similar tests and the standardized log likelihood ratio statistic summary when testing an affine hypothesis in an exponential family the ideal procedure is to calculate the exact similar test or an approximation to this based on the conditional distribution given the minimal sufficient statistic under the null hypothesis by contrast to this there is a primitive approach in which the marginal distribution of a test statistic is considered and any nuisance parameter appearing in the test statistic is replaced by an estimate we show here that when using standardized likelihood ratio statistics the primitive procedure is in fact an ideal procedure to order o n 3 2 as an example we consider inference for the mean of a log normal distribution in detail

unit impulse response matrix of unbounded medium by infinitesimal finite element cell method abstract to calculate the unit impulse response matrix of the unbounded medium the infinitesimal finite element cell method based solely on the finite element formulation and working exclusively in the time domain is developed a formulation can be derived for acceleration velocity and displacement unit impulse response matrices starting from the acceleration unit impulse impulse response matrix those of the velocity and displacement are constructed the algorithm to determine the acceleration unit impulse response matrix and its application are simpler than the other two alternatives as in the cloning algorithm the approach is based on similarity of the unbounded media corresponding to the interior and exterior boundaries of the infinitesimal finite element cell the derivation is performed exclusively in the time domain at each time station a linear system of equations is solved the consistent boundary method to analyse a layered medium in the frequency domain and the viscous dashpot boundary method are special cases of the infinitesimal finite element cell method the error is governed by the finite element discretization in the circumferential direction as the width of the finite element cell in the radial direction is infinitesimal the infinitesimal finite element cell method is thus exact in the finite element sense the method leads to highly accurate results for a vast class of problems ranging from a one dimensional spherical cavity to a rectangular foundation embedded in a half plane

topological sensitivity analysis for elliptic differential operators of order 2m abstract the topological derivative is defined as the first term of the asymptotic expansion of a given shape functional with respect to a small parameter that measures the size of a singular domain perturbation it has applications in many different fields such as shape and topology optimization inverse problems image processing and mechanical modeling including synthesis and or optimal design of microstructures fracture mechanics sensitivity analysis and damage evolution modeling the topological derivative has been fully developed for a wide range of second order differential operators in this paper we deal with the topological asymptotic expansion of a class of shape functionals associated with elliptic differential operators of order 2m m 1 the general structure of the polarization tensor is derived and the concept of degenerate polarization tensor is introduced we provide full mathematical justifications for the derived formulas including precise estimates of remainders

topological sensitivity analysis in heterogeneous anisotropic elasticity problem theoretical and computational aspects the topological sensitivity analysis for the heterogeneous and anisotropic elasticity problem in two dimensions is performed in this work the main result of the paper is an analytical closed form of the topological derivative for the total potential energy of the problem this derivative displays the sensitivity of the cost functional the energy in this case when a small singular perturbation is introduced in an arbitrary point of the domain in this case we consider a small disc with a completely different elastic material full mathematical justification for the derived formula and derivations of precise estimates for the remainders of the topological asymptotic expansion are provided finally the influence of the heterogeneity and anisotropy is shown through some numerical examples of structural topology optimization

practical use of higher order asymptotics for multiparameter exponential families recently developed asymptotics based on saddlepoint methods provide important practical methods for multiparameter exponential families especially in generalized linear models the aim here is to clarify and explore these attention is restricted to tests and confidence intervals regarding a single parametric function which can be represented as a natural parameter of a full rank exponential family excellent approximations to exact conditional inferences are often available in terms of simple adjustments to the signed square root of the likelihood ratio statistic

an enhanced aggregation method for topology optimization with local stress constraints abstract by introducing a new reduction parameter into the kreisselmeier steihauser k s function this paper presents a general k s formulation providing an approximation to the feasible region restricted by active constraints the approximation is highly accurate even when the aggregation parameter takes a relatively small value numerical difficulties such as high nonlinearity and serious violation of local constraints that may be exhibited by the original k s function are thus effectively alleviated in the considered topology optimization problem the material volume is to be minimized under local von mises stress constraints imposed on all the finite elements an enhanced aggregation algorithm based on the general k s function in conjunction with a removal and re generation strategy for selecting the active constraints is then proposed to treat the stress constraints of the optimization problem numerical examples are given to demonstrate the validity of the present algorithm it is shown that the proposed method can achieve reasonable solutions with a high computational efficiency in handling large scale stress constrained topology optimization problems

topological derivative for multi scale linear elasticity models applied to the synthesis of microstructures this paper proposes an algorithm for the synthesis optimization of microstructures based on an exact formula for the topological derivative of the macroscopic elasticity tensor and a level set domain representation the macroscopic elasticity tensor is estimated by a standard multi scale constitutive theory where the strain and stress tensors are volume averages of their microscopic counterparts over a representative volume element the algorithm is of simple computational implementation in particular it does not require artificial algorithmic parameters or strategies this is in sharp contrast with existing microstructural optimization procedures and follows as a natural consequence of the use of the topological derivative concept this concept provides the correct mathematical framework to treat topology changes such as those characterizing microstuctural optimization problems the effectiveness of the proposed methodology is illustrated in a set of finite element based numerical examples copyright 2010 john wiley sons ltd

the scaled boundary finite element method in structural dynamics the scaled boundary finite element method is extended to solve problems of structural dynamics the dynamic stiffness matrix of a bounded finite domain is obtained as a continued fraction solution for the scaled boundary finite element equation the inertial effect at high frequencies is modeled by high order terms of the continued fraction without introducing an internal mesh by using this solution and introducing auxiliary variables the equation of motion of the bounded domain is expressed in high order static stiffness and mass matrices standard procedures in structural dynamics can be applied to perform modal analyses and transient response analyses directly in the time domain numerical examples for modal and direct time domain analyses are presented rapid convergence is observed as the order of continued fraction increases a guideline for selecting the order of continued fraction is proposed and validated high computational efficiency is demonstrated for problems with stress singularity

development of pareto topology optimization considering thermal loads abstract in this research we developed a level set based topology optimization with a topological derivative formulation considering thermal load thermo elasticity equations were utilized to obtain the sensitivity of the objective function after inserting a small hole in the domain total strain energy and the maximum stress in the design domain were taken as the objective functions after taking the thermal loading effect into account the total strain energy density function became a nonhomogeneous function of the strain in addition temperature variation changed hooke s law from a linear homogeneous to a linear nonhomogeneous expression including a zero order term we derived the sensitivity value of the selected objective functions with respect to a perturbation in the structural domain under mechanical and thermal loads while considering these changes in the governing equations we performed several numerical optimization problems to demonstrate the validity of the present level set based pareto topology optimization two types of examples compliance and stress minimization were solved based on the chosen objective functions furthermore in the stress minimization examples the derived formula was extended to consider thermal effects in the failure theories for pressure independent and dependent materials

optimal topological design through insertion and configuration of finite sized heterogeneities in this paper we develop a procedure for optimal topological design by sequentially inserting finite sized non spherical inclusions or holes within a homogeneous domain we propose a new criterion for topology change that results in a trade off problem to achieve the greatest least change in the objective for the least greatest change in the size of the inclusion hole respectively we derive the material derivative of the proposed objective termed as the configurational derivative that describes sensitivity of arbitrary functionals to arbitrary motions of the inclusion hole as well as the domain boundaries we specifically utilize the sensitivity to position orientation and scaling of finite sized heterogeneities to effect topological design we simplify the configurational derivative to the special case of infinitesimally small spherical inclusions or holes and show that the developed derivative is a generalization of the classical topological derivative the computational implementation relies on b spline isogeometric approximations we demonstrate through a series of examples optimal topology achieved through sequential insertion of a heterogeneity of fixed shape and optimization of its configuration location orientation and scale

a new algorithm for topology optimization using a level set method the level set method has been recently introduced in the field of shape optimization enabling a smooth representation of the boundaries on a fixed mesh and therefore leading to fast numerical algorithms however most of these algorithms use a hamilton jacobi equation to connect the evolution of the level set function with the deformation of the contours and consequently they can hardly create new holes in the domain at least in 2d in this work we propose an evolution equation for the level set function based on a generalization of the concept of topological gradient this results in a new algorithm allowing for all kinds of topology changes

sensitivity analysis in kinematically incompatible models abstract a natural question that arises when working with the so called kinematically incompatible models is about the positioning of the internal artificial boundary that splits the domain of analysis into the sub domains for which the different incompatible models are established although the experience in modeling might provide an ad hoc solution to such matter it may also draw misleading conclusions here the sensitivity analysis furnishes a systematic and reliable framework to study the impact of the positioning of the artificial boundary over the solution of the problem in this sense the present work is concerned with the sensitivity analysis of the variational formulation corresponding to the kinematically incompatible models when the boundary over which the incompatibility between the models takes place is changed assuming the presence of a discontinuity in the fields over a given interface between two incompatible models this analysis allows to measure the sensitivity of a given cost functional when the location of such interface is changed the application for which this analysis is envisaged is to assess the correctness or incorrectness in the definition of the positioning of such coupling interface between dimensionally heterogeneous domains also some numerical results are provided to give numerical evidence of the usefulness of the present tool

higher order topological derivatives in elasticity the topological derivative provides the variation of a response functional when an infinitesimal hole of a particular shape is introduced into the domain in this work we compute higher order topological derivatives for elasticity problems so that we are able to obtain better estimates of the response when holes of finite sizes are introduced in the domain a critical element of our algorithm involves the asymptotic approximation for the stress on the hole boundary when the hole size approaches zero it consists of a composite expansion that is based on the responses of elasticity problems on the domain without the hole and on a domain consisting of a hole in an infinite space we present a simple example in which the higher order topological derivatives of the total potential energy are obtained analytically and by using the proposed asymptotic expansion we also use the finite element method to verify the topological asymptotic expansion when the analytical solution is unknown

a staggered approach to shape and topology optimization using the traction method and an evolutionary type advancing front algorithm abstract we investigate a novel approach for structural shape optimization on the basis of complementary shape and topological sensitivity analysis as in early approaches to shape optimization the domain variation is specified by modification of boundary nodal points hence leading to an updated lagrangian description for the course of optimization to overcome the formation of oscillating boundaries in the optimal design trials we employ the traction method to establish smooth descent directions for shape variation therein an auxiliary elastic problem is solved in which the shape sensitivity constitutes the external loading and the deformation of the auxiliary elastic body is used as a descent direction for shape variation rather than the shape sensitivity itself we complement this method through an evolutionary type element removal procedure that is based on the topological sensitivity such that an advancing front algorithm is gradually removing elements from the design boundary of the domain once the minimum topological sensitivity is no longer encountered at the design boundary we create a hole in the domain again using the topological sensitivity to specify its exact location and resume the element removal procedure for the newly established design boundary since this approach yields only a vague estimate of the true optimal shape of newly established holes the traction method is again used for shape variation of the extended design boundary

consistent infinitesimal finite element cell method three dimensional vector wave equation to calculate the unit impulse response matrix of an unbounded medium for use in a time domain analysis of unbounded medium structure interaction the consistent infinitesimal finite element cell method is developed for the three dimensional vector wave equation this is a boundary finite element procedure the discretization is only performed on the structure medium interface yielding a reduction of the spatial dimension by 1 the procedure is rigorous in the radial direction and exact in the finite element sense in the circumferential directions in contrast to the boundary element procedure the consistent infinitesimal finite element cell method does not require a fundamental solution and incorporates interfaces extending from the structure medium interface to infinity compatible with similarity without any additional computational effort a general anisotropic material can be processed the derivation is based on the finite element formulation and on similarity

saddlepoint approximations to the cdf of some statistics with nonnormal limit distributions abstract in standard saddlepoint approximations to the cumulative distribution function of a random variable the normal distribution has appeared to play a special role in this article we consider what happens when the normal base distribution is replaced by an arbitrary base distribution generalized versions of several standard formulas are presented the choice of a chi squared base or an inverse gaussian base is then considered in detail the generalized approximations are compared in two examples a linear combination of chi squared variables and the first passage time distribution for a random walk the former example considers approximations using the chi squared base that are slightly more accurate than their normal based counterparts in the latter example approximations based on the inverse gaussian are considerably more accurate than their normal based counterparts

the topological asymptotic for pde systems the elasticity case the aim of the topological sensitivity analysis is to obtain an asymptotic expansion of a design functional with respect to the creation of a small hole in this paper such an expansion is obtained and analyzed in the context of linear elasticity for general functionals and arbitrary shaped holes by using an adaptation of the adjoint method and a domain truncation technique the method is general and can be easily adapted to other linear pdes and other types of boundary conditions

efficient computation of order and mode of three dimensional stress singularities in linear elasticity by the boundary finite element method the boundary finite element method bfem a novel semi analytical boundary element procedure solely relying on standard finite element formulations is employed for the investigation of the orders and modes of three dimensional stress singularities which occur at notches and cracks in isotropic halfspaces as well as at free edges and free corners of layered plates after a comprehensive literature review and a concise introduction to the standard three dimensional bfem formulation for the static analysis of general unbounded structures we demonstrate the application of the bfem for the computation of the orders and modes of two dimensional and three dimensional stress singularities for several classes of problems within the framework of linear elasticity special emphasis is placed upon the investigation of stress concentration phenomena as they occur at straight free edges and at free corners of arbitrary opening angles in composite laminates in all cases the bfem computations agree excellently with available reference results the required computational effort is found to be considerably lower compared to e g standard finite element method fem computations in the case of free laminate corners numerous new results on the occurring stress singularities are presented it is found that free corner problems generally seem to involve a more pronounced criticality than the corresponding free edge situations

stress based shape and topology optimization with the level set method abstract this paper proposes a level set method to solve minimum stress and stress constrained shape and topology optimization problems the method solves a sub optimization problem every iteration to obtain optimal boundary velocities a p norm stress functional is used to aggregate stresses in a single constraint the shape sensitivity function is derived and a computational procedure based on a least squares interpolation approach is devised in order to compute sensitivities at the boundaries adaptive constraint scaling is used to enforce exact control of stress limits numerical results show that the method is able to solve the problem efficiently for single and multiple load cases obtaining solutions with smooth boundaries

topology optimization of steady navier stokes flow with body force abstract this paper presents the topology optimization of steady navier stokes flows with body forces that influence the optimal shape and topology of fluid flows based on the implicit expression of the fluid flow with the level set method an optimization problem is formulated and analyzed using the continuous adjoint method the shape and topological sensitivities are computed based on the adjoint and asymptotic analysis of the optimization problem in the optimization procedure the level set surface is evolved based on the shape sensitivity and nucleated based on the topological sensitivity simultaneously three kinds of body forces that are commonly used in the design of fluid devices i e constant nonuniform and solution dependent body forces are considered in the two dimensional and three dimensional numerical examples numerical results demonstrate that this method can effectively achieve the topology optimization of the navier stokes flows with body forces

incorporating topological derivatives into shape derivatives based level set methods shape derivatives and topological derivatives have been incorporated into level set methods to investigate shape optimization problems the shape derivative measures the sensitivity of boundary perturbations while the topological derivative measures the sensitivity of creating a small hole in the interior domain the combination of these two derivatives yields an efficient algorithm which has more flexibility in shape changing and may escape from a local optimal examples on finding the optimal shapes for maximal band gaps in photonic crystal and acoustic drum problems are demonstrated

topological and shape gradient strategy for solving geometrical inverse problems abstract in this paper we present a technique for shape reconstruction based on the topological and shape gradients the shape in consideration is a solution of an inverse conductivity problem to solve such a problem numerically we compute the topological gradient of a kohn vogelius type cost function when the domain under consideration is perturbed by the introduction of a small inclusion instead of a hole the reconstruction is done by considering the shape as a superposition of very thin elliptic inclusions to get a first approximation then we use a gradient type algorithm to perform a good reconstruction various numerical experiments of single and multiple inclusions demonstrate the viability of the designed algorithm

combination of topology optimization and optimal control method this paper presents the combination of topology optimization and optimal control method to find the optimal match between the material topology and control in the presented method the material topology is determined using the simp solid isotropic material with penalization method which has been popularly used in topology optimization in the simp method the design variable is relaxed and bounded in the interval 0 1 and the evolution of the design variable is usually implemented by the method of moving asymptotes mma which can be used to deal with optimization problem with multiple integral constraints and bound constraint of the design variable in the combination of topology optimization and optimal control method the control variable appears along with the design variable in order to evolve the control variable and design variable using mma simultaneously the control variable is regularized using a bound constraint and the corresponding bound constraint is projected onto the interval 0 1 which is the same as the bound constraint of the design variable the optimization problem is analyzed using the adjoint method to obtain the adjoint sensitivity during the optimization procedure the design and control variables are filtered by the helmholtz filters to ensure the smoothness of the distribution to ensure the minimum scale length and remove the gray area in the material topology the filtered design variable is projected by the threshold method the feasibility and robustness of the combination of these two methods are demonstrated by several test problems including heat transfer fluid flow and compliance minimization

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

stress based topology optimization method for steady state fluid structure interaction problems abstract this research developed a new stress based topology optimization method stom for a steady state fluid structure interaction fsi problem that minimizes the volume subject to the local stress constraints despite numerous studies on stom challenging optimization issues related to stress based topology optimization to procedures for fluid structure multiphysics systems still exist critical issues involved in creating a successful to for an fsi structure include the interpolation approach between the fluid equation and the structure equation with respect to locally defined design variables the mutual multiphysics coupling boundary conditions at dramatically evolving interfacing boundaries and a clear interpretation of the governing equations and the interaction boundary conditions for spatially varying intermediate design variables in addition to these three issues which are related to multiphysics equations there are three important considerations related to the stom the stress singularity issue the issues of multiple constraints and the highly nonlinear behavior of the stress constraints to resolve all of the aforementioned issues we applied a monolithic analysis integrating the qp relaxation method and the global p norm approach using the present method we created optimal layouts that minimize the volume constraining local stress values for a steady state fluid and structural interaction system

second order topological sensitivity analysis abstract the topological derivative provides the sensitivity of a given cost function with respect to the insertion of a hole at an arbitrary point of the domain classically this derivative comes from the second term of the topological asymptotic expansion dealing only with infinitesimal holes however for practical applications we need to insert holes of finite size therefore we consider one more term in the expansion which is defined as the second order topological derivative in order to present these ideas in this work we apply the topological shape sensitivity method as a systematic approach to calculate first as well as second order topological derivative for the poisson s equations taking the total potential energy as cost function and the state equation as constraint furthermore we also study the effects of different boundary conditions on the hole neumann and dirichlet both homogeneous finally we present some numerical experiments showing the influence of the second order topological derivative in the topological asymptotic expansion which has two main features it allows us to deal with hole of finite size and provides a better descent direction in optimization process

phase field relaxation of topology optimization with local stress constraints we introduce a new relaxation scheme for structural topology optimization problems with local stress constraints based on a phase field method in the basic formulation we have a pde constrained optimization problem where the finite element and design analysis are solved simultaneously the starting point of the relaxation is a reformulation of the material problem involving linear and 0 1 constraints only the 0 1 constraints are then relaxed and approximated by a cahn hilliard type penalty in the objective functional which yields convergence of minimizers to 0 1 designs as the penalty parameter decreases to zero a major advantage of this kind of relaxation opposed to standard approaches is a uniform constraint qualification that is satisfied for any positive value of the penalization parameter the relaxation scheme yields a large scale optimization problem with a high number of linear inequality constraints we discretize the problem by finite elements and solve the arising finite dimensional programming problems by a primal dual interior point method numerical experiments for problems with local stress constraints based on different criteria indicate the success and robustness of the new approach

topological sensitivity analysis for three dimensional linear elasticity problem in this work we use the topological shape sensitivity method to obtain the topological derivative for three dimensional linear elasticity problems adopting the total potential energy as cost function and the equilibrium equation as constraint this method based on classical shape sensitivity analysis leads to a systematic procedure to calculate the topological derivative in particular firstly we present the mechanical model later we perform the shape derivative of the corresponding cost function and finally we calculate the final expression for the topological derivative using the topological shape sensitivity method and results from classical asymptotic analysis around spherical cavities in order to point out the applicability of the topological derivative in the context of topology optimization problems we use this information as a descent direction to solve a three dimensional topology design problem furthermore through this example we also show that the topological derivative together with an appropriate mesh refinement strategy are able to capture high quality shapes even using a very simple topology algorithm

brittle and ductile failure constraints of stress based topology optimization method for fluid structure interactions abstract this study considers failure theories for brittle and ductile materials in the stress based topology optimization method stom for steady state fluid structure interactions fsi in some relevant studies the subject of the stress based topology optimization to minimize volumes with local von mises stress constraints has been researched however the various failure theories for ductile and brittle materials such as the maximum shear stress theory the brittle and ductile mohr coulomb theory and the drucker prager theory have not been considered for successful stom for fsi in addition to alleviating physics interpolation issues between structure and fluid and some numerical issues related to stom the mathematical characteristics of the various failure theories should be properly formulated and constrained to resolve all the involved computational issues the present study applies the monolithic analysis method the qp relaxation method and the p norm approach to the failure constraints the present topology optimization method can create optimal layouts while minimizing volume constraining local failure constraints for ductile and brittle materials for steady state fluid and structural interaction system

energy change to insertion of inclusions associated with the reissner mindlin plate bending model abstract the topological derivative concept has been proved to be useful in many relevant applications such as topology optimization inverse problems image processing multi scale constitutive modeling fracture mechanics and damage evolution modeling the topological asymptotic analysis has been fully developed for a wide range of problems modeled by partial differential equations on the other hand the topological derivatives associated with coupled problems have been derived only in their abstract forms in this paper therefore we deal with the reissner mindlin plate bending model which is written in the form of a coupled system of partial differential equations in particular the topological asymptotic analysis of the associated total potential energy is developed and the topological derivative with respect to the nucleation of a circular inclusion is derived in its closed form finally we provide the estimates for the remainders of the topological asymptotic expansion and perform a complete mathematical justification for the derived formulas

consistent infinitesimal finite element cell method in plane motion note 189 reference lch article 1995 005 record created on 2007 04 24 modified on 2016 08 08

is the improved likelihood ratio statistic really improved in the discrete case summary on the basis of some numerical studies we argue that bartlett adjustment of the likelihood ratio statistic for discrete data does not in general yield an improvement in the asymptotic error rate of the chi squared approximation also we argue that the small sample effect of the bartlett adjustment is unclear and that it is in no way comparable with the improvement obtained for continuous data

topology optimization with local stress constraint based on level set evolution via reaction diffusion abstract this work focuses the structural topology optimization problem of mass minimization subject to local stress constraints to this aim two related issues are addressed the first one is the successful strategy used to define local stress constraints by means of an augmented lagrangian approach the second and main contribution of the present paper is the use of a reaction diffusion equation to guide via evolution of a level set the design optimization sequence the advantages of this strategy are twofold firstly it allows the creation of new holes during the optimization process a significant feature for a true topological optimization method secondly reinitialization steps usually found in classical hamilton jacobi based evolution are eliminated with a significant improvement in convergence ease a set of benchmark examples in two dimensions are presented numerical results show the efficiency of the algorithm to create new holes identify stress concentrations and to provide stable optimization sequences converging to local minima defined by stress saturated designs

topological sensitivity analysis the so called topological derivative concept has been seen as a powerful framework to obtain the optimal topology for several engineering problems this derivative characterizes the sensitivity of the problem when a small hole is created at each point of the domain however the greatest limitation of this methodology is that when a hole is created it is impossible to build a homeomorphic map between the domains in study because they have not the same topology therefore some specific mathematical framework should be developed in order to obtain the derivatives this work proposes an alternative way to compute the topological derivative based on the shape sensitivity analysis concepts the main feature of this methodology is that all the mathematical procedure already developed in the context of shape sensitivity analysis may be used in the calculus of the topological derivative this idea leads to a more simple and constructive formulation than the ones found in the literature further to point out the straightforward use of the proposed methodology it is applied for solving some design problems in steady state heat conduction

strain energy change to the insertion of inclusions associated to a thermo mechanical semi coupled system abstract the topological derivative measures the sensitivity of a given shape functional with respect to an infinitesimal singular domain perturbation according to the literature the topological derivative has been fully developed for a wide range of one single physical phenomenon modeled by partial differential equations in addition the topological asymptotic analysis associated to multi physics problems has been reported in the literature only on the level of mathematical analysis of singularly perturbed geometrical domains in this work we present the topological derivative in its closed form for the total potential mechanical energy associated to a thermo mechanical semi coupled system when a small circular inclusion is introduced at an arbitrary point of the domain in particular we consider the linear elasticity system modeled by the navier equation coupled with the steady state heat conduction problem modeled by the laplace equation the mechanical coupling term comes out from the thermal stress induced by the temperature field since this term is non local we introduce a non standard adjoint state which allows to obtain a closed form for the topological derivative finally we provide a full mathematical justification for the derived formulas and develop precise estimates for the remainders of the topological asymptotic expansion

a new reconstruction method for the inverse potential problem abstract the inverse potential problem consists in reconstructing an unknown measure with support in a geometrical domain from a single boundary measurement in order to deal with this severely ill posed inverse problem we rewrite it as an optimization problem where a kohn vogelius type functional measuring the misfit between the solutions of two auxiliary problems is minimized one auxiliary problem contains information on the boundary measurement while the other one corresponds to the boundary excitation the solutions of the auxiliary problems coincide once the inverse problem is solved in order to minimize the kohn vogelius criterion its total variation with respect to a set of ball shaped perturbations on the measure is explicitly evaluated then a new method for solving the inverse potential problem based on the expression obtained is devised finally some numerical results are presented in order to show the effectiveness of the proposed reconstruction algorithm

topological derivative based topology optimization of structures subject to drucker prager stress constraints abstract an algorithm for topology optimization of elastic structures under plane stress subject to the drucker prager stress constraint is presented the algorithm is based on the use of the topological derivative of the associated objective functional in conjunction with a level set representation of the structure domain in this context a penalty functional is proposed to enforce the point wise stress constraint and a closed formula for its topological derivative is derived the resulting algorithm is of remarkably simple computational implementation it does not require post processing procedures of any kind and features only a minimal number of user defined algorithmic parameters this is in sharp contrast with current procedures for topological structural optimization with local stress constraints the effectiveness and efficiency of the algorithm presented here are demonstrated by means of numerical examples the examples show in particular that it can easily handle structural optimization problems with underlying materials featuring strong asymmetry in their tensile and compressive yield strengths

symmetry and lattice conditional independence in a multivariate normal distribution a class of multivariate normal models with symmetry restrictions given by a finite group and conditional independence restrictions given by a finite distributive lattice is defined and studied the statistical properties of these models including maximum likelihood inference invariance and hypothesis testing are discussed

saddlepoint approximations for tests of block independence sphericity and equal variances and covariances summary approximations for the null distribution of various test statistics arising in multivariate analysis using skovgaard s saddlepoint formula are discussed in each case an approximation is found with such accuracy as to obviate the need for exact computation

isogeometric topology optimization using trimmed spline surfaces in the present work a new spline based topology optimization using trimmed spline surfaces and the isogeometric analysis is proposed in the proposed approach the trimmed surface analysis which can treat topologically complex spline surfaces using trimming information provided by cad systems is employed for structural response analysis and sensitivity calculation in the topology optimization the outer and inner boundaries of design models are represented by a spline surface and trimming curves design variables used in this approach are the coordinates of control points of a spline surface and those of trimming curves new sensitivity formulations for the control points in the trimmed surface analysis are proposed and their efficiency and accuracy are verified the creation of new inner fronts during optimization is allowed for the topological flexibility an inner front merging algorithm is also presented the proposed spline based topology optimization is used to solve some benchmarking problems design space dependency which is one of serious shortcomings in conventional topology optimization approaches is naturally eliminated by the proposed spline based optimization design dependent load problems which are difficult to treat with conventional grid based topology optimization methods are easily dealt with by the proposed one it is also shown that post processing effort for converting to cad model is eliminated by using the same spline information in numerical analysis and design optimization

the topological derivative of stress based cost functionals in anisotropic elasticity the topological derivative of cost functionals j that depend on the stress through the displacement gradient assuming a linearly elastic material behavior is considered in a quite general 3d setting where both the background and the inhomogeneity may have arbitrary anisotropic elastic properties the topological derivative d j z of j quantifies the asymptotic behavior of j induced by the nucleation in the background elastic medium of a small anisotropic inhomogeneity of characteristic radius a at a specified location z the fact that the strain perturbation inside an elastic inhomogeneity remains finite for arbitrarily small a makes the small inhomogeneity asymptotics of stress based cost functionals quite different than that of the more usual displacement based functionals the asymptotic perturbation of j is shown to be of order o a 3 for a wide class of stress based cost functionals having smooth densities the topological derivative of j i e the coefficient of the o a 3 perturbation is established and computational procedures then discussed the resulting small inhomogeneity expansion of j is mathematically justified i e its remainder is proved to be of order o a 3 several 2d and 3d numerical examples are presented in particular demonstrating the proposed formulation of d j on cases involving anisotropic elasticity and non quadratic cost functionals

sounding of finite solid bodies by way of topological derivative this paper is concerned with an application of the concept of topological derivative to elastic wave imaging of finite solid bodies containing cavities building on the approach originally proposed in the elastostatic theory of shape optimization the topological derivative which quantifies the sensitivity of a featured cost functional due to the creation of an infinitesimal hole in the cavity free reference body is used as a void indicator through an assembly of sampling points where it attains negative values the computation of topological derivative is shown to involve an elastodynamic solution to a set of supplementary boundary value problems for the reference body which are here formulated as boundary integral equations for a comprehensive treatment of the subject formulas for topological sensitivity are obtained using three alternative methodologies namely i direct differentiation approach ii adjoint field method and iii limiting form of the shape sensitivity analysis the competing techniques are further shown to lead to distinct computational procedures methodologies i and ii are implemented within a bem based platform and validated against an analytical solution a set of numerical results is included to illustrate the utility of topological derivative for 3d elastic wave sounding of solid bodies an approach that may perform best when used as a pre conditioning tool for more accurate gradient based imaging algorithms despite the fact that the formulation and results presented in this investigation are established on the basis of a boundary integral solution the proposed methodology is readily applicable to other computational platforms such as the finite element and finite difference techniques

on the topological derivative in shape optimization in this paper the topological derivative for an arbitrary shape functional is defined examples are provided for elliptic equations and the elasticity system in the plane the topological derivative can be used for solving shape optimization problems in structural mechanics

proportionality of covariance matrices on considere l inference pour un modele statistique specifiant la proportionnalite entre deux distributions de wishart independantes

shape sensitivity analysis and the energy momentum tensor for the kinematic and static models of torsion abstract the aim of this paper is to bridge shape sensitivity analysis and configurational mechanics by means of a widespread use of the shape derivative concept this technique will be applied as a systematic procedure to obtain the eshelby s energy momentum tensor associated to the problem under consideration in order to highlight special features of this procedure and without loss of generality we focus our attention in the application of shape sensitivity analysis to the problem of twisted straight bars within the framework of linear elasticity kinematic and static variational formulations as well as the direct method of sensitivity analysis are used to perform shape derivatives of both models integral expressions of first and second order shape derivatives of the total potential energy and the complementary potential energy with respect to an arbitrary transverse cross section shape change are achieved these integral expressions put in evidence the relationship between shape sensitivity analysis and the first and second order eshelby s energy momentum tensors also the null divergence property of these tensors is easily proved by comparing in each case the domain and boundary integral shape derivative arrived at finally an example with a known exact solution corresponding to an elastic bar with elliptical transverse cross section submitted to twist is presented in order to illustrate the usefulness of these tensors to compute the corresponding shape derivatives

stochastic inequalities relating a class of log likelihood ratio statistics to their asymptotic chi 2 distribution for decomposable covariance selection models stochastic inequalities which relate the null distribution of the log likelihood ratio statistic to its asymptotic 2 distribution are obtained the implications are twofold first the null distribution of the log likelihood ratio statistic is seen to be stochastically larger than its asymptotic 2 distribution second a simple adjustment to the log likelihood ratio statistic similar in spirit to the bartlett adjustment yields a conservative test

products of ratios of gamma functions an application to the distribution of the test statistic for testing the equality of covariance matrices abstract an expansion of the ratio of two gamma functions is used to obtain an adequate representation for the product of ratios of gamma functions which enables the derivation of approximating expansions for the distribution of the test statistic used for testing the equality of several covariance matrices these asymptotic approximations are based on mixtures of gamma distributions and are obtained using a new expression of the fourier transform of the density function of the logarithm of the test statistic and also on a matching moments technique numerical studies show that these approximations are simple precise and easy to implement a computational module developed for mathematica software is presented together with an example of application

a level set based topology optimization method for simultaneous design of elastic structure and coupled acoustic cavity using a two phase material model abstract this papers proposes a level set based topology optimization method for the simultaneous design of acoustic and structural material distributions in this study we develop a two phase material model that is a mixture of an elastic material and acoustic medium to represent an elastic structure and an acoustic cavity by controlling a volume fraction parameter in the proposed model boundary conditions at the two phase material boundaries are satisfied naturally avoiding the need to express these boundaries explicitly we formulate a topology optimization problem to minimize the sound pressure level using this two phase material model and a level set based method that obtains topologies free from grayscales the topological derivative of the objective functional is approximately derived using a variational approach and the adjoint variable method and is utilized to update the level set function via a time evolutionary reaction diffusion equation several numerical examples present optimal acoustic and structural topologies that minimize the sound pressure generated from a vibrating elastic structure

testing for quaternion propriety we consider the problem of testing whether a quaternion valued gaussian random vector is proper the quaternion covariance matrix fully describes the second order properties of a quaternion random vector only if the distribution is proper the exact distribution of the likelihood ratio test under the hypothesis of propriety is derived for general sample size n and vector dimensionality p as this is in terms of meijer s g function various approximations are considered including box type and saddlepoint approximations we find in particular that a new approach matching the first three cumulants is easy to implement and extremely accurate

effective degrees of freedom and the likelihood ratio test summary normal theory problems involving several unknown variances may require use of estimates not having simple chi squared distributions confidence intervals are then commonly based on the use of effective degrees of freedom i e the fitting of a gamma distribution via the first two moments replacing parameters by estimates the confidence intervals given by this method are compared with those resulting from the likelihood ratio test inserting a bartlett adjustment factor to achieve close approximation by a chi squared distribution two special problems one concerning components of variance and one a generalization of the behrens fisher problem are studied in detail

a level set method for topology optimization of heat conduction problem under multiple load cases in this paper we present a numerical approach of topology optimization under multiple load cases for heat conduction problem this framework is based on the theories of topological derivative and shape derivative for elliptic system we employ level set model to implicitly represent geometric boundary of thermal conductive material introducing topological derivative will generate new topology in the design domain which suppresses the dependence of initial topology guess to some extent the shape optimization is obtained by combining shape derivative with level set method the functional of quadratic temperature gradient is taken as the objective function in our analysis which is subjected to the state equation of steady heat conduction and volume constrain the shape of material domain is treated as the design variable and the final result is achieved by updating level set function gradually we develop an effective numerical technique to implement the optimal design with multiple load cases for heat conduction problem numerical examples demonstrate that our proposed approach is effective and robust for topology optimization of heat conduction problem

the shape and topological optimizations connection abstract in 1973 jean cea introduced a topological shape optimization algorithm based on a fixed point method the recent topological gradient concept provides a mathematical justification of cea s powerful method the aim of the topological gradient is to compute the sensitivity of a cost function when we drill a little hole in the domain some optimality conditions are derived when classical shape gradient and topological gradient are used simultaneously and numerical results are shown both in mechanics and electromagnetics

regularized perimeter for topology optimization the perimeter functional is known to oppose serious difficulties when it has to be handled within a topology optimization procedure in this paper a regularized perimeter functional mbox per varepsilon defined for two and three dimensional domains is introduced on one hand the convergence of mbox per varepsilon to the exact perimeter when varepsilon tends to zero is proved on the other hand the topological differentiability of mbox per varepsilon for varepsilon 0 is analyzed these features lead to the design of a topology optimization algorithm suitable for perimeter dependent objective functionals several numerical results illustrate the method

defeaturing a posteriori error analysis via feature sensitivity it is well known that small geometric features within a cad model can significantly impact the computational cost and often undermine the reliability of finite element analysis engineers therefore resort to defeaturing or detail removal wherein the offending features are suppressed prior to computational analysis however this results in a defeaturing induced analysis error in this paper we estimate this error in an a posteriori sense through the novel concept of feature sensitivity the latter determines the first order change in quantities of interest when an arbitrary cluster of small geometric features is deleted from a model a formal theory and a set of associated algorithms are provided to compute the feature sensitivity associated with a scalar elliptic partial differential equation the theory is supported through numerical experiments in 2 d involving both internal and boundary features copyright 2008 john wiley sons ltd

on the discrete variant of the traction method in parameter free shape optimization abstract one of the major challenges in the parameter free approach to computational shape optimization is the avoidance of oscillating i e non smooth boundaries in the optimal design trials in order to achieve this we investigate a method for regularization that corresponds to the discrete variant of the so called traction method in this approach the design updates are generated in terms of a displacement field which is obtained as the solution to an auxiliary boundary value problem that is defined on the actual design domain the main idea herein is to apply fictitious nodal forces corresponding to the discrete sensitivity of the objective function we propose an algorithm in which constraint functions will be taken into account by using an augmented lagrangian formulation and a step length control ensures a sufficient decrease condition in terms of the objective function within each iteration we examine the benefits of the proposed regularization method on the basis of some numerical examples in comparison to an unregularized steepest descent algorithm

a modified scaled boundary finite element method for three dimensional dynamic soil structure interaction in layered soil summary this paper is devoted to the analysis of elastodynamic problems in 3d layered systems which are unbounded in the horizontal direction for this purpose a finite element model of the near field is coupled to a scaled boundary finite element model sbfem of the far field the sbfem is originally based on describing the geometry of a half space or full space domain by scaling the geometry of the near field far field interface using a radial coordinate a modified form of the sbfem for waves in a 2d layer is also available none of these existing formulations can be used to describe a 3d layered medium in this paper a modified sbfem for the analysis of 3d layered continua is derived based on the use of a scaling line instead of a scaling centre a suitable scaled boundary transformation is proposed the derivation of the corresponding scaled boundary finite element sbfe equations in displacement and stiffness is presented in detail the latter is a nonlinear differential equation with respect to the radial coordinate which has to be solved numerically for each excitation frequency considered in the analysis various numerical examples demonstrate the accuracy of the new method and its correct implementation these include rigid circular and square foundations embedded in or resting on the surface of layered homogeneous or inhomogeneous 3d soil deposits over rigid bedrock hysteretic damping is assumed in some cases the dynamic stiffness coefficients calculated using the proposed method are compared with analytical solutions or existing highly accurate numerical results copyright 2011 john wiley sons ltd

a topology optimization method based on the level set method incorporating a fictitious interface energy this paper proposes a new topology optimization method which can adjust the geometrical complexity of optimal configurations using the level set method and incorporating a fictitious interface energy derived from the phase field method first a topology optimization problem is formulated based on the level set method and the method of regularizing the optimization problem by introducing fictitious interface energy is explained next the reaction diffusion equation that updates the level set function is derived and an optimization algorithm is then constructed which uses the finite element method to solve the equilibrium equations and the reaction diffusion equation when updating the level set function finally several optimum design examples are shown to confirm the validity and utility of the proposed topology optimization method

a large deviation type approximation for the box class of likelihood ratio criteria abstract for a large class of tests related to the multivariate normal distribution a number of approximations to the distribution of the log likelihood ratio statistic are discussed some of the approximations require the use of a small personal computer for their calculation but this pays off in terms of giving very accurate approximations actually one of the approximations based on the use of a conjugate distribution works well for all sample sizes and all significance levels

improved likelihood ratio statistics for covariance selection models summary the expected value of the likelihood ratio statistic for covariance selection models when this statistic has a closed form is derived correct to terms of order n 2 n being the sample size then a bartlett type correction factor is available for such statistics by simulation the practical use of such a correction factor is illustrated and is compared with an alternative correction factor in a special case the null density of the corrected statistic is also considered

a level set approach for topology optimization with local stress constraints summary the purpose of this work is to present a level set based approach for the structural topology optimization problem of mass minimization submitted to local stress constraints the main contributions are threefold first the inclusion of local stress constraints by means of an augmented lagrangian approach within the level set context second the proposition of a constraint procedure that accounts for a continuous activation deactivation of a finite number of local stress constraints during the optimization sequence finally the proposition of a logarithmic scaling of the level set normal velocity as an additional regularization technique in order to improve the minimization sequence a set of benchmark tests in two dimensions achieving successful numerical results assesses the good behavior of the proposed method in these examples it is verified that the algorithm is able to identify stress concentrations and drive the design to a feasible local minimum copyright 2014 john wiley sons ltd