continuum topology optimization of buckling sensitive structures twoformulationsforcontinuum topologyoptimizationofstructurestakingbucklingconsiderationsinto account are developed implemented and compared in thee rst the structure undergoing a specie ed loading is modeled as a hyperelastic continuum at e nite deformations and is optimized to maximize the minimum critical buckling load in the second the structure under a similar loading is modeled as linear elastic and the critical buckling load is computed with linearized buckling analysis specie c issues addressed include usage of suitable mixing rules a node based design variable formulation techniques for eliminating regions devoid of structural material from the analysis problem and consistent design sensitivity analysis the performance of the formulations is demonstrated on the design of different structures when problems are solved with moderate loads and generous material usage constraints designs using compression and tension members are realized alternatively when fairly large loads together with very stringent material usage constraints are imposed structures utilizing primarily tension members result issues that arise when designing very light structures with stringent material usage constraints are discussed along with the importance of considering potential geometrical instabilities in the concept design of structural systems

first integrals integrating factors and λ symmetries of second order differential equations for a given second order ordinary differential equation ode several relationships among first integrals integrating factors and symmetries are studied the knowledge of a symmetry of the equation permits the determination of an integrating factor or a first integral by means of coupled first order linear systems of partial differential equations if two nonequivalent symmetries of the equation are known then an algorithm to find two functionally independent first integrals is provided these methods include and complete other methods to find integrating factors or first integrals that are based on variational derivatives or in the prelle singer method these results are applied to several odes that appear in the study of relevant equations of mathematical physics

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

voronoi cell finite element model based on micropolar theory of thermoelasticity for heterogeneous materials in this paper a new voronoi cell finite element model is developed for solving steady state heat conduction and micropolar thermoelastic stress analysis problems in arbitrary heterogeneous materials the method is based on the natural discretization of a multiple phase domain into basic structural elements by dirichlet tessellation tessellation process results in a network of polygons called voronoi polygons in this paper formulations are developed for treating these polygons as elements in a finite element mesh furthermore a composite voronoi cell finite element model is developed to account for the presence of a second phase inclusion within a polygonal element various numerical examples are executed for validating the effectiveness of this model in the analysis of the temperature and stress fields for micropolar elastic materials effective material properties are derived for microstructures containing different distributions of second phase

solving second order ordinary differential equations by extending the prelle singer method we propose a method for solving second order ordinary differential equations odes which is based on the ideas behind the prelle singer ps procedure for first order odes while the ps procedure treats differential equations des of the form y p x y q x y with p and q polynomials whose coefficients lie in the field of complex numbers our method is applicable to des of the form y p x y y q x y y the key to our approach is to focus not on the final solution but on the first order invariants of the equation our method is an attempt to address algorithmically the solution of second order odes with solutions in terms of elementary functions

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

higher order shell elements based on a cosserat model and their use in the topology design of structures for the purpose of carrying out topology optimization of shell structures we show that it is advantageous to use shell elements based on a classical shell theory such as the cosserat theory rather than elements based on the degenerated solid approach since the shell thickness appears explicitly in the formulation thereby greatly simplifying the sensitivity analysis one of the well known shell elements based on the cosserat shell theory is the four node element presented by simo et al comput methods appl mech engrg 72 1989 267 73 1989 53 although one could use this element the use of lower order elements often results in instabilities such as the checkerboard instability in the resulting topologies this provides the motivation for developing higher order shell elements based on a classical shell theory in this work we present the formulation and implementation details for six node and seven node triangular and nine node quadrilateral shell elements which are based on the variational formulation of simo et al and show that good accuracy is obtained even with coarse meshes in fairly demanding problems we also present the topology optimization formulation and some examples of optimal topologies that are obtained using this formulation

on the complete integrability and linearization of nonlinear ordinary differential equations ii third order equations we introduce a method for finding general solutions of third order nonlinear differential equations by extending the modified prelle singer method we describe a procedure to deduce all the integrals of motion associated with the given equation so that the general solution follows straightforwardly from these integrals the method is illustrated with several examples further we propose a powerful method of identifying linearizing transformations the proposed method not only unifies all the known linearizing transformations systematically but also introduces a new and generalized linearizing transformation in addition to the above we provide an algorithm to invert the non local linearizing transformation through this procedure the general solution for the original nonlinear equation can be obtained from the solution of the linear ordinary differential equation

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

interplay of symmetries and other integrability quantifiers in finite dimensional integrable nonlinear dynamical systems in this work we establish a connection between the extended prelle singer procedure and other widely used analytical methods to identify integrable systems in the case of n th order nonlinear ordinary differential equations odes by synthesizing these methods we bring out the interlink between lie point symmetries contact symmetries symmetries adjoint symmetries null forms darboux polynomials integrating factors the jacobi last multiplier and generalized symmetries corresponding to the n th order odes we also prove these interlinks with suitable examples by exploiting these interconnections the characteristic quantities associated with different methods can be deduced without solving the associated determining equations

post buckling analysis of shallow shells by the field boundary element method the non linear field boundary element technique is applied to the analysis of snap through phenomena in thin shallow shells the equilibrium path is traced by using the arc length method and the solution strategy is discussed in detail the results show that as compared to the approaches based on the popular symmetric variational galerkin finite element formulation the current approach based on an unsymmetric variational petrov galerkin field boundary element formulation gives a faster convergence while using fewer degrees of freedom the illustrative numerical examples deal with post buckling responses of several shallow shells with different geometries

interplay of symmetries null forms darboux polynomials integrating factors and jacobi multipliers in integrable second order differential equations in this work we establish a connection between the extended prellesinger procedure with five other analytical methods which are widely used to identify integrable systems in the contemporary liter

a hybrid strain finite element for plates and shells this paper describes a new hybrid strain finite element for geometrically linear analysis of plates and shells the formulation for materially linear problems is based on a mixed variational principle having strain and displacement rates as independently varied fields to facilitate extension to materially non linear analysis the variational principle is used in rate form and the plane stress assumption is not imposed a priori in the formulation when desired the plane stress assumption is imposed in a manner similar to imposition of fixed boundary conditions the element geometry is based on a nine noded quadrilateral with biquadratic interpolation of the displacement field the strain field is based on a bilinear interpolation with additional non linear terms chosen on the basis of eigenvalue analysis the element passes the required patch tests does not display either membrane or shear locking effects and is free of communicable spurious modes numerical results are presented for elastic analyses of several standard plate and shell test problems

a dual algorithm for the topology optimization of non linear elastic structures dual algorithms are ideally suited for the purpose of topology optimization since they work in the space of lagrange multipliers associated with the constraints to date dual algorithms have been applied only for linear structures here we extend this methodology to the case of non linear structures the perimeter constraint is used to make the topology problem well posed we show that the proposed algorithm yields a value of perimeter that is close to that specified by the user we also address the issue of manufacturability of these designs by proposing a variant of the standard dual algorithm which generates designs that are two dimensional although the loading and the geometry are three dimensional

extended voronoi cell finite element model for multiple cohesive crack propagation in brittle materials this paper introduces an extended voronoi cell finite element model x vcfem for modelling cohesive crack propagation in brittle materials with multiple cracks the cracks are modelled by a cohesive zone model and their incremental directions and growth lengths are determined in terms of the cohesive energy near the crack tip extension to vcfem is achieved through enhancements in stress functions in the assumed stress hybrid formulation in addition to polynomial terms the stress functions include branch functions in conjunction with level set methods and multi resolution wavelet functions in the vicinity of crack tips the wavelet basis functions are adaptively enriched to accurately capture crack tip stress concentrations conditions and methods of stability are enforced in x vcfem for improved convergence with propagating cracks two classes of problems are solved and compared with existing solutions in the literature for validation of the x vcfem algorithms the first set corresponds to results for static cracks while in the latter set the propagation of cohesive cracks are considered comparison of x vcfem simulation results with results in literature for several fracture mechanics problems validates the effectiveness of x vcfem copyright 2005 john wiley sons ltd

complex hill s equation and the complex periodic korteweg de vries equations on etudie la classe spectrale des operateurs differentiels l d 2 dx 2 q avec un potentiel q de periode un on traite des potentiels complexes et des operateurs auto adjoints

dual methods for discrete structural optimization problems the purpose of this paper is to present a mathematical programming method developed to solve structural optimization problems involving discrete variables we work in the following context the structural responses are computed by the finite elements method and convex and separable approximation schemes are used to generate a sequence of explicit approximate subproblems each of them is solved in the dual space with a subgradient based algorithm or with a variant of it specially developed to maximize the not everywhere differentiable dual function to show that the application field is large the presented applications are issued from different domains of structural design such as sizing of thin walled structures geometrical configuration of trusses topology optimization of membrane or 3 d structures and welding points numbering in car bodies the main drawback of using the dual approach is that the obtained solution is generally not the global optimum this is linked to the presence of a duality gap due to the non convexity of the primal discrete subproblems fortunately this gap can be quantified a maximum bound on its value can be computed moreover it turns out that the duality gap is decreasing for higher number of variables the maximum bound on the duality gap is generally negligible in the treated applications the developed algorithms are very efficient for 2 d and 3 d topology optimization where applications involving thousands of binary design variables are solved in a very short time copyright 2000 john wiley sons ltd

topology design with optimized self adaptive materials significant performance improvements can be obtained if the topology of an elastic structure is allowed to vary in shape optimization problems we study the optimal shape design of a two dimensional elastic continuum for minimum compliance subject to a constraint on the total volume of material the macroscopic version of this problem is not well posed if no restrictions are placed on the structure topology relaxation of the optimization problem via quasiconvexification or homogenization methods is required the effect of relaxation is to introduce a perforated microstructure that must be optimized simultaneously with the macroscopic distribution of material

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

on the complete integrability and linearization of certain second order nonlinear ordinary differential equations a method for finding general solutions of second order nonlinear ordinary differential equations by extending the prelle singer ps method is briefly discussed we explore integrating factors integrals of motion and the general solution associated with several dynamical systems discussed in the current literature by employing our modifications and extensions of the ps method we also introduce a novel way of deriving linearizing transformations from the first integrals to linearize the second order nonlinear ordinary differential equations to free particle equations we illustrate the theory with several potentially important examples and show that our procedure is widely applicable

a hybrid finite element method for stokes flow part ii stability and convergence studies abstract in part i we have presented a hybrid finite element method based on an assumed stress field which has the features i the unknowns in the final system of finite element equations are a the nodal velocities and b the constant term in the arbitrary pressure field over each element ii exact integrations were performed for each element in the following we present studies of stability and convergence of the above hybrid finite element method

topology design of structures using a dual algorithm and a constraint on the perimeter dual optimization algorithms are well suited for the topology design of continuum structures in discrete variables since in these problems the number of constraints is small in comparison to the number of design variables the raw dual algorithm which was originally proposed for the minimum compliance design problem worked well when a perimeter constraint was added in addition to the volume constraint however if the perimeter constraint was gradually relaxed by increasing the upper bound on the allowable perimeter the algorithm tended to behave erratically recently a simple strategy has been suggested which modifies the raw dual algorithm to make it more robust in the absence of the perimeter constraint in particular the problem of checkerboarding which is frequently observed with the use of lower order finite elements is eliminated in this work we show how the perimeter constraint can be incorporated in this improved algorithm so that it not only provides a designer with a control over the topology but also generates good topologies irrespective of the value of the upper bound on the perimeter

development and testing of stable invariant isoparametric curvilinear 2 and 3 d hybrid stress elements abstract linear and quadratic serendipity hybrid stress elements are examined in respect of stability coordinate invariance and optimality a formulation based upon symmetry group theory successfully addresses these issues in undistorted geometries and is fully detailed for plane elements the resulting least order stable invariant stress polynomials can be applied as astute approximations in distorted cases through a variety of tensor components and variational principles a distortion sensitivity study for two and three dimensional elements provides favourable numerical comparisons with the assumed displacement method

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

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

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

optimal design and relaxation of variational problems iii abstract this paper has attempted a synthesis of three subjects that have developed separately optimal design homogenization and relaxation in the calculus of variations the underlying theme is that of oscillations they occur with certain definite patterns in minimizing sequences for the variational problem the same patterns recur in nearly optimal designs and in the coefficients of the equation being homogenized each problem is resolved by determining the structure of those oscillations and above all their macroscopic averages it is those averages that solve the relaxed problem they also determine the optimal design and the solution of the homogenized equation we emphasize also the role of optimization the homogenized equations and composite materials of interest here come not from arbitrary mixtures but from those that are extremal since they correspond to minimizing sequences for the variational problem the effective properties of these composites attain the optimal bounds for given materials in fixed proportions

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

on the suppression of zero energy deformation modes based on the hellinger reissner principle and the deformation energy due to assumed stresses and displacements the problem of the kinematic deformation modes in assumed stress hybrid mixed finite elements has been examined basic schemes are developed for the choice of assumed stress terms that will suppress all kinematic deformation modes quadrilateral membrane and axisymmetric elements and three dimensional hexahedral elements are used to illustrate the suggested procedure

on the uniqueness of the harada norton group the definition of a group 2 8 a 5 wr2 type is given in 2 2 1 see also 2 3 1 and the notation in 2 1 4 and 2 1 5 for 2 hs 2 a group g satisfying the hypotheses of the main theorem exists its existence is a consequence of the existence of the monster constructed by r griess in 151 we know of no published work proving the uniqueness of f5 of course many properties of f were derived in harada s major work on f5 7 a group g satisfying the hypotheses of the main theorem will be said to be of f type let g be a group of f type and let a z be involutions in g as in the main theorem we consider the graph f defined as follows its vertex set is the conjugacy class a g two involutions x y e ag form an edge iff xy a we show that the hypotheses of the main theorem imply the uniqueness of r and that g aut t aut t and hence g is unique our paper relies on some properties of 2 hs 2 see 2 3 and some properties of co z g z as in the main theorem but we do not assume but rather derive the isomorphism type of c otherwise our paper is independent of 7 and we prove all properties of g which we require after some preliminary and important work in section 2 we start in section 3 to obtain properties of g and r r as above perhaps the most important result of section 3 is that c a has 8 nontrivial orbits on ag as given in the following table 261 0021 8693192 55 00

an algorithm for the topology optimization of geometrically nonlinear structures summary most papers on topology optimization consider that there is a linear relation between the strains and displacements of the structure implicitly assuming that the displacements of the structure are small however when the external loads applied to the structure are large the displacements also become large so it is necessary to suppose that there is a nonlinear relation between strains and displacements in this case we say that the structure is geometrically nonlinear in practice this means that the linear system that needs to be solved each time the objective function of the problem is evaluated is replaced by an ill conditioned nonlinear system of equations moreover the stiffness matrix and the derivatives of the problem also become harder to compute the objective of this work is to solve topology optimization problems under large displacements through a new optimization algorithm named sequential piecewise linear programming this method relies on the solution of convex piecewise linear programming subproblems that include second order information about the objective function to speed up the algorithm these subproblems are converted into linear programming ones the new algorithm is not only globally convergent to stationary points but our numerical experiments also show that it is efficient and robust copyright 2014 john wiley sons ltd

on the reduction methods for ordinary differential equations as tandard method based on the use of differential invariants of a lie group g e nables us to reduce any ordinary differential equation invariant under the action of g w e show that this method is applicable to vector fields more general than those associated with lie symmetries we characterize all such vector fields and study their relationship with nonlocal symmetries and symmetries govinder k s and leach p g l 1995 j phys a math gen 28 5349 59 muriel c and romero l 2001 ima j appl math 66 111 25

a robust dual algorithm for topology design of structures in discrete variables dual optimization algorithms for the topology optimization of continuum structures in discrete variables are gaining popularity in recent times since in topology design problems the number of constraints is small in comparison to the number of design variables good topologies can be obtained for the minimum compliance design problem when the perimeter constraint is imposed in addition to the volume constraint however when the perimeter constraint is relaxed the dual algorithm tends to give bad results even with the use of higher order finite element models as we demonstrate in this work since a priori one does not know what a good value of the perimeter to be specified is it is essential to have an algorithm which generates good topologies even in the absence of the perimeter constraint we show how the dual algorithm can be made more robust so that it yields good designs consistently in the absence of the perimeter constraint in particular we show that the problem of checkerboarding which is frequently observed with the use of lower order finite elements is eliminated

on the existence and stability conditions for mixed hybrid finite element solutions based on reissner s variational principle abstract the extensions of reissner s two field stress and displacement principle to the cases wherein the displacement field is discontinuous and or the stress field results in unreciprocated tractions at a finite number of surfaces interelement boundaries in a domain as for instance when the domain is discretized into finite elements is considered the conditions for the existence uniqueness and stability of mixed hybrid finite element solutions based on such discontinuous fields are summarized the reduction of these global conditions to local element level and the attendant conditions on the ranks of element matrices are discussed two examples of stable invariant least order elements a four node square planar element and an eight node cubic element are discussed in detail

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

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

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

a monolithic approach to fluid structure interaction using space time finite elements abstract the paper presents a simultaneous solution procedure for fluid structure interaction problems the structural motion is described by geometrically nonlinear elastodynamics the fluid is modeled by the incompressible navier stokes equations the space time finite element method is applied to both continua leading to an almost uniform discretization in which velocity variables are used for fluid and structure in order to enforce momentum conservation and geometric continuity at the interface a weighted residual formulation of coupling conditions is introduced the discretized model equations for fluid structure and coupling conditions are formulated in a single equation system the nonlinear system and the fluid mesh movement are solved in a single iteration loop two dimensional examples of membrane flutter and vortex excited plate vibrations demonstrate the efficiency of the methodology

a localized mixed hybrid method for imposing interfacial constraints in the extended finite element method xfem the paper proposes an approach for the imposition of constraints along moving or fixed immersed interfaces in the context of the extended finite element method an enriched approximation space enables consistent representation of strong and weak discontinuities in the solution fields along arbitrarily shaped material interfaces using an unfitted background mesh the use of lagrange multipliers or penalty methods is circumvented by a localized mixed hybrid formulation of the model equations in a defined region in the vicinity of the interface the original problem is re stated in its auxiliary formulation the availability of the auxiliary variable enables the consideration of a variety of interface constraints in the weak form the contribution discusses the weak imposition of dirichlet and neumann type interface conditions as well as continuity requirements not fulfilled a priori by the enriched approximation the properties of the proposed approach applied to two dimensional linear scalar and vector valued elliptic problems are investigated by studying the convergence behavior

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

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

adaptivity and convergence in the voronoi cell finite element model for analyzing heterogeneous materials in this paper an adaptive voronoi cell finite element model is presented for analyzing micromechanical response of composites and porous materials both elastic and elastic plastic materials are considered two error measures viz a traction reciprocity error and an error in the kinematic relation are formulated as indicators of the quality of vcfem solutions based on a posteriori evaluation of these error measures element adaptation is executed in two consecutive stages in the first stage displacement function adaptations on the element boundaries and matrix inclusion void interfaces are carried out to minimize the corresponding traction reciprocity errors this is accomplished through a sequence of h refinement and spectral p enrichment strategy in an optimal displacement direction following this an enrichment of matrix and inclusion stress functions or enrp adaptation is conducted to reduce the error in kinematic relations the complete process improves convergence characteristics of the vcfem solution numerical analysis is conducted to examine the potential of the resulting vcfem code in analyzing microstructures with different distributions sizes and shapes of heterogeneities the method is seen to perform very well for the wide variety of problems solved

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

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