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

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

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

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

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

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

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

on subsonic compressible flows in a two dimensional duct abstract this paper concerns subsonic flows passing a two dimensional duct for the steady compressible euler system if the bernoulli constant is uniform in the flow field the density at the entry and both the pressures at the entrance and the exit are given we show that the problem is generally ill posed but if we give the pressure at the exit with a constant difference then under the same other conditions as above we establish the existence of subsonic flows

poincare sections for a new three dimensional toroidal attractor a new 3d autonomous dynamical system proposed by li 2008 phys lett a 372 387 produces a chaotic attractor whose global topological properties are unusual the attractor has a rotation symmetry and only a single real fixed point for the parameters used in his study the symmetric complex pair of fixed points cannot be ignored they play a major role in organizing the motion on a surface of peculiar toroidal type we describe this attractor propose a simple intuitive model to understand it show that it is of toroidal type and of genus three construct a global poincar e surface of section with two disjoint components and use this section to locate unstable periodic orbits and determine their topological period we also show that its image attractor is of genus one and supports flow on a simple wrinkled torus finally we use the interplay between the original covering attractor and its image as an aid to understand why the li attractor is of genus three type

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

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

from quasiperiodicity to toroidal chaos analogy between the curry yorke map and the van der pol system the van der pol attractor exhibits a wide variety of behavior depending on the control parameter values limit cycles quasiperiodic motion on a torus mode locking period doubling banded chaos boundary crises torus wrinkling breakup of a torus and toroidal chaos the organization of these phenomena with respect to each other is well described by studying a partition of the control parameter plane of the curry yorke map

sequential subspace robustness assessment and sensitivity analysis to avoid an overconservative design and to ensure desired performance in an optimal way the product quality and robustness are considered in terms of the product performance mean and variance in this paper to facilitate robust design exploration under uncertainty a new sequential subspace robustness assessment method is presented to assess not only the mean and variance of performance but also their sensitivities with respect to design parameters the proposed method is based on the computational framework that integrates the univariate revolving integration and surrogate modeling of univariate integral functions the proposed framework enables consideration of bivariate interaction effects approximately by the aggregation of multiple revolving integration terms in a partial set of bivariate subspaces it is found that the proposed method provides better accuracy with comparable computational cost in assessing the statistical moments and sensitivities of product performance than existing methods suc

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

structure in the bifurcation diagram of the duffing oscillator we identify four levels of structure in the bifurcation diagram of the two well periodically driven duffing oscillator plotted as a function of increasing control parameter t the period of the driving term the superstructure or bifurcation peninsula repeats periodically as t increases by ensuremath sim 2 ensuremath pi beginning and ending with symmetric period one orbits whose local torsions differ by 2 within each bifurcation peninsula there is a systematic window structure the primary window structure is due to newhouse and newhouse like orbits fine structure is due to a farey sequence of well ordered orbits between the primary windows hyperfine structure consists of very narrow windows associated with non well ordered orbits we construct a template for the duffing oscillator a two dimensional return map and a one dimensional return map which describes the systematics of orbit creation and annihilation all structures are identified by topological indices our predictions are based on and compatible with numerical computations

enhanced two point diagonal quadratic approximation methods for design optimization abstract based on two point diagonal quadratic approximation referred to as tdqa developed by kim et al min soo kim jong rip kim jae young jeon dong hoon choi efficient mechanical system optimization using two point diagonal approximation in the nonlinear intervening variable space j ksme 15 2001 1257 126 enhanced two point approximation methods are proposed in this paper the suggested methods reinforce tdqa with new quadratic correction terms using the concept of tana 3 these methods overcome the disadvantage of tdqa when the derivatives at two design points have the same sign in addition the values and derivatives of the proposed approximation functions are completely equal to those of an original function at the two design points whether the derivatives at those points have the same sign or not several examples show the numerical performance and accuracy of the proposed methods compared to previous work and optimization examples show that these methods can successfully reach the optimum via sequential approximation optimization

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

a new three point approximation approach for design optimization problems in this paper a newly developed three point approximation scheme is proposed the expression of this scheme consists of a linear combination of the direct and reciprocal linear taylor expansions as well as of the lumped diagonal terms of the second order direct and inverse terms the unknown parameters of the expression are computed on the basis of the function and gradient values at three points in the design space based on this approach the accuracy of the existing constraint approximation methods can be improved the e ectiveness of the proposed approach is demonstrated on a number of numerical examples the numerical results are also compared with those of the previously published work copyright 2001 john wiley sons ltd

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

the residue harmonic balance for fractional order van der pol like oscillators when seeking a solution in series form the number of terms needed to satisfy some preset requirements is unknown in the beginning an iterative formulation is proposed so that when an approximation is available the number of effective terms can be doubled in one iteration by solving a set of linear equations this is a new extension of the newton iteration in solving nonlinear algebraic equations to solving nonlinear differential equations by series when fourier series is employed the method is called the residue harmonic balance in this paper the fractional order van der pol oscillator with fractional restoring and damping forces is considered the residue harmonic balance method is used for generating the higher order approximations to the angular frequency and the period solutions of above mentioned fractional oscillator the highly accurate solutions to angular frequency and limit cycle of the fractional order van der pol equations are obtained analytically the results that are obtained reveal that the proposed method is very effective for obtaining asymptotic solutions of autonomous nonlinear oscillation systems containing fractional derivatives the influence of the fractional order on the geometry of the limit cycle is investigated for the first time

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

multidimensional transonic shocks and free boundary problems for nonlinear equations of mixed type we are concerned with the existence and stability of multidimensional transonic shocks for the euler equations for steady potential compressible fluids the euler equations consisting of the conservation law of mass and the bernoulli law for the velocity can be written as the following second order nonlinear equation of mixed elliptic hyperbolic type for the velocity potential r r 1 1 div d d 0 where the density function q is

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

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

examples of steady subsonic flows in a convergent divergent approximate nozzle abstract we construct special solutions of the full euler system for steady compressible flows in a convergent divergent approximate nozzle and study the stability of the purely subsonic flows for a given pressure p 0 prescribed at the entry of the nozzle as the pressure p 1 at the exit decreases the flow patterns in the nozzle change continuously there appear subsonic flow subsonic sonic flow transonic flow and transonic shocks our results indicate that to determine a subsonic flow in a two dimensional nozzle if the bernoulli constant is uniform in the flow field then this constant should not be prescribed if the pressure density at the entry and the pressure at the exit of the nozzle are given if the bernoulli constant and both the pressures at the entrance and the exit are given the average of the density at the entrance is then totally determined

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

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

effective two point function approximation for design optimization anew two pointapproximationofafunctionthatisverystraightforwardtobuildandthatprovidesaccurateand stable approximation is presented earlier developments of the two point approximations had either incomplete matches at two data points or needed the solution of additional equations to get all of the parameters the present two point approximation is an incomplete second order taylor series expansion in terms of intervening variables thehessianmatrixhasonlydiagonalelements anditdependsondesignvariables theexponentofeachintervening design variable and the unknown constant of the second order terms are evaluated by matching the derivatives and the value of the approximation with the previous data point gradients and the value of the original function respectively all of theunknownsareidentie ed in aclosedform both thefunctionandthegradientof thetwo point approximation are equal to those of the original function at two data points several examples are given to show the accuracy and efe ciency of this method

oscillation sliding in a modified van der pol duffing electronic oscillator abstract some periodic behaviour exhibited by a modified van der pol duffing electronic oscillator near a degenerate hopf pitchfork bifurcation have been studied numerical continuation of these periodic orbits leads to the appearance of interesting phenomena after varying one of the characteristics of the oscillator oscillation sliding between two periodic regimes is detected in the region where oscillation sliding is present quasiperiodic oscillations invariant torus breakdown of the torus and the corresponding resonant periodic orbits are also found

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

steady euler flows with large vorticity and characteristic discontinuities in arbitrary infinitely long nozzles abstract we establish the existence and uniqueness of smooth solutions with large vorticity and weak solutions with vortex sheets entropy waves for the steady euler equations for both compressible and incompressible fluids in arbitrary infinitely long nozzles we first develop a new approach to establish the existence of smooth solutions without assumptions on the sign of the second derivatives of the horizontal velocity or the bernoulli and entropy functions at the inlet for the smooth case then the existence for the smooth case can be applied to construct approximate solutions to establish the existence of weak solutions with vortex sheets entropy waves by nonlinear arguments this is the first result on the global existence of solutions of the multidimensional steady compressible full euler equations with free boundaries which are not necessarily small perturbations of piecewise constant background solutions the subsonic sonic limit of the solutions is also shown finally through the incompressible limit we establish the existence and uniqueness of incompressible euler flows in arbitrary infinitely long nozzles for both the smooth solutions with large vorticity and the weak solutions with vortex sheets the methods and techniques developed here will be useful for solving other problems involving similar difficulties

dynamics of the two frequency torus breakdown in the driven double scroll circuit in this work we numerically identify three scenarios for the two frequency torus breakdown to chaos using the driven double scroll circuit with varying driving parameters two of these scenarios follow the curryyorke route to chaos for one scenario we identify the transition to chaos through the onset of a heteroclinic tangle and its heteroclinic points in the other scenario chaos appears via period doubling bifurcations the third scenario is through the type ii intermittency for which a quasiperiodic torus grows in size breaks by touching external saddle points and forms a heteroclinic saddle connection these dynamic scenarios have distinct structure evolutions for the curry yorke route chaos appears softly and alternates with phase locking while for the type ii intermittency chaos appears abruptly and is preserved for a large range of the varying driving parameter s1063 651x 98 05210 6

stability of spherically symmetric subsonic flows and transonic shocks under multidimensional perturbations abstract we develop a method that works in general product riemannian manifold to decompose the three dimensional steady full compressible euler system which is of elliptic hyperbolic composite mixed type for subsonic flows the method is applied to show stability of spherically symmetric subsonic flows and transonic shocks in space r 3 under multidimensional perturbations of boundary conditions

improved two point function approximations for design optimization two point approximations are developed by utilizing both the function and gradient information of two data points the objective of this work is to build a high quality approximation to realize computational savings in solving complex optimization and reliability analysis problems two developments are proposed in the new twopoint approximations 1 calculation of a correction term by matching with the previous known function value and supplementing it to the first order approximation for including the effects of higher order terms and 2 development of a second order approximation without the actual calculation of second order derivatives by using an approximate hessian matrix several highly nonlinear functions and structural examples are used for demonstrating the new two point approximations that improved the accuracy of existing first order methods evelopmentof new and improved constraint approximations has been an active area of research in the mathematical optimization community over the last two decades 1 3 more accurate function approximations reduce the finite element analysis cost and increase the search domain in each iteration of an optimization run recent developments in constraint approximations addressed methods for eigenvalues dynamic response static forces structural reliability etc some of the typical methods are summarized in the following kirsch4 developed a scaling factor for a stiffness matrix and approximated the displacements stresses and forces with respect to sizing and topology variables vanderplaats and salajegheh5 used two levels of approximations for discrete sizing and shape design of structures first for solving the continuous problem and next the discrete one using a dual theory canfield6 developed an approach for eigenvalues by approximating the modal strain and kinetic energies independently thomas et al 7 presented an approximation for the frequency response of damped structures by using the concept of ref 6 a multivariate spline approximation was developed by wang and grandhi8 making use of the previously generated exact finite element analyses similarly a hermite approximation for n dimensional problems used several data points and had the property of reproducing the function and gradient values at the known data points 9 canfield10 used multipoint data in building an approximate hessian matrix and constructed a second order approximation for improving the accuracy toropov et al 11 approximated functions as a linear combination or products of variables and the coefficients of the polynomial were computed by applying a least squared approach on multiple data points fadel et al 12 considered intermediate variables in terms of exponentials and they were computed by matching the approximate function gradients with the previous point s exact values this approach did not compare the function values of the previous point wang and grandhi13 used a single exponential for all of the variables and calculated it by matching the approximate function with the previous point exact value and the gradient information of the previous point was not utilized the proposed paper develops an improved two point approximation utilizing both function and gradient information of two data points in the new two point approximation two developments are proposed 1 calculation of a correction term based on two function values and

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

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

transonic potential flows in a convergent divergent approximate nozzle in this paper we prove existence uniqueness and regularity of certain perturbed subsonic supersonic transonic potential flows in a two dimensional riemannian manifold with convergent divergent metric which is an approximate model of the de laval nozzle in aerodynamics the result indicates that transonic flows obtained by quasi one dimensional flow model in fluid dynamics are stable with respect to the perturbation of the velocity potential function at the entry i e tangential velocity along the entry of the nozzle the proof is based upon linear theory of elliptic hyperbolic mixed type equations in physical space and a nonlinear iteration method

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

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

the method of moving asymptotes a new method for structural optimization a new method for non linear programming in general and structural optimization in particular is presented in each step of the iterative process a strictly convex approximating subproblem is generated and solved the generation of these subproblems is controlled by so called moving asymptotes which may both stabilize and speed up the convergence of the general process

compressible flow and transonic shock in a diverging nozzle the paper is devoted to the study of compressible flows and transonic shocks in diverging nozzles in the framework of the full compressible euler system consider a nozzle having a shape as a diverging truncated sector with generic opening angle if the upstream flow at the entrance is supersonic and is near to an axial symmetric flow and if all parameters of the upstream flow and the receiver pressure at the exit are suitably assigned then a transonic shock appears in the nozzle to determine the transonic shock and the flow in the nozzle leads to a free boundary value problem for a nonlinear partial differential equation we prove that the receiver pressure can uniquely determine the location of the transonic shock as well as the flow behind the shock such a conclusion was conjectured by courant and friedrichs and is confirmed theoretically in this paper for the divergent nozzles