aerodynamic shape optimization of aircraft wings using panel methods panel methods are frequently applied to aerodynamic shape optimization problems due to their fast turnaround time and ability to model arbitrary geometries despite being advantageous for design op

alternative approaches to asymptotic behaviour of eigenvalues of some unbounded jacobi matrices in this article we calculate the asymptotic behaviour of the point spectrum for some special self adjoint unbounded jacobi operators j acting in the hilbert space l 2 l 2 n for given sequences of positive numbers l n and real q n the jacobi operator is given by j sw ws q where q diag q n and w diag l n are diagonal operators s is the shift operator and the operator j acts on the maximal domain we consider a few types of the sequences q n and l n and present three different approaches to the problem of the asymptotics of eigenvalues of various classes of j s in the first approach to asymptotic behaviour of eigenvalues we use a method called successive diagonalization the second approach is based on analytical models that can be found for some special j s and the third method is based on an abstract theorem of rozenbljum

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

total solution for structural mechanics problems a concept of total solution for structural mechanics problems is proposed in this paper it aims to establish a systematic approach to provide a comprehensive solution for practical structural mechanics problems especially for traditional forward problems with incomplete input information load material property boundary condition and inverse problems with insufficient observations of effects displacement acceleration stress etc the approach for a total solution is to formulate such a structural mechanics problem as a parameter identification problem based on the forward solver of problem all the unknown parameterized information in this forward model is determined through an iterative procedure of conducting alternately forward and inverse or mixed analyses algorithms of implementing inverse and mixed analyses are developed which include a sensitivity matrix based method and a modified adaptive neural networks method numerical investigations have been made to demonstrate the feasibility and validity of the proposed approach as well as the implementation algorithms

articulated mechanism design with a degree of freedom constraint this paper deals with design of articulated mechanism using a truss based ground structure representation the proposed method can accommodate extremely large displacement by considering geometric non linearity in addition it can also control the mechanical degrees of freedom dof of the resultant mechanism by using a dof equation based on maxwell s rule the optimization is based on a relaxed formulation of an original integer problem and also involves developments directed at handling the redundancy inherent in the ground structure representation one planar test example is selected as the basis for the developments so as to compare the proposed method with other alternative approaches including a graph theoretical enumeration approach which guarantees the identification of the globally optimal solution also an inverter problem is treated where a continuation method is required in order to direct the optimization algorithm towards an integer solution copyright 2004 john wiley sons ltd

a spectral analysis for self adjoint operators generated by a class of second order difference equations abstract a qualitative spectral analysis for a class of second order difference equations is given central to the analysis of equations in this class is the observation that real valued solutions exhibit a type of stable asymptotic behavior for certain real values of the spectral parameter this asymptotic behavior leads to the characterization of the limit point and limit circle nature of these equations and is used to show that a strong nonsubordinacy criterion is satisfied on subintervals of r for equations of limit point type these subintervals are part of the absolutely continuous spectrum of the self adjoint realization of these equations by other means the nature of the discrete spectrum for these self adjoint realizations is also discussed

robust topology optimization of structures with imperfect geometry based on geometric nonlinear analysis abstract topology optimization often leads to structures consisting of slender elements which are particularly sensitive to geometric imperfections such imperfections might affect the structural stability and induce large displacement effects in these slender structures this paper therefore presents a robust approach to topology optimization which accounts for geometric imperfections and their potentially detrimental influence on the structural stability geometric nonlinear effects are incorporated in the optimization by means of a total lagrangian finite element formulation in the minimization of end compliance geometric imperfections are modeled as a vector valued random field in the design domain the resulting uncertain performance of the design is taken into account by minimizing a weighted sum of the mean and standard deviation of the compliance in the robust optimization problem these stochastic moments are typically estimated by means of sampling methods such as monte carlo simulation however these methods require multiple independent nonlinear finite element analyses in each design iteration of the optimization algorithm an efficient solution algorithm which uses adjoint differentiation in a second order perturbation method is therefore developed to estimate the stochastic moments during the optimization two applications with structures that exhibit different types of structural instabilities are examined in both cases it is demonstrated by means of an extensive monte carlo simulation that the deterministic design is very sensitive to imperfections while the design obtained by means of the proposed method is much more robust

path generation of articulated mechanisms by shape and topology variations in non linear truss representation this paper presents studies on an optimization based method for path generation of articulated mechanisms an extended truss ground structure approach is taken in which both the shape and topology of the truss are designed using cross sectional areas and nodal positions as design variables this leads to a technique for simultaneous type and dimensional synthesis of articulated mechanisms for the analysis part it is essential to control the mechanism configuration so that the mechanism remains within a given configuration space thus stabilizing the optimization process and resulting in realistic solutions this can be achieved by using the levenberg marquardt method the design method is illustrated by a number of design cases for both closed and open input and output paths

self adjointness of unbounded tridiagonal operators and spectra of their finite truncations abstract this paper addresses two different but related questions regarding an unbounded symmetric tridiagonal operator its self adjointness and the approximation of its spectrum by the eigenvalues of its finite truncations the sufficient conditions given in both cases improve and generalize previously known results it turns out that not only self adjointness helps to study limit points of eigenvalues of truncated operators but the analysis of such limit points is a key help to prove self adjointness several examples show the advantages of these new results compared with previous ones besides an application to the theory of continued fractions is pointed out

an enhanced hybrid method for the simulation of highly skewed non gaussian stochastic fields abstract in this paper an enhanced hybrid method ehm is presented for the simulation of homogeneous non gaussian stochastic fields with prescribed target marginal distribution and spectral density function the presented methodology constitutes an efficient blending of the deodatis micaletti method with a neural network based function approximation precisely the function fitting ability of neural networks based on the resilient back propagation rprop learning algorithm is employed to approximate the unknown underlying gaussian spectrum the resulting algorithm can be successfully applied for simulating narrow banded fields with very large skewness at a fraction of the computing time required by the existing methods its computational efficiency is demonstrated in three numerical examples involving fields that follow the beta and lognormal distributions

higher order multi resolution topology optimization using the finite cell method this article presents a detailed study on the potential and limitations of performing higher order multi resolution topology optimization with the finite cell method to circumvent stiffness overestimation in high contrast topologies a length scale is applied on the solution using filter methods the relations between stiffness overestimation the analysis system and the applied length scale are examined while a high resolution topology is maintained the computational cost associated with nested topology optimization is reduced significantly compared with the use of first order finite elements this reduction is caused by exploiting the decoupling of density and analysis mesh and by condensing the higher order modes out of the stiffness matrix

topology design optimization of geometrically non linear structures using meshfree method a topology optimization method using meshfree methods is developed for geometrically non linearly structures a density approach is used to optimally distribute the bulk material densities in a continuum design domain the reproducing kernel rk shape function is employed to discretize both displacement and bulk density fields thus the points can be located at any part of the design domain and be easily included in or excluded from the response analysis the well known convergence difficulty which normally occurs in the sub domain of low bulk density can be avoided by excluding the sub domain the numerical instability of bulk density solution due to the rank deficiency of system matrix is effectively prevented by properly selecting the number of independent design variables through numerous numerical examples we confirm that the developed method works very well even in the large deformation problems the sub domain exclusion scheme is found to be greatly beneficial in terms of computational costs compared with the results without the scheme

a mesh free method for static and free vibration analyses of thin plates of complicated shape a mesh free method is presented to analyze the static deflection and the natural frequencies of thin plates of complicated shape the present method uses moving least squares mls interpolation to construct shape functions based on a set of nodes arbitrarily distributed in the analysis domain discrete system equations are derived from the variational form of system equation for static analysis a penalty method is presented to enforce the essential boundary conditions for frequency analysis of free vibration the essential boundary conditions are represented through a weak form and imposed using orthogonal transformation techniques the present efg method together with techniques for imposing boundary conditions is coded in fortran numerical examples are presented for rectangular elliptical polygonal and complicated plates to demonstrate the convergence and efficiency of the present method

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

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

a quadratic layer element for analyzing stress waves in fgms and its application in material characterization abstract a novel method is presented for investigating elastic waves in functionally graded material fgm plates excited by plane pressure waves the fgm plate is first divided into quadratic layer elements qles a general solution for the equation of motion governing the qle has been derived the general solution is then used together with the boundary and continuity conditions to obtain the displacement and stress in the frequency domain for an arbitrary fgm plate the response of the plate to an incident pressure wave is obtained using the fourier transform techniques results obtained by the present method are compared with an existing method using homogeneous layer elements numerical examples are presented to investigate stress waves in fgm plates the relationship between the surface displacement response and the material property of quadratic fgm plates has been analytically obtained for the material characterization a computational inverse technique is also presented for characterizing material property of an arbitrary fgm plate from the surface displacement response data using present qle method as forward solver and genetic algorithm as the inverse operator this technique is utilized to reconstruct the material property of an actual sic c fgm

non convex dual forms based on exponential intervening variables with application to weight minimization we study the weight minimization problem in a dual setting we propose new dual formulations for non linear multipoint approximations with diagonal approximate hessian matrices which derive from separable series expansions in terms of exponential intervening variables these generally nonconvex approximations are formulated in terms of intervening variables with negative exponents and are therefore applicable to the solution of the weight minimization problem in a sequential approximate optimization sao framework problems in structural optimization are traditionally solved using sao algorithms like the method of moving asymptotes which require the approximate subproblems to be strictly convex hence during solution the nonconvex problems are approximated using convex functions and this process may in general be inefficient we argue based on falk s definition of the dual that it is possible to base the dual formulation on nonconvex approximations to this end we reintroduce a nonconvex approach to the weight minimization problem originally due to fleury and we explore certain convex and nonconvex forms for subproblems derived from the exponential approximations by the application of various methods of mixed variables we show in each case that the dual is well defined for the form concerned which may consequently be of use to the future code developers

a strategy to identify exciting forces acting on structures the strategy for identifying the external forces acting on structures sketched by turco comput method appl mech eng 1998 165 291 306 is extended to the dynamic case starting from the measurement of the stress or strain history in a suitable number of points of the structure the exciting forces are reconstructed this inverse problem is tackled in the frequency domain by using the standard tools of computational mechanics along with a classical approach to treat ill conditioned problems some numerical results relating to pin jointed trusses are discussed in order to validate the proposed strategy copyright 2005 john wiley sons ltd

spectral theory of certain unbounded jacobi matrices abstract using the conjugate operator method of mourre we study the spectral theory of a class of unbounded jacobi matrices we especially focus on the case where the off diagonal entries a n n 1 o 1 and diagonal ones b n n 1 o 1 with 0 r

spectral properties of some jacobi matrices with double weights abstract we study the spectral properties of jacobi matrices with the weights satisfying 2n 1 2n na or 2n 2n 1 na a 0 we show that for a 1 these are cases of spectral phase transitions in a we use a new method of estimating transfer matrix products to describe the absolutely continuous part of these operators for a 1 the existence of a spectral gap is proved we also show how the results for double weights can be used for the spectral analysis of the jacobi matrices related to some birth and death processes previously studied by janas and naboko

on concave constraint functions and duality in predominantly black and white topology optimization abstract we study the classical discrete solid void or black and white topology optimization problem in which minimum compliance is sought subject to constraints on the available material resource we assume that this problem is solved using methods that relax the discreteness requirements during intermediate steps and that the associated programming problems are solved using sequential approximate optimization sao algorithms based on duality more specifically we assume that the advantages of the well known falk dual are exploited such algorithms represent the state of the art in large scale topology optimization when multiple constraints are present an important example being the method of moving asymptotes mma we depart by noting that the aforementioned sao algorithms are invariably formulated using strictly convex subproblems we then numerically illustrate that strictly concave constraint functions like those present in volumetric penalization as recently proposed by bruns and co workers may increase the difficulty of the topology optimization problem when strictly convex approximations are used in the sao algorithm in turn volumetric penalization methods are of notable importance since they seem to hold much promise for generating predominantly solid void or discrete designs we then argue that the nonconvex problems we study may in some instances efficiently be solved using dual sao methods based on nonconvex strictly concave approximations which exhibit monotonicity with respect to the design variables indeed for the topology problem resulting from simp like volumetric penalization we show explicitly that convex approximations are not necessary even though the volumetric penalization constraint is strictly concave the maximum of the resulting dual subproblem still corresponds to the optimum of the original primal approximate subproblem

operators with singular continuous spectrum i general operators the baire category theorem implies that the family f of dense sets g in fixed metric space x is a candidate for generic sets since it is closed under countable intersections and if x is perfect has no isolated point then a f has uncountable intersections with any open ball in x

shape and topology optimization of compliant mechanisms using a parameterization level set method in this paper a parameterization level set method is presented to simultaneously perform shape and topology optimization of compliant mechanisms the structural shape boundary is implicitly embedded into a higher dimensional scalar function as its zero level set resultantly establishing the level set model by applying the compactly supported radial basis function with favorable smoothness and accuracy to interpolate the level set function the temporal and spatial hamilton jacobi equation from the conventional level set method is then discretized into a series of algebraic equations accordingly the original shape and topology optimization is now fully transformed into a parameterization problem namely size optimization with the expansion coefficients of interpolants as a limited number of design variables design of compliant mechanisms is mathematically formulated as a general optimization problem with a nonconvex objective function and two additionally specified constraints the structural shape boundary is then advanced as a process of renewing the level set function by iteratively finding the expansion coefficients of the size optimization with a sequential convex programming method it is highlighted that the present method can not only inherit the merits of the implicit boundary representation but also avoid some unfavorable features of the conventional discrete level set method such as the cfl condition restriction the re initialization procedure and the velocity extension algorithm finally an extensively investigated example is presented to demonstrate the benefits and advantages of the present method especially its capability of creating new holes inside the design domain

a consistent relaxation of optimal design problems for coupling shape and topological derivatives in this article we introduce and analyze a general procedure for approximating a black and white shape and topology optimization problem with a density optimization problem allowing for the presence of grayscale regions our construction relies on a regularizing operator for smearing the characteristic functions involved in the exact optimization problem and on an interpolation scheme which endows the intermediate density regions with fictitious material properties under mild hypotheses on the smoothing operator and on the interpolation scheme we prove that the features of the approximate density optimization problem material properties objective function etc converge to their exact counterparts as the smoothing parameter vanishes in particular the gradient of the approximate objective functional with respect to the density function converges to either the shape or the topological derivative of the exact objective these results shed new light on the connections between these two different notions of sensitivities for functions of the domain and they give rise to different numerical algorithms which are illustrated by several experiments

optimal design for polymer extrusion part i sensitivity analysis for nonlinear steady state systems we present a general framework to obtain analytical design sensitivities for steady state nonlinear systems where special emphasis is given to design variables that define prescribed boundary conditions the sensitivities are derived for a general response functional using both the direct and adjoint methods and are compared to show that the two sensitivity analysis methods yield identical expressions both adjoint and direct sensitivities for the generalized hele shaw system which models the flow of purely viscous non newtonian fluids through thin cavities are obtained using weak formulations and then discretized for the finite element analysis these sensitivities are used with numerical optimization to design polymer sheeting dies with minimum pressure drop and reduced velocity variation across the die exit

interpolation scheme for fictitious domain techniques and topology optimization of finite strain elastic problems abstract the focus of this paper is on interpolation schemes for fictitious domain and topology optimization approaches with structures undergoing large displacements numerical instability in the finite element simulations can often be observed due to excessive distortion in low stiffness regions a new energy interpolation scheme is proposed in order to stabilize the numerical simulations the elastic energy density in the solid and void regions is interpolated using the elastic energy densities for large and small deformation theory respectively the performance of the proposed method is demonstrated for a challenging test geometry as well as for topology optimization of minimum compliance and compliant mechanisms the effect of combining the proposed interpolation scheme with different hyperelastic material models is investigated as well numerical results show that the proposed approach alleviates the problems in the low stiffness regions and for the simulated cases results in stable topology optimization of structures undergoing large displacements

a commutator approach to absolute continuity for unbounded jacobi operators this paper uses commutator equations to study the absolute continuity of spectral measures associated with certain subclasses of unbounded self adjoint jacobi matrix operators determined by properties of the diagonal and subdiagonal sequences if the diagonal sequence is the zero sequence properties of the difference sequence of the subdiagonal determine the choice of a bounded operator for the commutator equation the structure of the resulting commutator leads to results on absolute continuity

review of parameter identification procedures in groundwater hydrology the inverse problem the purpose of this survey is to review parameter identification procedures in groundwater hydrology and to examine computational techniques which have been developed to solve the inverse problem parameter identification methods are classified under the error criterion used in the formulation of the inverse problem the problem of ill posedness in connection with the inverse problem is addressed typical inverse solution techniques are highlighted the review also includes the evaluation of methods used for computing the sensitivity matrix statistics which can be used to estimate the parameter uncertainty are outlined attempts have been made to compare and contrast representative inverse procedures and direction for future research is suggested

the generalized differential quadrature rule for initial value differential equations abstract the generalized differential quadrature rule gdqr proposed recently by the authors is applied here to solve initial value differential equations of the 2nd to 4th order differential quadrature expressions are derived based on the gdqr for these equations the hermite interpolation functions are used as trial functions to obtain the explicit weighting coefficients for an easy and efficient implementation of the gdqr the numerical solutions for example problems demonstrate that the gdqr has high efficiency and accuracy a detailed discussion on the present method is presented by comparing with other existing methods the present method can be extended to other types of differential equation systems

stress based topology optimization of continuum structures under uncertainties abstract this work addresses the use of the topology optimization approach to the design of continuum structures with failure constraints under the hypothesis of uncertainties in the spatial distribution of young s modulus to this end the first order perturbation approach is used to model the response of the structure and the midpoint discretization technique is used to represent the random field the objective is the minimization of the amount of material used in the design subjected to local stress constraints under uncertainties the probability of failure is bounded by the one sided chebychev inequality since the exact probability distribution function of the stress constraints is not known in advance the effective probability of failure of the obtained optimal designs is validated with the use of the monte carlo simulation approach indicating that the probability of failures of the topologies obtained with the stochastic approach is within the bounds provided by the one sided chebychev inequality the optimization problem is solved by means of the augmented lagrangian method in order to address the large number of constraints associated to this kind of formulation it is shown that the correlation length and the number of standard deviations considered in the formulation play an important role in both the obtained topology and effective probability of failure

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

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

topology optimization of non linear elastic structures and compliant mechanisms abstract a linear elastic response is assumed in most structural topology optimization problems while this assumption is valid for a wide variety of problems it is not valid for structures undergoing large displacements the elastic structural analysis used here accommodates geometric and material non linearities the material density field is filtered to enforce a length scale on the field variation and is penalized to remove less effective intermediate densities the filtering scheme is embedded in the structural analysis to resolve the non existent solution to the solid void topology problem in this way we know precisely what optimization problem is being solved the structural topology optimization formulation is also used to design compliant mechanisms

tangent operators and design sensitivity formulations for transient non linear coupled problems with applications to elastoplasticity tangent operators and design sensitivities are derived for transient non linear coupled problems the solution process and the formation of tangent operators are presented in a systematic manner and sensitivities for a generalized response functional are formulated via both the direct differentiation and adjoint methods the derived formulations are suitable for finite element implementations analyses of systems with materials that exhibit history dependent response may be obtained directly by applying the analyses of transient non linear coupled systems rate independent elastoplasticity is investigated as a case study and a problem with an analytical solution is analysed for demonstration purposes

asymptotics of large eigenvalues for some discrete unbounded jacobi matrices abstract the aim of this paper is to find asymptotic formulas for eigenvalues of self adjoint discrete operators in l 2 n given by some infinite symmetric jacobi matrices the approach used to calculate an asymptotic behaviour of eigenvalues is based on method of diagonalization janas and naboko s lemma j janas s naboko infinite jacobi matrices with unbounded entries asymptotics of eigenvalues and the transformation operator approach siam j math anal 36 2 2004 643 658 and the rozenbljum theorem g v rozenbljum near similarity of operators and the spectral asymptotic behaviour of pseudodifferential operators on the circle russian trudy maskov mat obshch 36 1978 59 84 the asymptotic formulas are given with use of eigenvalues and determinants of finite tridiagonal matrices

a density gradient approach to topology optimization under design dependent boundary loading abstract the paper proposes a density gradient based approach to topology optimization under design dependent boundary loading since there is no explicit boundary representation in density based topology optimization the design dependent boundary loads are implicitly imposed through a domain integration of spatial gradient of the density field the density gradient based loading is formally derived and justified based on the smoothed boundary method for numerical solution of pde the heaviside projection density filtering and local refinement are combined to efficiently control the thickness of the loading interface and the number of elements within it for problems with both loading and non loading boundary an auxiliary density field is introduced to keep track of the loading boundary both 2d and 3d heat conduction problems linear elasticity problems and coupled thermoelastic problems under design dependent boundary loading are presented to illustrate the effectiveness and efficiency of the method

an immersed boundary element method for level set based topology optimization summary in this paper we propose a new bem for level set based topology optimization in the proposed bem the nodal coordinates of the boundary element are replaced with the nodal level set function and the nodal coordinates of the eulerian mesh that maintains the level set function because this replacement causes the nodal coordinates of the boundary element to disappear the boundary element mesh appears to be immersed in the eulerian mesh therefore we call the proposed bem an immersed bem the relationship between the nodal coordinates of the boundary element and the nodal level set function of the eulerian mesh is clearly represented and therefore the sensitivities with respect to the nodal level set function are strictly derived in the immersed bem furthermore the immersed bem completely eliminates grayscale elements that are known to cause numerical difficulties in topology optimization by using the immersed bem we construct a concrete topology optimization method for solving the minimum compliance problem we provide some numerical examples and discuss the usefulness of the constructed optimization method on the basis of the obtained results copyright 2012 john wiley sons ltd

orthogonal polynomials spectral measures and absolute continuity abstract this paper studies the measure of orthogonality for a system of polynomials corresponding to an unbounded self adjoint jacobi matrix with finite row sums techniques of operator theory and functional analysis are used to study the spectral measure of this operator which gives the measure of orthogonality for the system of polynomials with a view toward obtaining results on absolute continuity

absolute continuity for unbounded jacobi matrices with constant row sums we investigate the spectral properties of a class of jacobi matrices in which the subdiagonal entries are quadratics and the row sums are constants

short note shape and topology optimization for electrothermomechanical microactuators using level set methods in this short note a shape and topology optimization method is presented for multiphysics actuators including geometrically nonlinear modeling based on an implicit free boundary parameterization method a level set model is established to describe structural design boundary by embedding it into the zero level set of a higher dimensional level set function the compactly supported radial basis functions csrbf are introduced to parameterize the implicit level set surface with a high level of accuracy and smoothness the original more difficult shape and topology optimization driven by the hamilton jacobi partial differential equation pde is transferred into a relatively easier parametric size optimization to which many well founded optimization algorithms can be applied thus the structural optimization is transformed to a numerical process that describes the design as a sequence of motions of the design boundaries by updating the expansion coefficients of the size optimization two widely studied examples are chosen to demonstrate the effectiveness of the proposed method

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

damage detection from changes in curvature mode shapes abstract a damage in a structure alters its dynamic characteristics the change is characterized by changes in the eigenparameters i e natural frequency damping values and the mode shapes associated with each natural frequency considerable effort has been spent in obtaining a relationship between the changes in eigenparameters the damage location and the damage size most of the emphasis has been on using the changes in the natural frequencies and the damping values to determine the location and the size of the damage in this paper a new parameter called curvature mode shape is investigated as a possible candidate for identifying and locating damage in a structure by using a cantilever and a simply supported analytical beam model it is shown here that the absolute changes in the curvature mode shapes are localized in the region of damage and hence can be used to detect damage in a structure the changes in the curvature mode shapes increase with increasing size of damage this information can be used to obtain the amount of damage in the structure finite element analysis was used to obtain the displacement mode shapes of the two models by using a central difference approximation curvature mode shapes were then calculated from the displacement mode shapes

distributed parameter optimization and topology design for non linear thermoelasticity abstract topology optimization has been the focus of considerable attention in the shape optimization community in recent years since significant performance improvements can be obtained if the topology is allowed to vary in shape optimization problems attention has mainly focussed on the topology design of an elastic continuum for minimum compliance subject to a volume constraint the macroscopic version of this problem is not well posed if no restrictions are placed on the structure topology the most widely used method for making the problem has been the so called homogenization method which introduces microstructure to the design space though there are a number of advantages to this method it also suffers from some drawbacks optimal designs generated using an optimal microstructure are difficult to manufacture while using sub optimal microstructures reverts the problem back to the original ill posed problem in addition extension of the homogenization method to problems involving non linear material behavior is quite difficult to address some of these issues a new method for making the compliance optimization problem well posed has recently been proposed this method introduces an additional constraint on the perimeter of the solid regions in the design to make the problem well posed since microstructure is not introduced the designs are easily manufacturable preliminary results for topology design using the perimeter method for problems where the material behavior is linear elastic have already been reported in the literature we show that the perimeter method can be used even when the material behavior involves material and geometric non linearities we formulate the distributed parameter optimization and topology design problems using the perimeter method for non linear thermoelasticity finite element optimization procedures based on this formulation are developed and numerical solutions for the distributed parameter optimization problem are presented though we use the compliance as the objective function one could optimize any objective function by making minor modifications in the method outlined here

improving the efficiency of large scale topology optimization through on the fly reduced order model construction summarytopology optimization of large scale structures is computationally expensive notably because of the cost of solving the equilibrium equations at each iteration reduced order models by projection also known as reduced basis models have been proposed in the past for alleviating this cost we propose here a new method for coupling reduced basis models with topology optimization to improve the efficiency of topology optimization of large scale structures the novel approach is based on constructing the reduced basis on the fly using previously calculated solutions of the equilibrium equations the reduced basis is thus adaptively constructed and enriched based on the convergence behavior of the topology optimization a direct approach and an approach with adjusted sensitivities are described and their algorithms provided the approaches are tested and compared on various 2d and 3d minimum compliance topology optimization benchmark problems computational cost savings by up to a factor of 12 are demonstrated using the proposed methods copyright textcopyright 2014 john wiley sons ltd