conditionally solvable path integral problems ii natanzon potentials new classes of exactly solvable potentials are discussed within the path integral formalism they are constructed from the hypergeometric and confluent natanzon potentials respectively it is found that they allow incorporation of four free parameters which give rise to fractional power behaviour long range and strongly anharmonic terms we find six different classes of such potentials

extending the class of solvable potentials i the infinite potential well with a sinusoidal bottom this is the first in a series of papers where we succeed in enlarging the class of exactly solvable potentials in one and three dimensions by obtaining solutions for new relativistic and nonrelativistic problems this is accomplished by constructing a matrix representation of the wave operator in a complete square integrable basis that makes it tridiagonal expanding the wave function in this basis makes the wave equation equivalent to a three term recursion relation for the expansion coefficients consequently finding solutions of the recursion relation is equivalent to solving the original problem doing so results in a larger class of solvable potentials the usual diagonal representation constraint results in a reduction from the larger class to the conventional class of solvable potentials giving the well known energy spectra and the corresponding wave functions moreover some of the new solvable problems show evidence of a klauder like phenomenon in the present work we give an exact solution for the infinite potential well with a bottom that has a sinusoidal shape

the caratheodory toeplitz problem with partial data abstract we treat a positive extension problem in an algebra of periodic doubly infinite operator matrices the given data have a stalactite type pattern the problem may be viewed as an operator valued caratheodory toeplitz problem with partially described data necessary and sufficient conditions are given for the existence of a solution the set of all solutions is described and a maximum entropy result is obtained as well in the matrix valued case the problem was also considered by alpay et al linear algebra appl 268 1998 247 where the problem was rephrased as an interpolation problem requiring symmetries and solutions were given in these terms we shall also interpret our results in the context of cyclostationary stochastic processes

the evolutionary structural optimization method theoretical aspects abstract in 1993 y m xie and g p steven introduced an approach called evolutionary structural optimization eso eso is based on the simple idea that the optimal structure maximum stiffness minimum weight can be produced by gradually removing the ineffectively used material from the design domain the design domain is constructed by the fe method and furthermore external loads and support conditions are applied to the element model considering the engineering aspects eso seems to have some attractive features the eso method is very simple to program via the fea packages and requires a relatively small amount of fea time additionally the eso topologies have been compared with analytical ones e g michell trusses and so far the results are quite promising on the other hand eso does not have a solid theoretical basis and consequently the eso minimization problem is still unresolved since the good agreement between the results cannot be just a coincidence in this paper we will study whether the gradual removal of material can be explained mathematically and whether the theoretical basis of eso can be outlined first a minimization problem solved by eso is examined based on the results of earlier publications it was assumed that the eso method minimizes the compliance volume product of a structure or a finite element model it was noted that the sequential linear programming slp based approximate optimization method followed by the simplex algorithm is equivalent to eso if the strain energy rejection criterion is utilized however eso should be applied so that the elements corresponding to the design domain are equally sized if this requirement is not met the rejection criterion which also considers the varying sizes of the elements should be used additionally the element stiffness matrices and element volumes should be linearly dependent on the design variables also linearly elastic material is assumed at each iteration the rejected elements should be removed completely most often only element removal is allowed in eso if the design variables are initially assigned values other than the maximum value however the elements should be allowed to reenter the design domain this subject obviously needs further study typically eso is applied to problems having a planar design domain with in plane forces only in these cases eso produces truss like equally stressed and maximum stiffness topologies it is often recommended that based on the topology optimization a new finite element discretization should be employed after that the sizing optimization procedure can be performed since eso seems to be producing truss like topologies eso should be applied to structural problems having pin jointed connections for other types of structures eso should be studied further finally it can be concluded that eso is not just an intuitive method as it has a very distinct theoretical basis it is also very simple to employ in engineering design problems for this reason eso has potential to become a tool for design engineers

path integral solution of a class of potentials related to the poschl teller potential some new exact path integral treatments are presented these are the path integrals for the symmetric top the smooth step the rosen morse and the manning rosen potential by appropriate spacetime transformations these path integral problems can be reduced to the path integral problem of the poschl teller potential

on solvable potentials related to so 2 2 ii natanzon potentials general natanzon potentials related to the so 2 2 group are studied the s matrices for systems under consideration are related to intertwining operators between weyl equivalent most degenerate principal series representations of so 2 2

algebraic solution for the natanzon hypergeometric potentials an algebraic method based on a strategy that makes use of a realization of the algebra so 2 1 in terms of differential operators is used to solve the bound state problem for the most general natanzon potentials for which the schrodinger equation can be reduced to hypergeometric form hence hypergeometric potentials

an efficient constraint handling method for genetic algorithms many real world search and optimization problems involve inequality and or equality constraints and are thus posed as constrained optimization problems in trying to solve constrained optimization problems using genetic algorithms gas or classical optimization methods penalty function methods have been the most popular approach because of their simplicity and ease of implementation however since the penalty function approach is generic and applicable to any type of constraint linear or nonlinear their performance is not always satisfactory thus researchers have developed sophisticated penalty functions specific to the problem at hand and the search algorithm used for optimization however the most difficult aspect of the penalty function approach is to find appropriate penalty parameters needed to guide the search towards the constrained optimum in this paper ga s population based approach and ability to make pair wise comparison in tournament selection operator are exploited to devise a penalty function approach that does not require any penalty parameter careful comparisons among feasible and infeasible solutions are made so as to provide a search direction towards the feasible region once sufficient feasible solutions are found a niching method along with a controlled mutation operator is used to maintain diversity among feasible solutions this allows a real parameter ga s crossover operator to continuously find better feasible solutions gradually leading the search near the true optimum solution gas with this constraint handling approach have been tested on nine problems commonly used in the literature including an engineering design problem in all cases the proposed approach has been able to repeatedly find solutions closer to the true optimum solution than that reported earlier

summing the spectral representations of poschl teller and rosen morse fixed energy amplitudes the spectral representations of the fixed energy amplitude of the symmetric and the general poschl teller potentials are summed via a sommerfeld watson transformation which leads to a simple closed form expression the result is used to write down a similar expression for the symmetric and general rosen morse potentials exploiting the close correspondence that exists between the two systems within the schrodinger theory and the path integral formalism via a duru kleinert transformation from the singularities of the latter amplitude the bound and continuum states of the general rosen morse potential are extracted

some convergence results in perimeter controlled topology optimization abstract the computation of optimal topologies of elastic continuum structures using a constraint on the perimeter is investigated predicting macroscopic black white topologies without the use of homogenization techniques this approach is presently one of the most attractive approaches in topology optimization mathematical justifications are given for both the relaxation of the discrete value constraint on the design variable and for the finite element discretizations it turns out that the way in which the perimeter has been calculated to date the numerical results will not approximate the intended original problem but one with a taxi cab perimeter which measures lengths of structural edges after projection onto the coordinate axes

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

supersymmetry operator transformations and exactly solvable potentials a large class of potentials can be solved algebraically by using supersymmetry and shape invariance the authors apply operator transformations f transformations to these algebraically solvable problems to obtain a larger class of solvable potentials the natanzon class of potentials which are not shape invariant the important condition which is independent of supersymmetry for finding new potentials from old ones using operator transformations is that the resulting schrodinger equation has a potential which does not depend on the state as a special case of the f transformation they rederive the previously known connection between the 3d harmonic oscillator the hydrogen atom and the morse potential they also discuss the lack of commutivity of susy and the f transformations

continuum structural topology design with genetic algorithms the genetic algorithm ga an optimization technique based on the theory of natural selection is applied to structural topology design problems after reviewing the ga and previous research in structural topology optimization we describe a binary material void design representation that is encoded in ga chromosome data structures this representation is intended to approximate a material continuum as opposed to discrete truss structures four examples showing the broad utility of the approach and representation are then presented a fifth example suggests an alternate representation that allows continuously variable material density concluding discussion suggests recommended uses of the technique and describes ongoing and possible future work

an enhanced genetic algorithm for structural topology optimization genetic algorithms gas have become a popular optimization tool for many areas of research and topology optimization an effective design tool for obtaining efficient and lighter structures in this paper a versatile robust and enhanced ga is proposed for structural topology optimization by using problem specific knowledge the original discrete black and white 0 1 problem is directly solved by using a bit array representation method to address the related pronounced connectivity issue effectively the four neighbourhood connectivity is used to suppress the occurrence of checkerboard patterns a simpler version of the perimeter control approach is developed to obtain a well posed problem and the total number of hinges of each individual is explicitly penalized to achieve a hinge free design to handle the problem of representation degeneracy effectively a recessive gene technique is applied to viable topologies while unusable topologies are penalized in a hierarchical manner an efficient fem based function evaluation method is developed to reduce the computational cost a dynamic penalty method is presented for the ga to convert the constrained optimization problem into an unconstrained problem without the possible degeneracy with all these enhancements and appropriate choice of the ga operators the present ga can achieve significant improvements in evolving into near optimum solutions and viable topologies with checkerboard free mesh independent and hinge free characteristics numerical results show that the present ga can be more efficient and robust than the conventional gas in solving the structural topology optimization problems of minimum compliance design minimum weight design and optimal compliant mechanisms design it is suggested that the present enhanced ga using problem specific knowledge can be a powerful global search tool for structural topology optimization copyright 2005 john wiley sons ltd

path integral treatment for the one dimensional natanzon potentials the green s function relative to the one dimensional natanzon potentials is exactly calculated by the path integral approach the energy spectrum the wave functions and the scattering function s are deduced

a class of exactly solvable potentials related to the jacobi polynomials the author investigates a family of solvable potentials related to the jacobi polynomials this one dimensional potential family depends on three parameters and is restricted to the domain xo so it can be interpreted as the radial part of a central potential in three dimensions with l 0 closed expressions are obtained for the bound state energy spectrum and the wavefunctions the supersymmetric partner of this potential is also determined and it is found not to belong to the same potential family it is shown that this potential family is a special subclass of the general six parameter natanzon potential class and similarities with another subclass the ginocchio potentials are pointed out some aspects of supersymmetric quantum mechanics and shape invariance are also discussed in connection with the potential family under study

path integral solutions for deformed poschl teller like and conditionally solvable potentials i discuss in this paper the behaviour of the solutions of the so called q hyperbolic potentials i e poschl teller like and conditionally solvable potentials in terms of the path integral formalism the differences in comparison to the usual poschl teller like potentials are investigated including the discrete energy spectra and the bound state wavefunctions we also point out the relation of the q deformation with curvature on hyperboloids

how to solve path integrals in quantum mechanics a systematic classification of feynman path integrals in quantum mechanics is presented and a table of solvable path integrals is given which reflects the progress made during the last 15 years including of course the main contributions since the invention of the path integral by feynman in 1942 an outline of the general theory is given which will serve as a quick reference for solving path integrals explicit formulas for the so called basic path integrals are presented on which the general scheme to classify and calculate path integrals in quantum mechanics is based

a level set method for structural topology optimization this paper presents a new approach to structural topology optimization we represent the structural boundary by a level set model that is embedded in a scalar function of a higher dimension such level set models are flexible in handling complex topological changes and are concise in describing the boundary shape of the structure furthermore a well founded mathematical procedure leads to a numerical algorithm that describes a structural optimization as a sequence of motions of the implicit boundaries converging to an optimum solution and satisfying specified constraints the result is a 3d topology optimization technique that demonstrates outstanding flexibility of handling topological changes fidelity of boundary representation and degree of automation we have implemented the algorithm with the use of several robust and efficient numerical techniques of level set methods the benefit and the advantages of the proposed method are illustrated with several 2d examples that are widely used in the recent literature of topology optimization especially in the homogenization based methods

representation reduction and solution space contraction in quasi exactly solvable systems in quasi exactly solvable problems partial analytic solutions energy spectrum and associated wavefunctions are obtained if some potential parameters are assigned specific values we introduce a new class in which exact solutions are obtained at a given energy for a special set of values of the potential parameters to obtain a larger solution space one varies the energy over a discrete set the spectrum by simply changing the value of a given integer a unified treatment that includes the standard as well as the new class of quasi exactly solvable problems is presented and a few examples are given the solution space is spanned by discrete square integrable basis functions in which the matrix representation of the hamiltonian is tridiagonal consequently the wave equation gives a three term recursion relation for the expansion coefficients of the wavefunction imposing quasi exact solvability constraints results in a complete reduction of the representation to the direct sum of a finite and an infinite component the finite is real and exactly solvable whereas the infinite is complex and associated with zero norm states consequently the whole physical space contracts to a finite dimensional subspace with normalizable states

conditionally solvable path integral problems some specific conditionally exactly solvable potentials are discussed within the path integral formalism they generalize the usually known potentials by the incorporation of fractional power behaviour and strongly anharmonic terms we find four different kinds of such potential the first is related to the coulomb potential the second is an anharmonic confinement potential and the third and fourth are related to the manning rosen potential

potentials of the heun class we review different methods of generating potentials such that the one dimensional schrodinger equation odse can be transformed into the hypergeometric equation we compare our results with previous studies and complement the subject with new findings our main result is to derive new classes of potentials such that the odse can be transformed into the heun equation and its confluent cases the generalized heun equation is also considered

exact solution of the schrodinger equation for a potential well with a barrier and other potentials a method is described with which exactly solvable one dimensional stationary schrodinger equations can be derived from solved differential equations the procedure is illustrated by the example of a schrodinger equation for a potential well with a barrier of the form u z v q2 tanh2 z q1 tanhz coshz q0 the eigenvalues and eigenfunctions of this potential are calculated exactly the results are explicit analytical expressions in closed form for the whole eigenvalue spectrum as well as for all the eigenfunctions

radial basis functions and level set method for structural topology optimization level set methods have become an attractive design tool in shape and topology optimization for obtaining lighter and more efficient structures in this paper the popular radial basis functions rbfs in scattered data fitting and function approximation are incorporated into the conventional level set methods to construct a more efficient approach for structural topology optimization rbf implicit modelling with multiquadric mq splines is developed to define the implicit level set function with a high level of accuracy and smoothness a rbf level set optimization method is proposed to transform the hamilton jacobi partial differential equation pde into a system of ordinary differential equations odes over the entire design domain by using a collocation formulation of the method of lines with the mathematical convenience the original time dependent initial value problem is changed to an interpolation problem for the initial values of the generalized expansion coefficients a physically meaningful and efficient extension velocity method is presented to avoid possible problems without reinitialization in the level set methods the proposed method is implemented in the framework of minimum compliance design that has been extensively studied in topology optimization and its efficiency and accuracy over the conventional level set methods are highlighted numerical examples show the success of the present rbf level set method in the accuracy convergence speed and insensitivity to initial designs in topology optimization of two dimensional 2d structures it is suggested that the introduction of the radial basis functions to the level set methods can be promising in structural topology optimization

algebraic solution for the natanzon confluent potentials an algebraic method is used to solve the bound state problem for the most general natanzon potential for which the schrodinger equation can be reduced to the confluent hypergeometric form hence confluent potentials the solution is obtained straightforwardly a simple argument is given to sustain that the natanzon potential is the most general confluent potential

a second class of solvable potentials related to the jacobi polynomials levai 1991 has used a simple method for generating solvable wave equations to construct potentials whose solutions include as factors jacobi polynomials of functions g x which solve specific differential equations application of this method to a previously unconsidered differential equation involving jacobi polynomials results in a new class of solvable potentials missing from earlier compilations an interesting property of these new potentials is that when two of their defining parameters are fixed they all possess the same energy eigenvalue spectrum independent of any change in a third parameter leading to an indefinite number of different potentials with the same energies

l2 series solutions of the dirac equation for power law potentials at rest mass energy we obtain solutions of the three dimensional dirac equation for radial power law potentials at rest mass energy as an infinite series of square integrable functions these are written in terms of the confluent hypergeometric function and chosen such that the matrix representation of the dirac operator is tridiagonal the wave equation results in a three term recursion relation for the expansion coefficients of the spinor wavefunction which is solved in terms of orthogonal polynomials these are modified versions of the meixner pollaczek polynomials and of the continuous dual hahn polynomials the choice depends on the values of the angular momentum and the power of the potential

path integration over compact and noncompact rotation groups applications of group theoretical methods in the path integral formalism of nonrelativistic quantum theory are considered analysis of the symmetry of the lagrangian leads to the expansion of the short time propagator in matrix elements of unitary irreducible representations of the symmetry group identification of the coordinates with the group parameters transforms the path integral to integrals over the group manifold the integration is performed using the orthogonality of the representations compact and noncompact rotation groups are considered where the corresponding path integral is embedded in euclidean and pseudo euclidean spaces respectively the unit sphere and unit hyperboloid may either be viewed as the group manifold itself or at least as a group quotient in the first case fourier analysis leads to an expansion in group characters in the second case an expansion in zonal spherical functions is obtained as examples the groups so n su 2 so n 1 1 and su 1 1 are explicitly discussed the path integral on so n m and so n m in bispherical coordinates is also treated

structural topology design optimization using genetic algorithms with a bit array representation abstract in this paper a bit array representation method for structural topology optimization using the genetic algorithm ga is implemented the importance of structural connectivity in a design is further emphasized by considering the total number of connected objects of each individual explicitly in an equality constraint function to evaluate the constrained objective function deb s constraint handling approach is further developed to ensure that feasible individuals are always better than infeasible ones in the population to improve the efficiency of the ga a violation penalty method is proposed to drive the ga search towards the topologies with higher structural performance less unusable material and fewer separate objects in the design domain an identical initialization method is also proposed to improve the ga performance in dealing with problems with long narrow design domains numerical results of structural topology optimization problems of minimum weight and minimum compliance designs show the success of this bit array representation method and suggest that the ga performance can be significantly improved by handling the design connectivity properly

structural optimization using sensitivity analysis and a level set method in the context of structural optimization we propose a new numerical method based on a combination of the classical shape derivative and of the level set method for front propagation we implement this method in two and three space dimensions for a model of linear or nonlinear elasticity we consider various objective functions with weight and perimeter constraints the shape derivative is computed by an adjoint method the cost of our numerical algorithm is moderate since the shape is captured on a fixed eulerian mesh although this method is not specifically designed for topology optimization it can easily handle topology changes however the resulting optimal shape is strongly dependent on the initial guess

numerical path integral techniques for long time dynamics of quantum dissipative systems recent progress in numerical methods for evaluating the real time path integral in dissipative harmonic environments is reviewed quasi adiabatic propagators constructed numerically allow convergence of the path integral with large time increments integration of the harmonic bath leads to path integral expressions that incorporate the exact dynamics of the quantum particle along the adiabatic path with an influence functional that describes nonadiabatic corrections the resulting quasi adiabatic propagator path integral is evaluated by efficient system specific quadratures in most regimes of parameter space although some cases are handled by grid monte carlo sampling exploiting the finite span of nonlocal influence functional interactions characteristic of broad condensed phase spectra leads to an iterative scheme for calculating the path integral over arbitrary time lengths no uncontrolled approximations are introduced and the resulting methodology converges to the exact quantum result with modest

changing dimension and time two well founded and practical techniques for path integration in quantum physics in a reasonably self contained presentation mathematical rigour is supplied to the important ideas of solving certain non gaussian path integrals by changes of dimension and or path dependent time transformations the resulting genuine path integral calculus neither requires discretization prescriptions nor sophisticated methods from the theory of stochastic differential equations the power of the calculus is illustrated by two standard quantum physics applications first the calculation of the time dependent propagator corresponding to a particle on the half line in a harmonic plus inverse square potential is shown to be a simple exercise second the first rigorous derivation of the energy dependent green function of the one dimensional morse system is given

reducing dimensionality in topology optimization using adaptive design variable fields topology optimization methodologies typically use the same discretization for the design variable and analysis meshes analysis accuracy and expense are thus directly tied to design dimensionality and optimization expense this paper proposes leveraging properties of the heaviside projection method hpm to separate the design variable field from the analysis mesh in continuum topology optimization hpm projects independent design variables onto element space over a prescribed length scale a single design variable therefore influences several elements creating a redundancy within the design that can be exploited to reduce the number of independent design variables without significantly restricting the design space the algorithm begins with sparse design variable fields and adapts these fields as the optimization progresses the technique is demonstrated on minimum compliance maximum stiffness problems solved using continuous optimization and genetic algorithms for the former the proposed algorithm typically identifies solutions having objective functions within 1 of those found using full design variable fields computational savings are minor to moderate for the minimum compliance formulation with a single constraint and are substantial for formulations having many local constraints when using genetic algorithms solutions are consistently obtained on mesh resolutions that were previously considered intractable copyright 2009 john wiley sons ltd

the general besselian and legendrian path integrals the general besselian and legendrian path integrals based on the confluent and hypergeometric natanzon potentials are calculated these two solutions cover all other path integral representations which are related to the radial harmonic oscillator and the modified poschl teller path integral

a moving superimposed finite element method for structural topology optimization level set methods are becoming an attractive design tool in shape and topology optimization for obtaining efficient and lighter structures in this paper a dynamic implicit boundary based moving superimposed finite element method s version fem or s fem is developed for structural topology optimization using the level set methods in which the variational interior and exterior boundaries are represented by the zero level set both a global mesh and an overlaying local mesh are integrated into the moving s fem analysis model a relatively coarse fixed eulerian mesh consisting of bilinear rectangular elements is used as a global mesh the local mesh consisting of flexible linear triangular elements is constructed to match the dynamic implicit boundary captured from nodal values of the implicit level set function in numerical integration using the gauss quadrature rule the practical difficulty due to the discontinuities is overcome by the coincidence of the global and local meshes a double mapping technique is developed to perform the numerical integration for the global and coupling matrices of the overlapped elements with two different co ordinate systems an element killing strategy is presented to reduce the total number of degrees of freedom to improve the computational efficiency a simple constraint handling approach is proposed to perform minimum compliance design with a volume constraint a physically meaningful and numerically efficient velocity extension method is developed to avoid the complicated pde solving procedure the proposed moving s fem is applied to structural topology optimization using the level set methods as an effective tool for the numerical analysis of the linear elasticity topology optimization problems for the classical elasticity problems in the literature the present s fem can achieve numerical results in good agreement with those from the theoretical solutions and or numerical results from the standard fem for the minimum compliance topology optimization problems in structural optimization the present approach significantly outperforms the well recognized ersatz material approach as expected in the accuracy of the strain field numerical stability and representation fidelity at the expense of increased computational time it is also shown that the present approach is able to produce structures near the theoretical optimum it is suggested that the present s fem can be a promising tool for shape and topology optimization using the level set methods copyright 2005 john wiley sons ltd

new class of conditionally exactly solvable potentials in quantum mechanics motivated by an idea of dutra 1993 we obtain a new class of one dimensional conditionally exactly solvable potentials for which the entire spectra can be obtained in an algebraic manner provided one of the potential parameters is assigned a fixed negative value it is shown that using shape invariant potentials as input one may generate different classes of such potentials even in more than one dimension we also illustrate that wkb and supersymmetry inspired wkb methods provide very good approximations for these potentials with the latter doing comparatively better

structural boundary design via level set and immersed interface methods we develop and test an algorithmic approach to the boundary design of elastic structures the goal of our approach is two fold first to develop a method which allows one to rapidly solve the two dimensional lam equations in arbitrary domains and compute for example the stresses and second to develop a systematic way of modifying the design to optimize chosen properties at the core our approach relies on two distinct steps given a design we first apply an explicit jump immersed interface method to compute the stresses for a given design shape we then use a narrow band level set method to perturb this shape and progress towards an improved design the equations of 2d linear elastostatics in the displacement formulation on arbitrary domains are solved quickly by domain embedding and the use of fast elastostatic solvers this effectively reduces the dimensionality of the problem by one once the stresses are found the level set method which represents the design structure through an embedded implicit function is used in the second step to alter the shape with velocities depending on the stresses in the current design criteria are provided for advancing the shape in an appropriate direction and for correcting the evolving shape when given constraints are violated

bilateral filtering for structural topology optimization filtering has been a major approach used in the homogenization based methods for structural topology optimization to suppress the checkerboard pattern and relieve the numerical instabilities in this paper a bilateral filtering technique originally developed in image processing is presented as an efficient approach to regularizing the topology optimization problem a non linear bilateral filtering process leads to a suitable problem regularization to eliminate the checkerboard instability pronounced edge preserving smoothing characteristics to favour the 0 1 convergence of the mass distribution and computational efficiency due to its single pass and non iterative nature thus we show that the application of the bilateral filtering brings more desirable effects of checkerboard free mesh independence crisp boundary computational efficiency and conceptual simplicity the proposed bilateral technique has a close relationship with the conventional domain filtering and range filtering the proposed method is implemented in the framework of a power law approach based on the optimality criteria and illustrated with 2d examples of minimum compliance design that has been extensively studied in the recent literature of topology optimization and its efficiency and accuracy are highlighted copyright 2005 john wiley sons ltd

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