application of the level set method to the finite element solution of two phase flows this paper presents a method to solve two phase flows using the finite element method on one hand the algorithm used to solve the navier stokes equations provides the neccessary stabilization for using the efficient and accurate three node triangles for both the velocity and pressure fields on the other hand the interface position is described by the zero level set of an indicator function to maintain accuracy even for large density ratios the pseudoconcentration function is corrected at the end of each time step using an algorithm successfully used in the finite difference context coupling of both problems is solved in a staggered way as demonstrated by the solution of a number of numerical tests the procedure allows dealing with problems involving two interacting fluids with a large density ratio copyright 2001 john wiley sons ltd

stress related topology optimization via level set approach abstract considering stress related objective or constraint functions in structural topology optimization problems is very important from both theoretical and application perspectives it has been known however that stress related topology optimization problem is challenging since several difficulties must be overcome in order to solve it effectively traditionally simp solid isotropic material with penalization method was often employed to tackle it although some remarkable achievements have been made with this computational framework there are still some issues requiring further explorations in the present work stress related topology optimization problems are investigated via a level set based approach which is a different topology optimization framework from simp numerical examples show that under appropriate problem formulations level set approach is a promising tool for stress related topology optimization problems

structured quadratic inverse eigenvalue problem i serially linked systems quadratic pencils arising from applications are often inherently structured factors contributing to the structure include the connectivity of elements within the underlying physical system and the mandatory nonnegativity of physical parameters for physical feasibility structural constraints must be respected consequently they impose additional challenges on the inverse eigenvalue problems which intend to construct a structured quadratic pencil from prescribed eigeninformation knowledge of whether a structured quadratic inverse eigenvalue problem is solvable is interesting in both theory and applications however the issue of solvability is problem dependent and has to be addressed structure by structure this paper considers one particular structure where the elements of the physical system if modeled as a mass spring system are serially linked the discussion recasts both undamped and damped problems in a framework of inequality systems that can be adapted for numerical computation some open questions are described

topology optimization of incompressible media using mixed finite elements abstract we present an alternative formulation for the topology optimization of structures made of incompressible materials a topic that cannot be tackled using most of the approaches of the current literature that are mainly based on displacement finite elements that are well known to be affected by the locking phenomenon a way out of the problem has recently been proposed in sigmund and clausen 2007 o sigmund p m clausen topology optimization using a mixed formulation an alternative way to solve pressure load problems comput methods appl mech engrg 196 13 16 2007 1874 1889 based on a displacement pressure finite element discretization the approach presented here consists in a truly mixed variational formulation coupled to a mixed fem discretization that uses the composite element of johnson and mercier for the discretization of the stress field by so doing the continuous and discrete inf sup conditions of the problem are automatically met even in the presence of incompressible materials a few numerical studies are presented to validate the theoretical framework for which the well known method of moving asymptotes mma is adopted for the numerical optimization of the problem different topologies in plane stress and plane strain conditions are presented with particular attention to the convergence of the last ones to pure 0 1 designs some forthcoming investigations are eventually highlighted including the solution of stress constrained topology optimization problems that find in the truly mixed setting their natural environment and the extension of the present formulation to deal with pressure load structural problems

topology optimization of fluid structure interaction problems in poroelasticity abstract this paper presents a method for applying topology optimization to fluid structure interaction problems in saturated poroelastic media the method relies on a multiple scale method applied to periodic media the resulting model couples the stokes flow in the pores of the structure with the deformation of the elastic skeleton through a macroscopic darcy type flow law the method allows to impose pressure loads for static problems through a one way coupling while transient problems are fully coupled modeling the interaction between fluid and solid the material distribution is determined by topology optimization in order to optimize the performance of a shock absorber and test the pressure loading capabilities and optimization of an internally pressurized lid

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

computing interface motion in compressible gas dynamics a hamilton jacobi level set formulation of the equations of motion for propagating interfaces has been introduced recently by osher and sethian this formulation allows fronts to self intersect develop singularities and change topology the numerical algorithms based on this approach handle topological merging and breaking naturally work in any number of space dimensions and do not require that the moving front be written as a function instead the moving front is embedded as a particular level set in a fixed domain partial differential equation numerical techniques borrowed from hyperbolic conservation laws are then used to accurately capture the complicated surface motion that satisfies the global entropy condition for propagating fronts given by sethian in this paper we analyze the coupling of this level set formulation to a system of conservation laws for compressible gas dynamics we study both conservative and non conservative differencing of the level set function and compare the two approaches to illustrate the capability of the method we study the compressible rayleigh taylor and kelvin helmholtz instabilities for air air and air helium boundaries we perform numerical convergence studies of the method over a range of parameters and analyze the accuracy of this approach applied to these problems

a newly developed qp relaxation method for element connectivity parameterization to achieve stress based topology optimization for geometrically nonlinear structures the aim of this work is to present a novel computational approach to employ the stress based topology optimization method stom to minimize the volume subject to the locally defined stress constraints of a geometrically nonlinear structure in the framework of the element connectivity parameterization ecp method considering the locally defined stress constraints in topology optimization to is a classic and challenging engineering problem and successful optimization procedures have recently been developed using the density based to method for linear elastic structures however no study has yet considered the static failure constraint when using to for a geometrically nonlinear structure therefore the present study develops a novel computational approach for the stom for a geometrically nonlinear structure to successfully optimize a geometrically nonlinear structure the unstable element issue must be properly addressed in addition to the stress singularity issue the existence of a large number of constraints and the highly nonlinear behavior of the local stress constraints to effectively resolve these issues this research adopts the ecp method to interpolate and optimize the connectivities among solid finite elements furthermore we find that a stress singularity issue linked to the local optima issue arises in the ecp method that is different from that of the density based to by investigating the singularity behavior in detail we develop a new qp relaxation method that is suitable for the ecp method to demonstrate the improved capability of the proposed ecp method with the modified qp relaxation several two dimensional to problems are solved

topology optimization for turbulent flow with spalart allmaras model abstract in this research a new finite element fe based topology optimization to for turbulent flow was developed using the spalart allmaras s a equation which is one of the reynolds averaged navier stokes rans equations despite many innovative works on the subject of fluidic to it is rare to consider the influence of turbulent flow in to to consider the effect of complex turbulent fluid motion this research considered the s a model developed mainly for aerodynamic flows for a successful to one primary issue is modification of the s a turbulent model to account for topological evolution during the optimization process to address this issue we proposed the addition of penalization terms to the original governing equations to show the validity of the present approach and the effect of turbulent flow on optimal layouts some two dimensional benchmark designs studied for laminar flow were reconsidered by considering the effect of turbulent flow the eddy viscosity values were increased at some local regions due to the boussinesq hypothesis and naturally optimal layouts affected by the spatially varying viscosity were obtained in turbulent flow it was also found that the balance between the inertia force and the viscosity force plays an important role in topological designs

an alternative truly mixed formulation to solve pressure load problems in topology optimization abstract the paper deals with an alternative formulation for the topology optimization of structures acted upon by pressure loads exploiting finite elements techniques that are able to handle incompressible materials the method firstly presented in o sigmund p m clausen topology optimization using a mixed formulation an alternative way to solve pressure load problems comput methods appl mech engrg 196 2007 1874 1889 33 consists in exploiting the modeling of fluid incompressibility within a topology optimization framework the implementation of a fluid phase enables to transfer pressure loads from the domain boundaries to the evolving edges of optimal design without relying on more complex techniques traditionally employed to recover the load application surfaces at each step of the minimization process in this context the main numerical trouble is therefore the application of finite elements techniques to solve incompressible materials analysis this topic in fact cannot be tackled using most of the approaches of the current literature that are mainly based on displacement finite elements which are well known to be affected by the locking phenomenon while sigmund and clausen 2007 uses a displacement pressure finite element discretization to solve the problem the approach herein presented consists in the adoption of a truly mixed variational formulation coupled to a discretization based on the johnson and mercier finite element that both pass the inf sup conditions of the problem even in the presence of incompressible materials the well known method of moving asymptotes mma is adopted in the numerical studies presented along with a particular density interpolation to model the presence of a fluid and solid phase within the same design the adopted scheme is especially conceived to avoid the arising of numerical instabilities that may arise within the optimization procedure when handling incompressible material moreover the accuracy and stability in stress evaluation provided by the truly mixed setting are herein exploited to introduce an alternative procedure that implements pressure constraints to avoid optimal designs that present cavities filled by fluid

a mixed fem approach to stress constrained topology optimization we present an alternative topology optimization formulation capable of handling the presence of stress constraints in a straightforward fashion the main idea is to adopt a mixed finite element discretization scheme wherein not only displacements as usual but also stresses are the variables entering the formulation by doing so any stress constraint may be handled within the optimization procedure without resorting to post processing operation typical of displacement based techniques that may also cause a loss in accuracy in stress computation if no smoothing of the stress is performed two dual variational principles of hellinger reissner type are presented in continuous and discrete form that which included in a rather general topology optimization problem in the presence of stress constraints that is solved by the method of moving asymptotes int j numer meth engng 1984 24 3 359 373 extensive numerical simulations are performed and ongoing extensions outlined including the optimization of elastoplastic and incompressible media copyright 2007 john wiley sons ltd

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

a numerical method for quadratic eigenvalue problems of gyroscopic systems abstract we consider the quadratic eigenvalues problem qep of gyroscopic systems 2 m g k x 0 where m m g g and k k r n n with m being positive definite guo numerical solution of a quadratic eigenvalue problem linear algebra and its applications 385 2004 391 406 showed that all eigenvalues of the qep can be found by solving the maximal solution of a nonlinear matrix equation z a z 1 a q with quadratic convergence when the qep has no eigenvalues on the imaginary axis the convergence becomes linear or more slower guo 2004 when the qep allows purely imaginary eigenvalues having even partial multiplicities in this paper we consider the general case when the qep has eigenvalues on the imaginary axis we propose an eigenvalue shifting technique to transform the original gyroscopic system to a new gyroscopic system which shifts purely imaginary eigenvalues to eigenvalues with nonzero real parts while keeps other eigenpairs unchanged this transformation ensures that the new method for computing the maximal solution of the nonlinear matrix equation converges quadratically numerical examples illustrate the efficiency of our method

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

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

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

topology optimization using a mixed formulation an alternative way to solve pressure load problems abstract a shortcoming of the traditional density based approach to topology optimization is the handling of design dependent loads that relate to boundary data such as for example pressure loads previous works have introduced spline and iso density curves or alternative parametrization schemes to determine the load surfaces in this work we suggest a new way to solve pressure load problems in topology optimization using a mixed displacement pressure formulation for the underlying finite element problem we define the void phase to be an incompressible hydrostatic fluid in this way we can transfer pressure loads through the fluid without any needs for special load surface parametrizations the method is easily implemented in the standard density approach and is demonstrated to work efficiently for both 2d and 3d problems by extending the method to a three phase solid fluid void design method we also demonstrate design of water containing dams

topology optimization for stationary fluid structure interaction problems using a new monolithic formulation this paper outlines a new procedure for topology optimization in the steady state fluid structure interaction fsi problem a review of current topology optimization methods highlights the difficulties in alternating between the two distinct sets of governing equations for fluid and structure dynamics hereafter the fluid and structural equations respectively and in imposing coupling boundary conditions between the separated fluid and solid domains to overcome these difficulties we propose an alternative monolithic procedure employing a unified domain rather than separated domains which is not computationally efficient in the proposed analysis procedure the spatial differential operator of the fluid and structural equations for a deformed configuration is transformed into that for an undeformed configuration with the help of the deformation gradient tensor for the coupling boundary conditions the divergence of the pressure and the darcy damping force are inserted into the solid and fluid equations respectively the proposed method is validated in several benchmark analysis problems topology optimization in the fsi problem is then made possible by interpolating young s modulus the fluid pressure of the modified solid equation and the inverse permeability from the damping force with respect to the design variables

toward a stress based topology optimization procedure with indirect calculation of internal finite element information abstract in this work a novel computational approach is developed for the gradient based stress based topology optimization method where the volume is minimized according to locally defined stress constraints of static failure criteria in the framework of tailored finite element fe software without direct access to an internal finite element information database tailored finite element codes that require substantial understanding and modification reprogramming or do not directly provide internal finite element information have rarely been used for stress based topology optimization with solid isotropic material with penalization simp methods therefore much research has been confined to two dimensional problems with rectilinear basic finite elements as complex three dimensional geometries with advanced finite element formulations are not supported to overcome this problem we developed a new computational procedure for sensitivity analysis without direct access to an internal information database a task that has previously been regarded as almost impossible since the calculation of linear strain displacement matrices is required in the sensitivity analysis the present procedure includes a node selection algorithm to efficiently calculate the matrices of irregular shaped finite elements by displacement perturbations the benefits of the present approach are that well established powerful finite element codes i e commercial or sophisticated public fe codes can be easily incorporated for linear stress based topology optimization and any type of finite element formulation can be readily employed in contrast to classical sensitivity analysis small computations are used for sensitivity analysis in this work to demonstrate the validity and efficiency of the present procedure and approach several topology optimization problems with 3d and shell elements are solved

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

an efficient algorithm based on lanczos type of bcr to solve constrained quadratic inverse eigenvalue problems abstract this paper proposes the lanczos type of biconjugate residual bcr algorithm for solving the quadratic inverse eigenvalue problem l 2 x 2 l 1 x l 0 x 0 where l 2 l 1 and l 0 should be partially bisymmetric under a prescribed submatrix constraint an analysis reveals that the algorithm obtains the solutions of the constrained quadratic inverse eigenvalue problem in finitely many steps in the absence of round off errors finally numerical results are performed to confirm the analysis and to illustrate the efficiency of the proposed algorithm

numerical modelling of impulse wave generated by fast landslides the damage caused by impulse waves generated in water bodies by fast landslides can be very high in terms of human lives and economic losses the complex phenomena taking place in this highly unsteady process are difficult to model because three interacting phases air water and soil are involved solutions currently available are based on either closed form equations supported experimentally or the depth integrated navier stokes equations the latter although of more general applicability requires knowledge of the evolution of the bathimetry and slide drag forces and their applicability may be restricted by the steep slopes existing in most real cases to avoid these limitations the authors propose the solution of the full navier stokes equations using indicator functions to assign the material properties to each spatial point in the domain the method performance is illustrated by comparison against the experimental results obtained in a physical model of an actual case

inverse problems for damped vibrating systems abstract linear damped vibrating systems are defined by three real definite matrices m 0 d 0 and k 0 the mass damping and stiffness matrices respectively it is assumed that all eigenvalues of the system are simple and nonreal so that the eigenvectors columns of a matrix x c c n n are also complex it is shown that when properly defined the eigenvectors have a special structure consistent with x c x r i i where x r r n n x r is nonsingular and is orthogonal by taking advantage of this structure solutions of the inverse problem are obtained i e given complete information on the eigenvalues and eigenvectors it is shown how m d and k can be found three points of view are developed and compared namely using spectral theory structure preserving similarities and factorisation theory

stress related topology optimization of continuum structures involving multi phase materials considering stress constraints in structural topology optimization is very important from both theoretical and application perspectives most of the corresponding studies in literature however are only focused on the problems involving single phase homogenous materials in the present paper stress constrained topology optimization of continuum structures involving multi phase heterogeneous materials is investigated a level set based variational consistent solution framework is developed numerical examples are also presented and discussed to illustrate the effectiveness of the proposed approach

a monolithical fluid structure interaction algorithm applied to the piston problem abstract an investigation of time marching computational fluid structure interaction algorithms is presented the analysis is applied to the piston problem attention is focussed on the time integration properties of the coupling algorithms the staggered scheme is first investigated where fluid and structure are alternately integrated by separate solvers in a predictor corrector fashion this algorithm suffers from a time lag between the integration of the fluid and structure the influence of the time lag is investigated by the comparison of different predictions for the structure a novel monolithical algorithm is then introduced in order to annihilate the time lag this algorithm integrates fluid structure and interaction as a single system by an implicit algorithm linear acoustic as well as nonlinear euler equations for gas dynamics are investigated the numerical results of the staggered scheme reveal a non physical deviation of the mean position of the piston at higher cfl numbers the deviation of the mean position is not present in the calculation with the monolithical scheme stability analysis shows the unconditional stability of the monolithical scheme for the acoustic equations whereas the staggered scheme has a limited domain of stability this domain can be enlarged by an improvement of the structural prediction analysis of the damping shows an energy production in the staggered scheme while the monolithical scheme has no energy production term the analyses lead to the formulation of the interaction consistency law which prescribes the relation for the time discretisation between fluid and structure solvers and their boundary conditions

a variational level set method for the topology optimization of steady state navier stokes flow the smoothness of topological interfaces often largely affects the fluid optimization and sometimes makes the density based approaches though well established in structural designs inadequate this paper presents a level set method for topology optimization of steady state navier stokes flow subject to a specific fluid volume constraint the solid fluid interface is implicitly characterized by a zero level contour of a higher order scalar level set function and can be naturally transformed to other configurations as its host moves a variational form of the cost function is constructed based upon the adjoint variable and lagrangian multiplier techniques to satisfy the volume constraint effectively the lagrangian multiplier derived from the first order approximation of the cost function is amended by the bisection algorithm the procedure allows evolving initial design to an optimal shape and or topology by solving the hamilton jacobi equation two classes of benchmarking examples are presented in this paper 1 periodic microstructural material design for the maximum permeability and 2 topology optimization of flow channels for minimizing energy dissipation a number of 2d and 3d examples well demonstrated the feasibility and advantage of the level set method in solving fluid solid shape and topology optimization problems

inverse eigenvalue problems for damped vibrating systems first let us describe what is understood here by a damped vibrating system consider a system that is determined by n generalized coordinates ql r q t and associtated kinetic energy potential energy and dis sipation functions these are supposed to be homogeneous quadratic forms in the generalized velocities coordinates and velocities respectively and independent of the time motions of such a system are then governed by differential equations of the form aij j cq o 0 1 where q is the column vector of coordinates the dots denote derivatives with respect to time and a b c are n x n matrices associated with the respective quadratic forms in particular they are generally real and sym metric with a positive definite and b c nonnegative or positive definite it is well known that solutions of such a system are intimately connected with the algebraic properties of the matrix valued function l i a3 2 ba c 0 2 in the terminology of 1 21 l i is known as a selfadjoint matrix polynomial a number l and a nonzero vector x are called an eigenvalue and associated right eigenvector of l 3 if det l o and l x o generalized eigenvectors or jordan chains which will be defined shortly 238

a symmetric inverse vibration problem with overdamped modes abstract several previously published results have addressed the inverse eigenvalue problem for lumped parameter non conservative systems these inverse results give conditions which allow the construction of mass normalized velocity and position coefficient matrices based on given eigenvalues and eigenvectors previous theories have examined the construction of symmetric coefficients given complex and zero eigenvalues rigid bodies here the theory of real symmetric inverse eigenvalue problems is extended to include the possibility of specifying real eigenvalues corresponding to overdamped modes specifically conditions are given that allow the construction of real symmetric mass normalized damping and stiffness matrices given specified eigenvalues and eigenvectors some of which may correspond to overdamped modes

failure mitigation in optimal topology design using a coupled nonlinear continuum damage model abstract this paper presents a novel framework for performing topology optimization of structures while accounting for material damage a quasi static non local brittle damage model is coupled to a linear finite element analysis code for modeling the structural response and the initiation and propagation of damage the optimization problem is parameterized using simp variables and failure mitigation is achieved through the enforcement of constraints on the maximum local damage intensity we derive a computationally efficient adjoint sensitivity formulation that accounts for the path dependence of the coupled analysis problem the algorithm is validated through a series of numerical examples

stress constraints sensitivity analysis in structural topology optimization abstract sensitivity analysis is an essential issue in the structural optimization field the calculation of the derivatives of the most relevant quantities displacements stresses strains in optimum design of structures allows to estimate the structural response when changes in the design variables are introduced this essential information is used by the most frequent conventional optimization algorithms slp mma feasible directions in order to reach the optimal solution according to this idea the sensitivity analysis of the stress constraints in topology optimization problems is a crucial aspect to obtain the optimal solution when stress constraints are considered maximum stiffness approaches usually involve one linear constraint and one non linear objective function thus the computation of the required sensitivity analysis does not mean a crucial limitation however in the topology optimization problem with stress constraints efficient and accurate computation of the derivatives is needed in order to reach appropriate optimal solutions in this paper a complete analytic and efficient procedure to obtain the sensitivity analysis of the stress constraints in topology optimization of continuum structures is analyzed first order derivatives and second order directional derivatives of the stress constraints are analyzed and included in the optimization procedure in addition topology optimization problems usually involve thousands of design variables and constraints thus an efficient implementation of the algorithms used in the computation of the sensitivity analysis is developed in order to reduce the computational cost required finally the sensitivity analysis techniques presented in this paper are tested by solving some application examples

inverse eigenvalue problems a collection of inverse eigenvalue problems are identified and classified according to their characteristics current developments in both the theoretic and the algorithmic aspects are summarized and reviewed in this paper this exposition also reveals many open questions that deserve further study an extensive bibliography of pertinent literature is attached

improvements in the treatment of stress constraints in structural topology optimization problems topology optimization of continuum structures is a relatively new branch of the structural optimization field since the basic principles were first proposed by bendsoe and kikuchi in 1988 most of the work has been dedicated to the so called maximum stiffness or minimum compliance formulations however since a few years different approaches have been proposed in terms of minimum weight with stress and or displacement constraints these formulations give rise to more complex mathematical programming problems since a large number of highly non linear local constraints must be taken into account in an attempt to reduce the computational requirements in this paper we propose different alternatives to consider stress constraints and some ideas about the numerical implementation of these algorithms finally we present some application examples

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

solutions to a quadratic inverse eigenvalue problem abstract in this paper we consider the quadratic inverse eigenvalue problem qiep of constructing real symmetric matrices m c and k of size n n with m c k 0 so that the quadratic matrix polynomial q 2 m c k has m n m 2 n prescribed eigenpairs it is shown that for almost all prescribed eigenpairs the qiep has a solution with m nonsingular if m m and has only solutions with q 0 otherwise where m n 1 1 8 n 2 we also derive the expression of the general solution of the qiep for both cases furthermore we develop an algorithm for finding a particular solution to the qiep with m positive definite if it exists

an inverse problem for undamped gyroscopic systems linear undamped gyroscopic systems are defined by three real matrices m 0 k 0 and g g t g the mass stiffness and gyroscopic matrices respectively in this paper an inverse problem is considered given complete information about eigenvalues and eigenvectors l diag l 1 l 2 l 2 n 1 l 2 n c 2 n x 2 n and x x 1 x 2 x 2 n 1 x 2 n c n x 2 n where the diagonal elements of l are all purely imaginary x is of full row rank n and both l and x are closed under complex conjugation in the sense that l 2 email protected 2 j email protected c x 2 email protected 2 j email protected c n for j 1 n find m k and g such that email protected email protected kx 0 the solvability condition for the inverse problem and a solution to the problem are presented and the results of the inverse problem are applied to develop a method for model updating