reinforcement of reissner mindlin plates abstract a new formulation of the problem of computing the layout of reinforcement of reissner mindlin plates for minimum compliance is presented bending and transverse shear stiffness properties of plates with an arbitrary but finite number of local rib directions and widths are computed using standard homogenization techniques these properties are then expressed in terms of only four variables that fully describe the anisotropy of the plate the optimization problem is solved in two stages consisting of a local four dimensional maximization problem where a given amount of material is optimally allocated into an arbitrary number of fine scale stiffeners of different widths and orientations and a global one dimensional optimization problem where the optimum spatial layout of material is determined a discussion of implementation issues is included and an example is solved to illustrate the approach

the t k diagnosability for regular networks the t k diagnosis strategy can significantly enhance the system s self diagnosing capability at the expense of no more than k fault free processors vertices being mistakenly diagnosed as faulty under the pmc model it is a generalization of the precise and pessimistic diagnosis strategies of system level diagnosis on multiprocessor systems it can detect up to t faulty processors vertices which might include at most k misdiagnosed processors vertices where k is typically a small number in the case k ge 1 to our knowledge there is no known t k diagnosis algorithm for general regular networks in this paper we first propose a general t k diagnosis k ge 1 algorithm for some m regular networks these m regular networks satisfying some conditions could establish the t k diagnosis algorithm say t k g diag to determine the t k diagnosability the complexity of this algorithm is only o n log n when n ge 2 m or o nm when n where n is the number of vertices in the network second we present a complete proof that the network g is actually t k diagnosable finally we establish the t k diagnosability 1 le k le 3 of some regular networks including an n dimensional alternating group graph an n dimensional split star network a l n hypermesh and an n l star graph which are well known interconnection networks proposed for multiprocessor systems

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

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

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

leader following consensus of multi agent systems under fixed and switching topologies the leader following consensus problem of higher order multi agent systems is considered in the system the dynamics of each agent and the leader is a linear system the control of each agent using local information is designed and detailed analysis of the leader following consensus is presented for both fixed and switching interaction topologies which describe the information exchange between the multi agent systems the design technique is based on algebraic graph theory riccati inequality and lyapunov inequality simulations indicate the capabilities of the algorithms

fault tolerant edge and vertex pancyclicity in alternating group graphs abstract in j m chang j s yang fault tolerant cycle embedding in alternating group graphs appl math comput 197 2008 760 767 the authors claim that every alternating group graph agn is n 4 fault tolerant edge 4 pancyclic which means that if the number of faults f n 4 then every edge in agn f is contained in a cycle of length l for every 4 l n 2 f they also claim that agn is n 3 fault tolerant vertex pancyclic which means that if f n 3 then every vertex in agn f is contained in a cycle of length l for every 3 l n 2 f their proofs are not complete they left a few important things unexplained in this paper we fulfill these gaps and present another proofs that agn is n 4 fault tolerant edge 4 pancyclic and n 3 fault tolerant vertex pancyclic

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

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

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

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

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

a homogenization method for shape and topology optimization abstract shape and topology optimization of a linearly elastic structure is discussed using a modification of the homogenization method introduced by bendsoe and kikuchi together with various examples which may justify validity and strength of the present approach for plane structures

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

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

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

extra diagnosability and good neighbor diagnosability of n dimensional alternating group graph ag n under the pmc model abstract the h extra diagnosability and g good neighbor diagnosability are two important diagnostic strategies at system level that can significantly enhance the system s self diagnosing capability the h extra diagnosability ensures that every component of the system after removing a set of faulty vertices has at least h 1 vertices the g good neighbor diagnosability guarantees that after removing some faulty vertices every vertex in the remaining system has at least g neighbors in this paper we analyze the extra diagnosability and good neighbor diagnosability in a well known n dimensional alternating group graph a g n proposed for multiprocessor systems under the pmc model we first establish that the 1 extra diagnosability of a g n n 5 is 4 n 10 then we prove that the 2 extra diagnosability of a g n n 5 is 6 n 17 next we address that the 3 extra diagnosability of a g n n 5 is 8 n 25 finally we obtain that the g restricted connectivity and the g good neighbor diagnosability of a g n n 5 are 2 g 2 n 2 g 2 4 g and 2 g 2 n 2 g 2 4 2 g for 1 g 2 respectively

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

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

panconnectivity and pancyclicity of the 3 ary n cube network under the path restrictions the k ary n cube denoted by q n k is one of the most important interconnection networks for parallel computing in this paper we consider the problem of embedding paths and cycles into 3 ary n cubes under the path restrictions let p be a path in q n 3 we show that when v p 2n 3 there exists a path of any length from n 1 to v q n 3 p 1 between two arbitrary nodes in q n 3 p we also prove that when e p 2n 1 there exists a cycle of any length from e p n to v q n 3 in q n 3 passing through p our results are best possible in some sense

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

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

state agreement for continuous time coupled nonlinear systems two related problems are treated in continuous time first the state agreement problem is studied for coupled nonlinear differential equations the vector fields can switch within a finite family associated to each vector field is a directed graph based in a natural way on the interaction structure of the subsystems generalizing the work of moreau under the assumption that the vector fields satisfy a certain subtangentiality condition it is proved that asymptotic state agreement is achieved if and only if the dynamic interaction digraph has the property of being sufficiently connected over time the proof uses nonsmooth analysis second the rendezvous problem for kinematic point mass mobile robots is studied when the robots fields of view have a fixed radius the circumcenter control law of ando e ieee trans robotics automation 15 1999 pp 818 828 is shown to solve the problem the rendezvous problem is a kind of state agreement problem but the interaction structure is state dependent

online identification of continuous time systems with unknown time delay in this note we present a recursive algorithm for online identification of systems with unknown time delay the proposed algorithm can be interpreted as an approximate nonlinear least squares corresponding to modified normalized or un normalized least squares when the normalizing factor spl gamma 0 or spl gamma 0 respectively both algorithms are essentially extensions to general least squares methodology simulation studies demonstrate the characteristics and performance of these algorithms

optimization of a plate with holes abstract we consider a simply supported plate with constant thickness defined on an unknown multiply connected domain we optimize its shape according to some given performance functional our method is of fixed domain type easy to be implemented based on a fictitious domain approach and the control variational method the algorithm that we introduce is of gradient type and performs simultaneous topological and boundary variations numerical experiments are also included and show its efficiency

automatic semigroup acts to give a general framework for the theory of automatic groups and semigroups we introduce the notion of automaticity for semigroup acts we investigate their basic properties and discuss how the property of being automatic behaves under changing the generators of the acting semigroup and under changing the generators of the semigroup act in particular we prove that under some conditions on the acting semigroup the automaticity of the act is invariant under changing the generators since automatic semigroups can be seen as a special case of automatic semigroup acts our result generalizes and extends the corresponding result on automatic semigroups where the semigroup s satisfies s sss ss we also give a geometric approach in terms of the fellow traveller property and discuss the solvability of the equality problem in automatic semigroup acts our notion gives rise to a variety of definitions of automaticity depending on the set chosen as a semigroup act and we discuss future research directions

spatial frequency control for the systematic generation of optimal candidate designs having various topological complexities abstract in practical engineering design problems there are some design and manufacturing considerations that are difficult or infeasible to express in terms of an objective function or a constraint among them we pay attention to the topological complexity of optimized designs which are difficult to quantify in this situation a set of optimal candidate designs having different topological complexities not just a single optimal design is preferred in this work the mean spatial frequency is proposed as a means to measure the topological complexity of an optimized design to maximize the system performance and to control the mean spatial frequency the topology design optimization in the m band wavelet transformed multiscale design space is proposed in the proposed scheme the mean frequency is controlled effectively by choosing different design space resolution in the multiscale design space and the performance maximization is treated as the objective function of the topology optimization the procedure to transform the original design space into the multiscale design space by the m band daubechies wavelet is also explained in some details

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

on discrete time convergence for general linear multi agent systems under dynamic topology this note aims to develop the nonnegative matrix theory in particular the product properties of infinite row stochastic matrices which is widely used for multiple integrator agents to deal with the convergence analysis of general discrete time linear multi agent systems mass with the proposed approach it is finally shown both theoretically and by simulation that the consensus for all the agents can be reached exponentially fast under relaxed conditions i e the individual uncoupled system is allowed to be strictly unstable in the discrete time sense and it is only required that the joint of the communication topologies has a spanning tree frequently enough moreover a least convergence rate as well as an upper bound for the strictly unstable mode which are independent of the switching mode of the system are specified as well

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

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